Topological insulator - Knowledge (XXG)

921:(i.e., the incremental change in voltage due to an incremental change in temperature). Topological insulators are often composed of heavy atoms, which tends to lower thermal conductivity and are therefore beneficial for thermoelectrics. A recent study also showed that good electrical characteristics (i.e., electrical conductivity and Seebeck coefficient) can arise in topological insulators due to band inversion-driven warping of the bulk band structure. Often, the electrical conductivity and Seebeck coefficient are conflicting properties of thermoelectrics and difficult to optimize simultaneously. Band warping, induced by band inversion in a topological insulator, can mediate the two properties by reducing the effective mass of electrons/holes and increasing the valley degeneracy (i.e., the number of electronic bands that are contributing to charge transport). As a result, topological insulators are generally interesting candidates for thermoelectric applications. 586:) Hamiltonian that is topologically nontrivial. This system replicates the effective Hamiltonians from all universal classes of 1- to 3-D topological insulators. Interestingly, topological properties of Floquet topological insulators could be controlled via an external periodic drive rather than an external magnetic field. An atomic lattice empowered by distance selective Rydberg interaction could simulate different classes of FTI over a couple of hundred sites and steps in 1, 2 or 3 dimensions. The long-range interaction allows designing topologically ordered periodic boundary conditions, further enriching the realizable topological phases. 953:(MBE). MBE has so far been the most common experimental technique. The growth of thin film topological insulators is governed by weak van der Waals interactions. The weak interaction allows to exfoliate the thin film from bulk crystal with a clean and perfect surface. The van der Waals interactions in epitaxy also known as van der Waals epitaxy (VDWE), is a phenomenon governed by weak van der Waal's interactions between layered materials of different or same elements in which the materials are stacked on top of each other. This approach allows the growth of layered topological insulators on other substrates for 1823:. These crystal structures can consist of a large number of elements. Band structures and energy gaps are very sensitive to the valence configuration; because of the increased likelihood of intersite exchange and disorder, they are also very sensitive to specific crystalline configurations. A nontrivial band structure that exhibits band ordering analogous to that of the known 2D and 3D TI materials was predicted in a variety of 18-electron half-Heusler compounds using first-principles calculations. These materials have not yet shown any sign of intrinsic topological insulator behavior in actual experiments. 88: 1128:). The resulted single crystals have a well-defined crystallographic orientation; their composition, thickness, size, and the surface density on the desired substrate can be controlled. The thickness control is particularly important for 3D TIs in which the trivial (bulky) electronic channels usually dominate the transport properties and mask the response of the topological (surface) modes. By reducing the thickness, one lowers the contribution of trivial bulk channels into the total conduction, thus forcing the topological modes to carry the electric current. 126: 1001:

influence the growth rate and the ratio of species of source materials present at the substrate interface. Furthermore, in MBE, samples can be grown layer by layer which results in flat surfaces with smooth interface for engineered heterostructures. Moreover, MBE synthesis technique benefits from the ease of moving a topological insulator sample from the growth chamber to a characterization chamber such as angle-resolved photoemission spectroscopy (ARPES) or

7314: 946: 7742: 7766: 36: 7778: 7754: 6839: 1778:. Different materials will have different wave propagation properties, and thus different vector bundles. If we consider all insulators (materials with a band gap), this creates a space of vector bundles. It is the topology of this space (modulo trivial bands) from which the "topology" in topological insulators arises. 1378:

on different substrates and the resulting lattice mismatch. Generally, regardless of the substrate used, the resulting films have a textured surface that is characterized by pyramidal single-crystal domains with quintuple-layer steps. The size and relative proportion of these pyramidal domains vary

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at the interface, the substrate and thin film are expected to have similar lattice constants. MBE has an advantage over other methods due to the fact that the synthesis is performed in high vacuum hence resulting in less contamination. Additionally, lattice defect is reduced due to the ability to

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with factors that include film thickness, lattice mismatch with the substrate and interfacial chemistry-dependent film nucleation. The synthesis of thin films have the stoichiometry problem due to the high vapor pressures of the elements. Thus, binary tetradymites are extrinsically doped as n-type (

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symmetries are usually significant in quantum mechanics, they have no effect on the topology here. Instead, the three symmetries typically considered are time-reversal symmetry, particle-hole symmetry, and chiral symmetry (also called sublattice symmetry). Mathematically, these are represented as,

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Topological insulators are challenging to synthesize, and limited in topological phases accessible with solid-state materials. This has motivated the search for topological phases on the systems that simulate the same principles underlying topological insulators. Discrete time quantum walks (DTQW)

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of the space indicates how many different "islands" of insulators exist amongst the metallic states. Insulators in the connected component containing the vacuum state are identified as "trivial", and all other insulators as "topological". The connected component in which an insulator lies can be

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topological invariant was constructed and the importance of the time reversal symmetry was clarified in the work by Kane and Mele. Subsequently, Bernevig, Taylor L. Hughes and Zhang made a theoretical prediction that 2D topological insulator with one-dimensional (1D) helical edge states would be

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The first step of topological insulators identification takes place right after synthesis, meaning without breaking the vacuum and moving the sample to an atmosphere. That could be done by using angle-resolved photoemission spectroscopy (ARPES) or scanning tunneling microscopy (STM) techniques.

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The physical vapor deposition (PVD) technique does not suffer from the disadvantages of the exfoliation method and, at the same time, it is much simpler and cheaper than the fully controlled growth by molecular-beam epitaxy. The PVD method enables a reproducible synthesis of single crystals of

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Tu, Ngoc Han, Tanabe, Yoichi; Satake, Yosuke, Huynh, Khuong Kim; Le, Phuoc Huu, Matsushita, Stephane Yu; Tanigaki, Katsumi (2017). "Large-Area and Transferred High-Quality Three-Dimensional Topological Insulator Bi2–x Sb x Te3–y Se y Ultrathin Film by Catalyst-Free Physical Vapor Deposition".

1278:. However, the use of sapphire as substrate has not been so encouraging due to a large mismatch of about 15%. The selection of appropriate substrate can improve the overall properties of TI. The use of buffer layer can reduce the lattice match hence improving the electrical properties of TI. 1818:

The field of topological insulators still needs to be developed. The best bismuth chalcogenide topological insulators have about 10 meV bandgap variation due to the charge. Further development should focus on the examination of both: the presence of high-symmetry electronic bands and simply

187:, local (symmetry-preserving) perturbations cannot damage this surface state. This is unique to topological insulators: while ordinary insulators can also support conductive surface states, only the surface states of topological insulators have this robustness property. 598:

if superconductivity is induced on the surface of 3D topological insulators via proximity effects. (Note that Majorana zero-mode can also appear without topological insulators.) The non-trivialness of topological insulators is encoded in the existence of a gas of

607:: the gapless surface states of topological insulators are symmetry-protected (i.e., not topological), while the gapless surface states in quantum Hall effect are topological (i.e., robust against any local perturbations that can break all the symmetries). The 6457:

Bansal, Namrata; Kim, Yong Seung; Edrey, Eliav; Brahlek, Matthew; Horibe, Yoichi; Iida, Keiko; Tanimura, Makoto; Li, Guo-Hong; Feng, Tian; Lee, Hang-Dong; Gustafsson, Torgny; Andrei, Eva; Oh, Seongshik (2011-10-31). "Epitaxial growth of topological insulator

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S. The choice of chalcogenides is related to the van der Waals relaxation of the lattice matching strength which restricts the number of materials and substrates. Bismuth chalcogenides have been studied extensively for TIs and their applications in

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The first models of 3D topological insulators were proposed by B. A. Volkov and O. A. Pankratov in 1985, and subsequently by Pankratov, S. V. Pakhomov, and Volkov in 1987. Gapless 2D Dirac states were shown to exist at the band inversion contact in

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Further measurements includes structural and chemical probes such as X-ray diffraction and energy-dispersive spectroscopy but depending on the sample quality, the lack of sensitivity could remain. Transport measurements cannot uniquely pinpoint the

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Hsieh, D.; D. Hsieh; Y. Xia; L. Wray; D. Qian; A. Pal; J. H. Dil; F. Meier; J. Osterwalder; C. L. Kane; G. Bihlmayer; Y. S. Hor; R. J. Cava; M. Z. Hasan (2009). "Observation of Unconventional Quantum Spin Textures in Topological Insulators".

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Xu, Y; Miotkowski, I.; Liu, C.; Tian, J.; Nam, H.; Alidoust, N.; Hu, J.; Shih, C.-K; Hasan, M.Z.; Chen, Y.-P. (2014). "Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator".

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are now believed to exhibit topological surface states. In some of these materials, the Fermi level actually falls in either the conduction or valence bands due to naturally-occurring defects, and must be pushed into the bulk gap by

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Although the topological classification and the importance of time-reversal symmetry was pointed in the 2000s, all the necessary ingredients and physics of topological insulators were already understood in the works from the 1980s.

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An (informal) phase diagram with topological insulators, trivial insulators, and conductors. There is no path from the topological insulators to the trivial insulators that does not cross the conducting phase. The diagram depicts a

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Chang, Cui-Zu; Zhang, Jinsong; Feng, Xiao; Shen, Jie; Zhang, Zuocheng; Guo, Minghua; Li, Kang; Ou, Yunbo; Wei, Pang (2013-04-12). "Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator".

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Lin, Hsin; L. Andrew Wray; Yuqi Xia; Suyang Xu; Shuang Jia; Robert J. Cava; Arun Bansil; M. Zahid Hasan (July 2010). "Half-Heusler ternary compounds as new multifunctional experimental platforms for topological quantum phenomena".

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Hasan, M. Zahid; Xu, Su-Yang; Neupane, M (2015). "Topological Insulators, Topological Dirac semimetals, Topological Crystalline Insulators, and Topological Kondo Insulators". In Ortmann, F.; Roche, S.; Valenzuela, S. O. (eds.).

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realized in quantum wells (very thin layers) of mercury telluride sandwiched between cadmium telluride. The transport due to 1D helical edge states was indeed observed in the experiments by Molenkamp's group in 2007.

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Mellnik, A. R; Lee, J. S; Richardella, A; Grab, J. L; Mintun, P. J; Fischer, M. H; Vaezi, A; Manchon, A; Kim, E. -A; Samarth, N; Ralph, D. C (2014). "Spin-transfer torque generated by a topological insulator".

603:. Dirac particles which behave like massless relativistic fermions have been observed in 3D topological insulators. Note that the gapless surface states of topological insulators differ from those in the 524:

S) with slightly Sn - doping, exhibits an intrinsic semiconductor behavior with Fermi energy and Dirac point lie in the bulk gap and the surface states were probed by the charge transport experiments.

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Chadov, Stanislav; Xiao-Liang Qi; Jürgen Kübler; Gerhard H. Fecher; Claudia Felser; Shou-Cheng Zhang (July 2010). "Tunable multifunctional topological insulators in ternary Heusler compounds".

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Jerng, Sahng-Kyoon; Joo, Kisu; Kim, Youngwook; Yoon, Sang-Moon; Lee, Jae Hong; Kim, Miyoung; Kim, Jun Sung; Yoon, Euijoon; Chun, Seung-Hyun (2013). "Ordered growth of topological insulator

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Noh, H.-J.; H. Koh; S.-J. Oh; J.-H. Park; H.-D. Kim; J. D. Rameau; T. Valla; T. E. Kidd; P. D. Johnson; Y. Hu; Q. Li (2008). "Spin-orbit interaction effect in the electronic structure of

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transformed into an ordinary insulator without passing through an intermediate conducting state. In other words, topological insulators and trivial insulators are separate regions in the

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Zhang, X.M.; Liu, E.K.; Liu, Z.Y.; Liu, G.D.; Wu, G.H.; Wang, W.H. (2013-04-01). "Prediction of topological insulating behavior in inverse Heusler compounds from first principles".

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Hasan, M. Zahid; Xu, Su-Yang; Neupane, Madhab (2015), "Topological Insulators, Topological Dirac semimetals, Topological Crystalline Insulators, and Topological Kondo Insulators",

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Fully bulk-insulating or intrinsic 3D topological insulator states exist in Bi-based materials as demonstrated in surface transport measurements. In a new Bi based chalcogenide (Bi

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Zhang, Guanhua; Qin, Huajun; Teng, Jing; Guo, Jiandong; Guo, Qinlin; Dai, Xi; Fang, Zhong; Wu, Kehui (2009-08-03). "Quintuple-layer epitaxy of thin films of topological insulator

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with the Hamiltonian; and a unitary operator which anti-commutes with the Hamiltonian. All combinations of the three together with each spatial dimension result in the so-called

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transformed into a trivial one without untwisting the bands, which closes the band gap and creates a conducting state. Thus, due to the continuity of the underlying field, the

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Chiatti, Olivio; Riha, Christian; Lawrenz, Dominic; Busch, Marco; Dusari, Srujana; Sánchez-Barriga, Jaime; Mogilatenko, Anna; Yashina, Lada V.; Valencia, Sergio (2016-06-07).

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Hsieh, D.; Y. Xia; D. Qian; L. Wray; F. Meier; J. H. Dil; J. Osterwalder; L. Patthey; A. V. Fedorov; H. Lin; A. Bansil; D. Grauer; Y. S. Hor; R. J. Cava; M. Z. Hasan (2009).

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labelled by the type of discrete symmetry (time-reversal symmetry, particle-hole symmetry, and chiral symmetry) has a corresponding group of topological invariants (either

819: 278: 917:(p-type thermoelectrics). High thermoelectric power conversion efficiency is realized in materials with low thermal conductivity, high electrical conductivity, and high 168:

of the material. But in a topological insulator, these bands are, in an informal sense, "twisted", relative to a trivial insulator. The topological insulator cannot be

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The surface states of topological insulators can have exotic properties. For example, in time-reversal symmetric 3D topological insulators, surface states have their

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Cui, Hongmei; Liu, Hong; Wang, Jiyang; Li, Xia; Han, Feng; Boughton, R.I. (2004-11-15). "Sonochemical synthesis of bismuth selenide nanobelts at room temperature".

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Alegria, L. D.; Schroer, M. D.; Chatterjee, A.; Poirier, G. R.; Pretko, M.; Patel, S. K.; Petta, J. R. (2012-08-06). "Structural and Electrical Characterization of

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It was proposed in 2008 and 2009 that topological insulators are best understood not as surface conductors per se, but as bulk 3D magnetoelectrics with a quantized

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Roy, Rahul (2009-05-21). "Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect".

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effect. This can be revealed by placing topological insulators in magnetic field. The effect can be described in language similar to that of the hypothetical

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König, Markus; Wiedmann, Steffen; Brüne, Christoph; Roth, Andreas; Buhmann, Hartmut; Molenkamp, Laurens W.; Qi, Xiao-Liang; Zhang, Shou-Cheng (2007-11-02).

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Essin, Andrew M.; Moore, Joel E.; Vanderbilt, David (2009-04-10). "Magnetoelectric Polarizability and Axion Electrodynamics in Crystalline Insulators".

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topological invariants cannot be measured using traditional transport methods, such as spin Hall conductance, and the transport is not quantized by the

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locked at a right-angle to their momentum (spin-momentum locking). At a given energy the only other available electronic states have different spin, so

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Due to the weak van der Waals bonding, which relaxes the lattice-matching condition, TI can be grown on a wide variety of substrates such as Si(111),

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Bismuth chalcogenides have been successfully grown on different substrates. In particular, Si has been a good substrate for the successful growth of

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Witting, Ian T.; Chasapis, Thomas C.; Ricci, Francesco; Peters, Matthew; Heinz, Nicholas A.; Hautier, Geoffroy; Snyder, G. Jeffrey (June 2019).

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Shuichi Murakami (2007). "Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase".

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The properties of topological insulators and their surface states are highly dependent on both the dimension of the material and its underlying

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Richardella, A.; Zhang, D. M.; Lee, J. S.; Koser, A.; Rench, D. W.; Yeats, A. L.; Buckley, B. B.; Awschalom, D. D.; Samarth, N. (2010-12-27).

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Despite their origin in quantum mechanical systems, analogues of topological insulators can also be found in classical media. There exist

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Hsieh, D.; Xia, Y.; Wray, L.; Qian, D.; Pal, A.; Dil, J. H.; Osterwalder, J.; Meier, F.; Bihlmayer, G.; Kane, C. L.; et al. (2009).

1442:). Due to the weak van der Waals bonding, graphene is one of the preferred substrates for TI growth despite the large lattice mismatch. 5348:

Potter, Andrew C.; Lee, Patrick A. (23 March 2012). "Topological superconductivity and Majorana fermions in metallic surface states".

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Qi, Xiao-Liang; Hughes, Taylor L.; Zhang, Shou-Cheng (2008-11-24). "Topological field theory of time-reversal invariant insulators".

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Later sets of theoretical models for the 2D topological insulator (also known as the quantum spin Hall insulators) were proposed by

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Behnia, Kamran; Balicas, Luis; Kopelevich, Yakov (2007-09-21). "Signatures of Electron Fractionalization in Ultraquantum Bismuth".

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Khanikaev, Alexander B.; Hossein Mousavi, S.; Tse, Wang-Kong; Kargarian, Mehdi; MacDonald, Allan H.; Shvets, Gennady (March 2013).

217:. Some combinations of dimension and symmetries forbid topological insulators completely. All topological insulators have at least 53: 49: 582:

have been proposed for making Floquet topological insulators (FTI). This periodically driven system simulates an effective (

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Heremans, Joseph P.; Cava, Robert J.; Samarth, Nitin (2017-09-05). "Tetradymites as thermoelectrics and topological insulators".

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allows a full characterization of the wave propagation properties of a material by assigning a matrix to each wave vector in the

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Wang, Debao; Yu, Dabin; Mo, Maosong; Liu, Xianming; Qian, Yitai (2003-06-01). "Preparation and characterization of wire-like

1872: 1782: 982: 466: 295: 1231:. The van der Waals interaction in TIs exhibit important features due to low surface energy. For instance, the surface of 7727: 7338: 1002: 973:

method for the growth of a crystalline material on a crystalline substrate to form an ordered layer. MBE is performed in

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He, Cheng; Ni, Xu; Ge, Hao; Sun, Xiao-Chen; Chen, Yan-Bin; Lu, Ming-Hui; Liu, Xiao-Ping; Chen, Yan-Feng (December 2016).

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Buot, F. A. (1973-09-01). "Weyl Transform and the Magnetic Susceptibility of a Relativistic Dirac Electron Gas".

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falls within the bulk band gap which is traversed by topologically-protected spin-textured Dirac surface states.

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MBE is an appropriate technique for the growth of high quality single-crystal films. In order to avoid a huge

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Chiu, C.; J. Teo; A. Schnyder; S. Ryu (2016). "Classification of topological quantum matter with symmetries".

2330: 7809: 7483: 5226:"Discrete-Time Quantum-Walk & Floquet Topological Insulators via Distance-Selective Rydberg-Interaction" 2009: 997: 150: 570: 395:, and in particular "strong topological insulators" exist that cannot be reduced to multiple copies of the 7128: 6694:

Kong, D.; Dang, W.; Cha, J.J.; Li, H.; Meister, S.; Peng, H. K.; Cui, Y (2010). "SFew-layer nanoplates of

6402:"Review of 3D topological insulator thin-film growth by molecular beam epitaxy and potential applications" 940: 222: 146: 125: 1789:

This space can be restricted under the presence of symmetries, changing the resulting topology. Although

7534: 7447: 6017: 600: 280:, allow classification of insulators as trivial or topological, and can be computed by various methods. 1724: 824: 762: 727: 697: 668: 639: 610: 391:

In 2007, it was predicted that 3D topological insulators might be found in binary compounds involving

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The most promising applications of topological insulators are spintronic devices and dissipationless

562: 332: 2618:"Supersymmetry in heterojunctions: Band-inverting contact on the basis of Pb1-xSnxTe and Hg1-xCdxTe" 594:

Spin-momentum locking in the topological insulator allows symmetry-protected surface states to host

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heterostructures. Existence of interface Dirac states in HgTe/CdTe was experimentally verified by

284: 198:, connected only by conducting phases. In this way, topological insulators provide an example of a 169: 7765: 5285:"Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator" 873:. In addition, topological insulator materials have also found practical applications in advanced 802: 261: 7604: 7594: 7343: 7009: 6983: 6951: 6925: 6828: 6799:"Josephson current mediated by ballistic topological states in Bi2Te2.3Se0.7 single nanocrystals" 6779: 6745: 6648: 6570: 6522: 6488: 6439: 6301: 6267: 6237: 6195: 6005: 5971: 5943: 5901: 5662: 5620: 5592: 5566: 5453: 5419: 5391: 5357: 5330: 5296: 5265: 5237: 5201: 5167: 5136: 5102: 5091:"Toward simulation of topological phenomena with one-, two-, and three-dimensional quantum walks" 5071: 5045: 5014: 4980: 4949: 4915: 4884: 4850: 4798: 4756: 4636: 4554: 4512: 4485: 4451: 4396: 4350: 4324: 4296: 4270: 4099: 4071: 4037: 3966: 3914: 3810: 3768: 3737: 3695: 3659: 3633: 3602: 3560: 3533: 3499: 3437: 3403: 3372: 3338: 3308: 3282: 3211: 3177: 3150: 3124: 3097: 3063: 3036: 3018: 2991: 2949: 2918: 2884: 2853: 2819: 2788: 2754: 2723: 2681: 2569: 2535: 2504: 2449: 2407: 2376: 2342: 2311: 2277: 2237: 2211: 2177: 2143: 2052: 2018: 1985: 1959: 1932: 1357: 1204: 958: 874: 540: 485: 419: 347: 288: 7432: 1764: 190:

This leads to a more formal definition of a topological insulator: an insulator which cannot be

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Read, N.; Sachdev, Subir (1991). "Large-N expansion for frustrated quantum antiferromagnets".

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Liang Fu; C. L. Kane; E. J. Mele (2007-03-07). "Topological insulators in three dimensions".

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from the absence of a magnetic field. In this way, topological insulators are an example of

985:. The gaseous elements then condense on the wafer where they react with each other to form 7707: 7328: 7245: 5514:

Wen, Xiao-Gang (1991). "Mean Field Theory of Spin Liquid States with Finite Energy Gaps".

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various layered quasi-two-dimensional materials including topological insulators (i.e.,

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Fu, Liang; Kane, C. L. (2007-07-02). "Topological insulators with inversion symmetry".

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Thus far, the field of topological insulators has been focused on bismuth and antimony

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Fu, Liang; C. L. Kane (2007-07-02). "Topological insulators with inversion symmetry".

2937: 2669: 2617: 2265: 2199: 2131: 2072:"Band inversion mechanism in topological insulators: A guideline for materials design" 2071: 17: 7798: 7642: 7624: 7609: 7589: 7493: 7462: 7293: 7051: 7030: 6832: 6526: 6305: 6009: 5596: 5457: 5269: 5140: 4888: 4802: 4744: 4489: 3814: 3259: 3238: 3040: 2641: 2573: 2181: 1775: 796: 502: 320: 203: 195: 173: 7013: 6955: 6939: 6783: 6443: 6241: 5947: 5666: 5395: 5205: 5075: 5018: 4953: 4354: 4075: 3918: 3663: 3606: 3376: 3329:

Hasan, M. Zahid; Moore, Joel E. (2011). "Three-Dimensional Topological Insulators".

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Stolyarov, V.S.; Yakovlev, D.S.; Kozlov, S.N.; Skryabina, O.V.; Lvov, D.S. (2020).

6143: 5334: 5318: 4778: 4558: 4534: 4300: 4292: 4218: 3741: 3537: 3441: 3101: 2995: 2922: 2857: 2792: 2727: 2056: 1936: 1137: 788: 551: 547:

who showed that the Faraday rotation was quantized by the fine structure constant.

3521: 3085: 2906: 2841: 2776: 2040: 5993: 5852: 5588: 5284: 5090: 3621: 2938:"Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells" 7699: 7417: 7386: 7366: 7152:"Topological insulators promise computing advances, insights into matter itself" 5492: 5155: 5124: 4593: 724: 472:

Shortly thereafter symmetry-protected surface states were also observed in pure

134: 7005: 6843: 6345: 5379: 5189: 4967:

Cayssol, Jérôme; Dóra, Balázs; Simon, Ferenc; Moessner, Roderich (2013-01-28).

4473: 3757:"Observation of Unconventional Quantum Spin Textures in Topological Insulators" 3655: 3490:

Kane, C. L.; Mele, E. J. (2005-11-23). "Quantum Spin Hall Effect in Graphene".

3304: 3146: 3032: 2233: 2165: 2095: 7614: 7452: 7288: 7069: 6823: 6798: 6510: 5260: 4623:

Wu, Liang; Salehi, M.; Koirala, N.; Moon, J.; Oh, S.; Armitage, N. P. (2016).

3837: 3683: 2492: 858: 465:. This prediction is of particular interest due to the observation of charge 6947: 6680: 6600: 6518: 6435: 6353: 6289: 6225: 6151: 6108: 5931: 5827: 5713: 5650: 5535: 5387: 5197: 5132: 5010: 4945: 4786: 4717: 4601: 4542: 4481: 4129: 3996: 3902: 3798: 3725: 3590: 3368: 3207: 2979: 2711: 2649: 2565: 2500: 2437: 2372: 2307: 2173: 2113: 1950:

Hasan, M.Z.; Moore, J.E. (2011). "Three-Dimensional Topological Insulators".

1920: 505:

or gating. The surface states of a 3D topological insulator is a new type of

59:

Please replace inadequate primary references with secondary sources. See the

7672: 7498: 7283: 7168: 5642: 5441: 5154:

Kitagawa, Takuya; Rudner, Mark S.; Berg, Erez; Demler, Eugene (2010-09-24).

4968: 4903: 4659: 4624: 3790: 3684:"A tunable topological insulator in the spin helical Dirac transport regime" 3582: 3476: 2971: 2703: 981:, the elements are heated in different electron beam evaporators until they 430: 303: 35: 7206: 7187: 7114: 6775: 6426: 6401: 6297: 6233: 6001: 5939: 5819: 5788: 5745:

Yue, Zengji; Xue, Gaolei; Liu, Juan; Wang, Yongtian; Gu, Min (2017-05-18).

5731: 5705: 5658: 5500: 5449: 5326: 5002: 4937: 4880: 4794: 4725: 4668: 4609: 4550: 4428: 4226: 4137: 4067: 4014: 3910: 3893: 3868: 3806: 3733: 3598: 3529: 3433: 3390:

Hsieh, David; Dong Qian; Andrew L. Wray; Yuqi Xia; Yusan Hor; Robert Cava;

3093: 2987: 2914: 2849: 2784: 2719: 2523: 2445: 2395: 2048: 1928: 453:

points and the bulk features massive Dirac fermions. Additionally, bulk Bi

180:, which is topologically trivial) is forced to support a conducting state. 5680:

Yue, Zengji; Cai, Boyuan; Wang, Lan; Wang, Xiaolin; Gu, Min (2016-03-01).

5543: 4572:

Wilczek, Frank (1987-05-04). "Two applications of axion electrodynamics".

153:, meaning that electrons can only move along the surface of the material. 6877: 6860: 6258:

Geim, A. K.; Grigorieva, I. V. (2013). "Van der Waals heterostructures".

3504: 3287: 3129: 3068: 3023: 2954: 2889: 2824: 2759: 2023: 565:, can be manipulated by topological insulators. The effect is related to 473: 291:

is strongly suppressed and conduction on the surface is highly metallic.

183:

Since this results from a global property of the topological insulator's

161: 6281: 5770: 4872: 4410: 3717: 3425: 2936:

Bernevig, B. Andrei; Hughes, Taylor L.; Zhang, Shou-Cheng (2006-12-15).

2104: 1912: 7722: 7689: 7667: 7647: 6861:"Topological Insulator Film Growth by Molecular Beam Epitaxy: A Review" 6838: 6217: 5033: 3867:

Chen, Xi; Ma, Xu-Cun; He, Ke; Jia, Jin-Feng; Xue, Qi-Kun (2011-03-01).

970: 694:

topological invariants was demonstrated which provide a measure of the

392: 6893:"10 symmetry classes and the periodic table of topological insulators" 6767: 6671: 6615: 6592: 5923: 5067: 4346: 3988: 3394:(2008). "A Topological Dirac insulator in a quantum spin Hall phase". 2557: 2467:

Tokura, Yoshinori; Yasuda, Kenji; Tsukazaki, Atsushi (February 2019).

2299: 7657: 7652: 7258: 4121: 4059: 2429: 974: 418:

The first 3D topological insulator to be realized experimentally was

177: 7105: 7088: 6972:

Hasan, M. Zahid; Kane, Charles L. (2010). "Topological Insulators".

4708: 4683: 1786:

identified with a number, referred to as a "topological invariant".

929:

Topological insulators can be grown using different methods such as

5976: 5625: 5571: 5242: 5107: 4641: 4401: 3971: 2540: 2524:"Acoustic topological insulator and robust one-way sound transport" 2070:

Zhu, Zhiyong; Cheng, Yingchun; Schwingenschlögl, Udo (2012-06-01).

509:(2DEG) where the electron's spin is locked to its linear momentum. 407:

2D Topological insulators were first realized in system containing

121:

topological invariant, since there are two "islands" of insulators.

7632: 7253: 6988: 6930: 6750: 6653: 6575: 6493: 6272: 6200: 5906: 5892:

Nanostructures Grown by Metal–Organic Chemical Vapor Deposition".

5424: 5362: 5301: 5172: 5050: 4985: 4920: 4855: 4761: 4517: 4456: 4329: 4275: 4104: 4042: 3773: 3700: 3638: 3565: 3408: 3343: 3182: 2686: 2412: 2347: 2282: 2216: 2148: 1964: 532: 124: 86: 561:

In 2014, it was shown that magnetic components, like the ones in

535:

of particle physics. The effect was reported by researchers at

5747:"Nanometric holograms based on a topological insulator material" 4371:

Kushwaha, S. K.; Pletikosić, I.; Liang, T.; et al. (2015).

2873:"$ {Z}_{2}$ Topological Order and the Quantum Spin Hall Effect" 218: 45:

reads like a scientific review article and potentially contains

7210: 5034:"Periodic table for topological insulators and superconductors" 5032:

Kitaev, Alexei; Lebedev, Vladimir; Feigel’man, Mikhail (2009).

4385:

S bulk crystal topological insulator with excellent properties"

2616:

Pankratov, O. A.; Pakhomov, S. V.; Volkov, B. A. (1987-01-01).

2266:"Periodic table for topological insulators and superconductors" 176:

of a topological insulator with a trivial insulator (including

156:

A topological insulator is an insulator for the same reason a "

7263: 1891:

Moore, Joel E. (2010). "The birth of topological insulators".

29: 6859:

Ginley, Theresa P.; Wang, Yong; Law, Stephanie (2016-11-23).

6842:

Text was copied from this source, which is available under a

791:

discovered in 1991.) More generally (in what is known as the

3934:"2D layered transport properties from topological insulator 3682:

Hsieh, D.; Xia, Y.; Qian, D.; Wray, L.; et al. (2009).

939:(PVD), solvothermal synthesis, sonochemical technique and 889:

Some of the most well-known topological insulators are also

133:

for a 3D time-reversal symmetric topological insulator. The

27:

State of matter with insulating bulk but conductive boundary

3869:"Molecular Beam Epitaxial Growth of Topological Insulators" 2592:"Two-dimensional massless electrons in an inverted contact" 1254:

is usually terminated by Te due to its low surface energy.

2670:"Quantum Spin Hall Insulator State in HgTe Quantum Wells" 2331:"Symmetry-Protected Topological Phases of Quantum Matter" 4261:

observed by angle-resolved photoemission spectroscopy".

6373:"Topological Insulators: Fundamentals and Perspectives" 437:, and many other measurements, it was observed that Bi 229:. So-called "topological invariants", taking values in 6844:

Creative Commons Attribution 4.0 International License

4694:(7428). Springer Science and Business Media LLC: 165. 5844:

Are Topological Insulators Promising Thermoelectrics?

2806:

Bernevig, B. Andrei; Zhang, Shou-Cheng (2006-03-14).

2007:

Topological Order and the Quantum Spin Hall Effect".

1727: 827: 805: 765: 730: 700: 671: 642: 613: 360: 264: 235: 98: 6400:

He, Liang; Kou, Xufeng; Wang, Kang L. (2013-01-31).

5841:

Toriyama, Michael; Snyder, G. Jeffrey (2023-11-06),

5804:"The Thermoelectric Properties of Bismuth Telluride" 7698: 7623: 7567: 7527: 7476: 7410: 7359: 7352: 7321: 7244: 6479:film on Si(111) with atomically sharp interface". 4580:(18). American Physical Society (APS): 1799–1802. 1742: 842: 813: 780: 745: 715: 686: 657: 628: 375: 272: 250: 221:from particle number conservation, and often have 113: 6186:thin films on dielectric amorphous SiO2 by MBE". 5156:"Exploring topological phases with quantum walks" 558:, which is a bulk insulator at low temperatures. 496:. Many semiconductors within the large family of 7196:"The Strange Topology That Is Reshaping Physics" 2130:Qi, Xiao-Liang; Zhang, Shou-Cheng (2011-10-14). 1819:synthesized materials. One of the candidates is 7156:Proceedings of the National Academy of Sciences 4450:(19). American Physical Society (APS): 195424. 3832:, John Wiley & Sons, Ltd, pp. 55–100, 4747:(2010-03-12). "Topological Kondo Insulators". 2611: 2609: 2590:Volkov, B. A.; Pankratov, O. A. (1985-08-25). 665:invariants. An experimental method to measure 7222: 4817:"Weird materials could make faster computers" 4366: 4364: 8: 6022:: CS1 maint: multiple names: authors list ( 2132:"Topological insulators and superconductors" 335:group in 2D topological insulators in 2007. 213:, and can be classified using the so-called 5089:Panahiyan, S.; Fritzsche, S. (2021-01-05). 2585: 2583: 949:Schematic of the components of a MBE system 160:" (ordinary) insulator is: there exists an 145:is a material whose interior behaves as an 7356: 7312: 7229: 7215: 7207: 3677: 3675: 3673: 3620:Hasan, M. Zahid; Kane, Charles L. (2010). 2663: 2661: 2659: 1774:Mathematically, this assignment creates a 7177: 7167: 7104: 7021:Kane, Charles L.; Moore, Joel E. (2011). 6987: 6929: 6876: 6822: 6749: 6736:with highly tunable chemical potential". 6670: 6652: 6574: 6492: 6425: 6271: 6199: 5975: 5905: 5778: 5721: 5624: 5570: 5423: 5361: 5300: 5259: 5241: 5171: 5106: 5049: 4984: 4919: 4854: 4760: 4707: 4658: 4640: 4516: 4455: 4418: 4400: 4328: 4274: 4103: 4041: 4004: 3970: 3892: 3772: 3699: 3637: 3564: 3503: 3407: 3342: 3331:Annual Review of Condensed Matter Physics 3286: 3181: 3128: 3067: 3022: 2953: 2888: 2823: 2758: 2685: 2539: 2411: 2346: 2335:Annual Review of Condensed Matter Physics 2281: 2215: 2147: 2103: 2022: 1963: 1952:Annual Review of Condensed Matter Physics 1734: 1730: 1729: 1726: 1446:Lattice mismatch of different substrates 834: 830: 829: 826: 807: 806: 804: 772: 768: 767: 764: 737: 733: 732: 729: 707: 703: 702: 699: 678: 674: 673: 670: 649: 645: 644: 641: 620: 616: 615: 612: 490:angle-resolved photoemission spectroscopy 435:angle-resolved photoemission spectroscopy 367: 363: 362: 359: 266: 265: 263: 242: 238: 237: 234: 105: 101: 100: 97: 73:Learn how and when to remove this message 4908:Journal of the Physical Society of Japan 3361:10.1146/annurev-conmatphys-062910-140432 2365:10.1146/annurev-conmatphys-031214-014740 2198:Hasan, M. Z.; Kane, C. L. (2010-11-08). 1982:10.1146/annurev-conmatphys-062910-140432 1863:Periodic table of topological invariants 1808:periodic table of topological insulators 1760:Periodic table of topological invariants 1444: 944: 852:periodic table of topological invariants 723:topological order. (Note that the term 433:with a small electronic band gap. Using 215:periodic table of topological insulators 206:that defines ordinary states of matter. 7089:"Topological insulators: Star material" 2871:Kane, C. L.; Mele, E. J. (2005-09-28). 2741:Kane, C. L.; Mele, E. J. (2005-11-23). 1883: 931:metal-organic chemical vapor deposition 6015: 5224:Khazali, Mohammadsadegh (2022-03-03). 2743:"Quantum Spin Hall Effect in Graphene" 306:topological insulators, among others. 6854: 6852: 6395: 6393: 6367: 6365: 6363: 6319: 6317: 6315: 6253: 6251: 5219: 5217: 5215: 3862: 3860: 3858: 3856: 3324: 3322: 2259: 2257: 2255: 2253: 2251: 2193: 2191: 2125: 2123: 1750:topology by definition of the state. 7: 7753: 2200:"Colloquium: Topological insulators" 1132:Bismuth-based topological insulators 1081:PVD growth of topological insulators 965:MBE growth of topological insulators 227:symmetry-protected topological order 7777: 2003:Kane, C. L.; Mele, E. J. (2005). "Z 969:Molecular beam epitaxy (MBE) is an 755:has also been used to describe the 3229:Kane, C. L.; Moore, J. E. (2011). 449:(SS) crossing between any pair of 429:. Bismuth in its pure state, is a 25: 7124:"Focus on Topological Insulators" 4904:"Topological Insulator Materials" 3955:single crystals and micro flakes" 2469:"Magnetic topological insulators" 2396:"Photonic topological insulators" 1802:; an anti-unitary operator which 1299:can be grown on top of various Bi 469:in 2D graphene and pure bismuth. 411:quantum wells sandwiched between 7776: 7764: 7752: 7741: 7740: 6837: 4969:"Floquet topological insulators" 1843:Topological quantum field theory 1743:{\displaystyle \mathbb {Z} _{2}} 850:or trivial) as described by the 843:{\displaystyle \mathbb {Z} _{2}} 781:{\displaystyle \mathbb {Z} _{2}} 746:{\displaystyle \mathbb {Z} _{2}} 716:{\displaystyle \mathbb {Z} _{2}} 687:{\displaystyle \mathbb {Z} _{2}} 658:{\displaystyle \mathbb {Z} _{2}} 629:{\displaystyle \mathbb {Z} _{2}} 376:{\displaystyle \mathbb {Z} _{2}} 251:{\displaystyle \mathbb {Z} _{2}} 149:while its surface behaves as an 114:{\displaystyle \mathbb {Z} _{2}} 34: 6940:10.1016/j.commatsci.2012.12.013 6918:Computational Materials Science 909:(n-type thermoelectrics) and Sb 204:Landau symmetry-breaking theory 6144:10.1016/j.jcrysgro.2004.08.015 5319:10.1103/PhysRevLett.100.096407 4779:10.1103/physrevlett.104.106408 4682:Samuel Reich, Eugenie (2012). 4535:10.1103/physrevlett.102.146805 4219:10.1103/PhysRevLett.103.146401 1873:Photonic topological insulator 577:Floquet topological insulators 554:insulators were identified in 467:quantum Hall fractionalization 461:has been predicted to have 3D 1: 7339:Spontaneous symmetry breaking 6101:10.1016/S0022-0248(03)01019-4 5808:Advanced Electronic Materials 3522:10.1103/PhysRevLett.95.226801 3086:10.1103/PhysRevLett.98.106803 2907:10.1103/PhysRevLett.95.146802 2842:10.1103/PhysRevLett.96.106802 2777:10.1103/PhysRevLett.95.226801 2264:Kitaev, Alexei (2009-05-14). 2041:10.1103/PhysRevLett.95.146802 1003:scanning tunneling microscopy 871:quantum anomalous Hall effect 7137:Moore, Joel E. (July 2011). 5994:10.1021/acs.nanolett.6b05260 5853:10.26434/chemrxiv-2023-3nvl3 5589:10.1103/RevModPhys.88.035005 2642:10.1016/0038-1098(87)90934-3 1838:Topological quantum computer 1781:Specifically, the number of 814:{\displaystyle \mathbb {Z} } 507:two-dimensional electron gas 273:{\displaystyle \mathbb {Z} } 166:valence and conduction bands 6616:"Coherent heteroepitaxy of 5493:10.1103/physrevlett.66.1773 5283:Fu, L.; C. L. Kane (2008). 5125:10.1103/physreva.103.012201 4902:Ando, Yoichi (2013-10-15). 4594:10.1103/physrevlett.58.1799 590:Properties and applications 567:metal–insulator transitions 563:spin-torque computer memory 7826: 7519:Spin gapless semiconductor 7428:Nearly free electron model 7122:Murakami, Shuichi (2010). 7064:. Wiley. pp. 55–100. 7052:10.1088/2058-7058/24/02/36 7006:10.1103/RevModPhys.82.3045 6346:10.1038/natrevmats.2017.49 5380:10.1103/physrevb.85.094516 5190:10.1103/physreva.82.033429 5038:AIP Conference Proceedings 4474:10.1103/physrevb.78.195424 4293:10.1209/0295-5075/81/57006 3656:10.1103/RevModPhys.82.3045 3305:10.1103/PhysRevB.76.045302 3260:10.1088/2058-7058/24/02/36 3147:10.1103/PhysRevB.76.045302 3033:10.1103/PhysRevB.79.195322 2808:"Quantum Spin Hall Effect" 2622:Solid State Communications 2329:Senthil, T. (2015-03-01). 2270:AIP Conference Proceedings 2234:10.1103/RevModPhys.82.3045 2166:10.1103/RevModPhys.83.1057 2096:10.1103/PhysRevB.85.235401 1848:Topological quantum number 1757: 7736: 7468:Density functional theory 7443:electronic band structure 7310: 7070:10.1002/9783527681594.ch4 6975:Reviews of Modern Physics 6824:10.1038/s43246-020-0037-y 6511:10.1016/j.tsf.2011.07.033 6406:Physica Status Solidi RRL 6124:Journal of Crystal Growth 6081:Journal of Crystal Growth 5261:10.22331/q-2022-03-03-664 4973:Physica Status Solidi RRL 3838:10.1002/9783527681594.ch4 3626:Reviews of Modern Physics 3200:10.1088/1367-2630/9/9/356 2493:10.1038/s42254-018-0011-5 2204:Reviews of Modern Physics 2136:Reviews of Modern Physics 937:physical vapor deposition 7805:Condensed matter physics 7638:Bogoliubov quasiparticle 7382:Quantum spin Hall effect 7274:Bose–Einstein condensate 7238:Condensed matter physics 7139:"Topological Insulators" 7023:"Topological Insulators" 6803:Communications Materials 6326:Nature Reviews Materials 5536:10.1103/physrevb.44.2664 4739:Dzero, Maxim; Sun, Kai; 3622:"Topological Insulators" 3231:"Topological Insulators" 1858:Quantum spin Hall effect 1798:which commutes with the 1311:buffers. Table 1 shows 1229:thermoelectric materials 1140:based materials such as 891:thermoelectric materials 537:Johns Hopkins University 403:Experimental realization 7169:10.1073/pnas.1611504113 6641:Applied Physics Letters 6563:Applied Physics Letters 5643:10.1126/science.1234414 5442:10.1126/science.1167733 4749:Physical Review Letters 4660:10.1126/science.aaf5541 4574:Physical Review Letters 4505:Physical Review Letters 4199:Physical Review Letters 3791:10.1126/science.1167733 3583:10.1126/science.1146509 3492:Physical Review Letters 3477:10.1103/PhysRevA.8.1570 3056:Physical Review Letters 2972:10.1126/science.1133734 2877:Physical Review Letters 2812:Physical Review Letters 2747:Physical Review Letters 2704:10.1126/science.1148047 2010:Physical Review Letters 397:quantum spin Hall state 7129:New Journal of Physics 7062:Topological Insulators 6427:10.1002/pssr.201307003 5820:10.1002/aelm.201800904 5706:10.1126/sciadv.1501536 5003:10.1002/pssr.201206451 4938:10.7566/jpsj.82.102001 3894:10.1002/adma.201003855 3830:Topological Insulators 3170:New Journal of Physics 2473:Nature Reviews Physics 1821:half-Heusler compounds 1744: 950: 941:molecular beam epitaxy 901:and its alloys with Bi 844: 815: 782: 747: 717: 688: 659: 630: 601:helical Dirac fermions 445:alloy exhibits an odd 377: 333:Laurens W. Molenkamp's 274: 252: 223:time-reversal symmetry 138: 122: 115: 18:Topological insulators 7514:Topological insulator 7448:Anderson localization 7087:Brumfiel, G. (2010). 5751:Nature Communications 4389:Nature Communications 1796:anti-unitary operator 1745: 948: 845: 816: 783: 748: 718: 689: 660: 631: 550:In 2012, topological 378: 346:in 2005, and also by 275: 253: 202:not described by the 143:topological insulator 128: 116: 90: 7392:Aharonov–Bohm effect 7279:Fermionic condensate 6878:10.3390/cryst6110154 1783:connected components 1725: 825: 803: 763: 728: 698: 669: 640: 611: 358: 262: 233: 151:electrical conductor 147:electrical insulator 96: 7783:Physics WikiProject 7458:tight binding model 7438:Fermi liquid theory 7423:Free electron model 7372:Quantum Hall effect 7353:Electrons in solids 7200:Scientific American 7044:2011PhyW...24b..32K 6998:2010RvMP...82.3045H 6815:2020CoMat...1...38S 6760:2010NanoL..10.2245K 6663:2010ApPhL..97z2104R 6585:2009ApPhL..95e3114Z 6503:2011TSF...520..224B 6418:2013PSSRR...7...50H 6338:2017NatRM...217049H 6282:10.1038/nature12385 6210:2013Nanos...510618J 6136:2004JCrGr.271..456C 6093:2003JCrGr.253..445W 5986:2017NanoL..17.2354T 5916:2012NanoL..12.4711A 5771:10.1038/ncomms15354 5763:2017NatCo...815354Y 5698:2016SciA....2E1536Y 5635:2013Sci...340..167C 5581:2016RvMP...88c5005C 5528:1991PhRvB..44.2664W 5485:1991PhRvL..66.1773R 5434:2009Sci...323..919H 5372:2012PhRvB..85i4516P 5311:2008PhRvL.100i6407F 5252:2022Quant...6..664K 5182:2010PhRvA..82c3429K 5117:2021PhRvA.103a2201P 5060:2009AIPC.1134...22K 4995:2013PSSRR...7..101C 4930:2013JPSJ...82j2001A 4873:10.1038/nature13534 4865:2014Natur.511..449M 4771:2010PhRvL.104j6408D 4700:2012Natur.492..165S 4651:2016Sci...354.1124W 4586:1987PhRvL..58.1799W 4527:2009PhRvL.102n6805E 4466:2008PhRvB..78s5424Q 4411:10.1038/ncomms11456 4339:2014NatPh..10..956X 4285:2008EL.....8157006N 4211:2009PhRvL.103n6401H 4114:2010NatMa...9..546L 4052:2010NatMa...9..541C 3981:2016NatSR...627483C 3885:2011AdM....23.1162C 3783:2009Sci...323..919H 3718:10.1038/nature08234 3710:2009Natur.460.1101H 3648:2010RvMP...82.3045H 3575:2007Sci...317.1729B 3514:2005PhRvL..95v6801K 3469:1973PhRvA...8.1570B 3426:10.1038/nature06843 3418:2008Natur.452..970H 3353:2011ARCMP...2...55H 3297:2007PhRvB..76d5302F 3252:2011PhyW...24b..32K 3192:2007NJPh....9..356M 3139:2007PhRvB..76d5302F 3078:2007PhRvL..98j6803F 2964:2006Sci...314.1757B 2948:(5806): 1757–1761. 2899:2005PhRvL..95n6802K 2834:2006PhRvL..96j6802B 2769:2005PhRvL..95v6801K 2696:2007Sci...318..766K 2634:1987SSCom..61...93P 2550:2016NatPh..12.1124H 2485:2019NatRP...1..126T 2422:2013NatMa..12..233K 2357:2015ARCMP...6..299S 2292:2009AIPC.1134...22K 2226:2010RvMP...82.3045H 2158:2011RvMP...83.1057Q 2088:2012PhRvB..85w5401Z 2033:2005PhRvL..95n6802K 1974:2011ARCMP...2...55H 1913:10.1038/nature08916 1905:2010Natur.464..194M 1853:Quantum Hall effect 1814:Future developments 1447: 959:integrated circuits 919:Seebeck coefficient 867:quantum Hall effect 797:random Hamiltonians 605:quantum Hall effect 556:samarium hexaboride 289:"U"-turn scattering 7344:Critical phenomena 7150:Ornes, S. (2016). 6218:10.1039/C3NR03032F 3959:Scientific Reports 3873:Advanced Materials 1740: 1445: 951: 840: 811: 778: 743: 713: 684: 655: 626: 596:Majorana particles 571:Bose–Hubbard model 541:Rutgers University 486:antimony telluride 373: 348:B. Andrei Bernevig 270: 248: 139: 123: 111: 7792: 7791: 7678:Exciton-polariton 7563: 7562: 7535:Thermoelectricity 6768:10.1021/nl101260j 6672:10.1063/1.3532845 6593:10.1063/1.3200237 6266:(7459): 419–425. 5924:10.1021/nl302108r 5619:(6129): 167–170. 5565:(35005): 035005. 5418:(5916): 919–922. 5350:Physical Review B 5160:Physical Review A 5095:Physical Review A 5068:10.1063/1.3149495 5044:(1). AIP: 22–30. 4849:(7510): 449–451. 4444:Physical Review B 4347:10.1038/nphys3140 3989:10.1038/srep27483 3847:978-3-527-68159-4 3767:(5916): 919–922. 3559:(5845): 1729–31. 3457:Physical Review A 3275:Physical Review B 3117:Physical Review B 3011:Physical Review B 2680:(5851): 766–770. 2558:10.1038/nphys3867 2534:(12): 1124–1129. 2300:10.1063/1.3149495 2076:Physical Review B 1899:(7286): 194–198. 1833:Topological order 1794:respectively: an 1713: 1712: 979:ultra-high vacuum 875:magnetoelectronic 863:quantum computers 757:topological order 753:topological order 498:Heusler materials 482:bismuth telluride 413:cadmium telluride 83: 82: 75: 16:(Redirected from 7817: 7780: 7779: 7768: 7756: 7755: 7744: 7743: 7683:Phonon polariton 7575:Amorphous magnet 7555:Electrostriction 7550:Flexoelectricity 7545:Ferroelectricity 7540:Piezoelectricity 7397:Josephson effect 7377:Spin Hall effect 7357: 7334:Phase transition 7316: 7299:Luttinger liquid 7246:States of matter 7231: 7224: 7217: 7208: 7203: 7191: 7181: 7171: 7146: 7133: 7118: 7108: 7083: 7055: 7027: 7017: 6991: 6960: 6959: 6933: 6913: 6907: 6906: 6904: 6903: 6889: 6883: 6882: 6880: 6856: 6847: 6841: 6836: 6826: 6794: 6788: 6787: 6753: 6735: 6734: 6733: 6725: 6724: 6714: 6713: 6712: 6704: 6703: 6691: 6685: 6684: 6674: 6656: 6636: 6635: 6634: 6626: 6625: 6611: 6605: 6604: 6578: 6560: 6559: 6558: 6550: 6549: 6537: 6531: 6530: 6496: 6481:Thin Solid Films 6478: 6477: 6476: 6468: 6467: 6454: 6448: 6447: 6429: 6397: 6388: 6387: 6385: 6384: 6369: 6358: 6357: 6321: 6310: 6309: 6275: 6255: 6246: 6245: 6203: 6194:(21): 10618–22. 6185: 6184: 6183: 6175: 6174: 6162: 6156: 6155: 6130:(3–4): 456–461. 6119: 6113: 6112: 6087:(1–4): 445–451. 6078: 6077: 6076: 6068: 6067: 6057: 6056: 6055: 6047: 6046: 6034: 6028: 6027: 6021: 6013: 5979: 5958: 5952: 5951: 5909: 5891: 5890: 5889: 5881: 5880: 5868: 5862: 5861: 5860: 5859: 5838: 5832: 5831: 5799: 5793: 5792: 5782: 5742: 5736: 5735: 5725: 5686:Science Advances 5677: 5671: 5670: 5628: 5607: 5601: 5600: 5574: 5554: 5548: 5547: 5522:(6): 2664–2672. 5511: 5505: 5504: 5468: 5462: 5461: 5427: 5406: 5400: 5399: 5365: 5345: 5339: 5338: 5304: 5280: 5274: 5273: 5263: 5245: 5221: 5210: 5209: 5175: 5151: 5145: 5144: 5110: 5086: 5080: 5079: 5053: 5029: 5023: 5022: 4988: 4979:(1–2): 101–108. 4964: 4958: 4957: 4923: 4899: 4893: 4892: 4858: 4837: 4831: 4830: 4828: 4827: 4813: 4807: 4806: 4764: 4741:Galitski, Victor 4736: 4730: 4729: 4711: 4679: 4673: 4672: 4662: 4644: 4635:(6316): 1124–7. 4620: 4614: 4613: 4569: 4563: 4562: 4520: 4500: 4494: 4493: 4459: 4439: 4433: 4432: 4422: 4404: 4368: 4359: 4358: 4332: 4311: 4305: 4304: 4278: 4260: 4259: 4258: 4250: 4249: 4237: 4231: 4230: 4194: 4193: 4192: 4184: 4183: 4173: 4172: 4171: 4163: 4162: 4148: 4142: 4141: 4122:10.1038/nmat2771 4107: 4086: 4080: 4079: 4060:10.1038/nmat2770 4045: 4030:Nature Materials 4025: 4019: 4018: 4008: 3974: 3954: 3953: 3952: 3944: 3943: 3929: 3923: 3922: 3896: 3864: 3851: 3850: 3825: 3819: 3818: 3776: 3752: 3746: 3745: 3703: 3694:(7259): 1101–5. 3679: 3668: 3667: 3641: 3617: 3611: 3610: 3568: 3548: 3542: 3541: 3507: 3505:cond-mat/0411737 3487: 3481: 3480: 3452: 3446: 3445: 3411: 3387: 3381: 3380: 3346: 3326: 3317: 3316: 3290: 3288:cond-mat/0611341 3270: 3264: 3263: 3235: 3226: 3220: 3219: 3185: 3165: 3159: 3158: 3132: 3130:cond-mat/0611341 3112: 3106: 3105: 3071: 3069:cond-mat/0607699 3051: 3045: 3044: 3026: 3024:cond-mat/0607531 3006: 3000: 2999: 2957: 2955:cond-mat/0611399 2933: 2927: 2926: 2892: 2890:cond-mat/0506581 2868: 2862: 2861: 2827: 2825:cond-mat/0504147 2803: 2797: 2796: 2762: 2760:cond-mat/0411737 2738: 2732: 2731: 2689: 2665: 2654: 2653: 2613: 2604: 2603: 2587: 2578: 2577: 2543: 2519: 2513: 2512: 2464: 2458: 2457: 2430:10.1038/nmat3520 2415: 2400:Nature Materials 2391: 2385: 2384: 2350: 2326: 2320: 2319: 2285: 2261: 2246: 2245: 2219: 2210:(4): 3045–3067. 2195: 2186: 2185: 2151: 2142:(4): 1057–1110. 2127: 2118: 2117: 2107: 2067: 2061: 2060: 2026: 2024:cond-mat/0506581 2000: 1994: 1993: 1967: 1947: 1941: 1940: 1888: 1868:Bismuth selenide 1749: 1747: 1746: 1741: 1739: 1738: 1733: 1700: 1699: 1698: 1676: 1675: 1674: 1666: 1665: 1629: 1628: 1627: 1563: 1562: 1561: 1519: 1518: 1517: 1509: 1508: 1496: 1495: 1494: 1486: 1485: 1473: 1472: 1471: 1463: 1462: 1448: 1441: 1440: 1439: 1431: 1430: 1420: 1419: 1418: 1410: 1409: 1399: 1398: 1397: 1389: 1388: 1377: 1375: 1374: 1366: 1365: 1354: 1353: 1352: 1344: 1343: 1333: 1331: 1330: 1322: 1321: 1298: 1297: 1296: 1288: 1287: 1277: 1276: 1275: 1267: 1266: 1253: 1251: 1250: 1242: 1241: 1202: 1201: 1200: 1192: 1191: 1181: 1180: 1179: 1171: 1170: 1160: 1159: 1158: 1150: 1149: 1127: 1126: 1125: 1117: 1116: 1106: 1105: 1104: 1096: 1095: 1076: 1074: 1073: 1065: 1064: 1056: 1055: 1030: 1028: 1027: 1019: 1018: 994:lattice mismatch 849: 847: 846: 841: 839: 838: 833: 820: 818: 817: 812: 810: 787: 785: 784: 779: 777: 776: 771: 752: 750: 749: 744: 742: 741: 736: 722: 720: 719: 714: 712: 711: 706: 693: 691: 690: 685: 683: 682: 677: 664: 662: 661: 656: 654: 653: 648: 635: 633: 632: 627: 625: 624: 619: 545:THz spectroscopy 494:bismuth selenide 478:bismuth selenide 382: 380: 379: 374: 372: 371: 366: 279: 277: 276: 271: 269: 257: 255: 254: 249: 247: 246: 241: 120: 118: 117: 112: 110: 109: 104: 78: 71: 67: 38: 30: 21: 7825: 7824: 7820: 7819: 7818: 7816: 7815: 7814: 7795: 7794: 7793: 7788: 7732: 7713:Granular matter 7708:Amorphous solid 7694: 7619: 7605:Antiferromagnet 7595:Superparamagnet 7568:Magnetic phases 7559: 7523: 7472: 7433:Bloch's theorem 7406: 7348: 7329:Order parameter 7322:Phase phenomena 7317: 7308: 7240: 7235: 7194: 7162:(37): 10223–4. 7149: 7136: 7121: 7106:10.1038/466310a 7099:(7304): 310–1. 7095:(Nature News). 7086: 7080: 7058: 7025: 7020: 6971: 6968: 6966:Further reading 6963: 6915: 6914: 6910: 6901: 6899: 6897:topocondmat.org 6891: 6890: 6886: 6858: 6857: 6850: 6796: 6795: 6791: 6732: 6729: 6728: 6727: 6723: 6720: 6719: 6718: 6716: 6711: 6708: 6707: 6706: 6702: 6699: 6698: 6697: 6695: 6693: 6692: 6688: 6637:on GaAs (111)B" 6633: 6630: 6629: 6628: 6624: 6621: 6620: 6619: 6617: 6613: 6612: 6608: 6557: 6554: 6553: 6552: 6548: 6545: 6544: 6543: 6541: 6539: 6538: 6534: 6475: 6472: 6471: 6470: 6466: 6463: 6462: 6461: 6459: 6456: 6455: 6451: 6399: 6398: 6391: 6382: 6380: 6371: 6370: 6361: 6323: 6322: 6313: 6257: 6256: 6249: 6182: 6179: 6178: 6177: 6173: 6170: 6169: 6168: 6166: 6164: 6163: 6159: 6121: 6120: 6116: 6079:nanocrystals". 6075: 6072: 6071: 6070: 6066: 6063: 6062: 6061: 6059: 6058:and flake-like 6054: 6051: 6050: 6049: 6045: 6042: 6041: 6040: 6038: 6036: 6035: 6031: 6014: 5960: 5959: 5955: 5888: 5885: 5884: 5883: 5879: 5876: 5875: 5874: 5872: 5870: 5869: 5865: 5857: 5855: 5840: 5839: 5835: 5801: 5800: 5796: 5757:: ncomms15354. 5744: 5743: 5739: 5692:(3): e1501536. 5679: 5678: 5674: 5609: 5608: 5604: 5556: 5555: 5551: 5513: 5512: 5508: 5473:Phys. Rev. Lett 5470: 5469: 5465: 5408: 5407: 5403: 5347: 5346: 5342: 5289:Phys. Rev. Lett 5282: 5281: 5277: 5223: 5222: 5213: 5153: 5152: 5148: 5088: 5087: 5083: 5031: 5030: 5026: 4966: 4965: 4961: 4901: 4900: 4896: 4839: 4838: 4834: 4825: 4823: 4815: 4814: 4810: 4738: 4737: 4733: 4709:10.1038/492165a 4681: 4680: 4676: 4622: 4621: 4617: 4571: 4570: 4566: 4502: 4501: 4497: 4441: 4440: 4436: 4384: 4380: 4376: 4370: 4369: 4362: 4323:(12): 956–963. 4313: 4312: 4308: 4257: 4254: 4253: 4252: 4248: 4245: 4244: 4243: 4241: 4239: 4238: 4234: 4191: 4188: 4187: 4186: 4182: 4179: 4178: 4177: 4175: 4170: 4167: 4166: 4165: 4161: 4158: 4157: 4156: 4154: 4150: 4149: 4145: 4088: 4087: 4083: 4027: 4026: 4022: 3951: 3948: 3947: 3946: 3942: 3939: 3938: 3937: 3935: 3931: 3930: 3926: 3866: 3865: 3854: 3848: 3827: 3826: 3822: 3754: 3753: 3749: 3681: 3680: 3671: 3619: 3618: 3614: 3550: 3549: 3545: 3489: 3488: 3484: 3454: 3453: 3449: 3389: 3388: 3384: 3328: 3327: 3320: 3272: 3271: 3267: 3233: 3228: 3227: 3223: 3167: 3166: 3162: 3114: 3113: 3109: 3053: 3052: 3048: 3008: 3007: 3003: 2935: 2934: 2930: 2870: 2869: 2865: 2805: 2804: 2800: 2740: 2739: 2735: 2667: 2666: 2657: 2615: 2614: 2607: 2589: 2588: 2581: 2521: 2520: 2516: 2466: 2465: 2461: 2393: 2392: 2388: 2328: 2327: 2323: 2263: 2262: 2249: 2197: 2196: 2189: 2129: 2128: 2121: 2069: 2068: 2064: 2006: 2002: 2001: 1997: 1949: 1948: 1944: 1890: 1889: 1885: 1881: 1829: 1816: 1765:Bloch's theorem 1762: 1756: 1728: 1723: 1722: 1718: 1697: 1694: 1693: 1692: 1690: 1673: 1670: 1669: 1668: 1664: 1661: 1660: 1659: 1657: 1626: 1623: 1622: 1621: 1619: 1560: 1557: 1556: 1555: 1553: 1516: 1513: 1512: 1511: 1507: 1504: 1503: 1502: 1500: 1493: 1490: 1489: 1488: 1484: 1481: 1480: 1479: 1477: 1470: 1467: 1466: 1465: 1461: 1458: 1457: 1456: 1454: 1438: 1435: 1434: 1433: 1429: 1426: 1425: 1424: 1422: 1417: 1414: 1413: 1412: 1408: 1405: 1404: 1403: 1401: 1396: 1393: 1392: 1391: 1387: 1384: 1383: 1382: 1380: 1373: 1370: 1369: 1368: 1364: 1361: 1360: 1359: 1356: 1351: 1348: 1347: 1346: 1342: 1339: 1338: 1337: 1335: 1329: 1326: 1325: 1324: 1320: 1317: 1316: 1315: 1312: 1310: 1306: 1302: 1295: 1292: 1291: 1290: 1286: 1283: 1282: 1281: 1279: 1274: 1271: 1270: 1269: 1265: 1262: 1261: 1260: 1258: 1249: 1246: 1245: 1244: 1240: 1237: 1236: 1235: 1232: 1225: 1221: 1217: 1212: 1208: 1199: 1196: 1195: 1194: 1190: 1187: 1186: 1185: 1183: 1178: 1175: 1174: 1173: 1169: 1166: 1165: 1164: 1162: 1157: 1154: 1153: 1152: 1148: 1145: 1144: 1143: 1141: 1134: 1124: 1121: 1120: 1119: 1115: 1112: 1111: 1110: 1108: 1103: 1100: 1099: 1098: 1094: 1091: 1090: 1089: 1087: 1083: 1072: 1069: 1068: 1067: 1063: 1060: 1059: 1058: 1054: 1051: 1050: 1049: 1046: 1026: 1023: 1022: 1021: 1017: 1014: 1013: 1012: 1009: 1005:(STM) studies. 987:single crystals 955:heterostructure 927: 916: 912: 908: 904: 900: 896: 887: 885:Thermoelectrics 828: 823: 822: 801: 800: 766: 761: 760: 731: 726: 725: 701: 696: 695: 672: 667: 666: 643: 638: 637: 614: 609: 608: 592: 579: 529:magnetoelectric 523: 519: 515: 463:Dirac particles 460: 456: 444: 440: 427: 423: 405: 361: 356: 355: 352:Shoucheng Zhang 340:Charles L. Kane 312: 260: 259: 236: 231: 230: 200:state of matter 99: 94: 93: 79: 68: 65:(February 2024) 58: 54:primary sources 39: 28: 23: 22: 15: 12: 11: 5: 7823: 7821: 7813: 7812: 7810:Semiconductors 7807: 7797: 7796: 7790: 7789: 7787: 7786: 7774: 7771:Physics Portal 7762: 7750: 7737: 7734: 7733: 7731: 7730: 7725: 7720: 7718:Liquid crystal 7715: 7710: 7704: 7702: 7696: 7695: 7693: 7692: 7687: 7686: 7685: 7680: 7670: 7665: 7660: 7655: 7650: 7645: 7640: 7635: 7629: 7627: 7625:Quasiparticles 7621: 7620: 7618: 7617: 7612: 7607: 7602: 7597: 7592: 7587: 7585:Superdiamagnet 7582: 7577: 7571: 7569: 7565: 7564: 7561: 7560: 7558: 7557: 7552: 7547: 7542: 7537: 7531: 7529: 7525: 7524: 7522: 7521: 7516: 7511: 7509:Superconductor 7506: 7501: 7496: 7491: 7489:Mott insulator 7486: 7480: 7478: 7474: 7473: 7471: 7470: 7465: 7460: 7455: 7450: 7445: 7440: 7435: 7430: 7425: 7420: 7414: 7412: 7408: 7407: 7405: 7404: 7399: 7394: 7389: 7384: 7379: 7374: 7369: 7363: 7361: 7354: 7350: 7349: 7347: 7346: 7341: 7336: 7331: 7325: 7323: 7319: 7318: 7311: 7309: 7307: 7306: 7301: 7296: 7291: 7286: 7281: 7276: 7271: 7266: 7261: 7256: 7250: 7248: 7242: 7241: 7236: 7234: 7233: 7226: 7219: 7211: 7205: 7204: 7192: 7147: 7134: 7119: 7084: 7078: 7056: 7018: 6982:(4): 3045–67. 6967: 6964: 6962: 6961: 6908: 6884: 6848: 6789: 6744:(6): 2245–50. 6730: 6721: 6709: 6700: 6686: 6647:(26): 262104. 6631: 6622: 6606: 6555: 6546: 6532: 6473: 6464: 6449: 6412:(1–2): 50–63. 6389: 6359: 6311: 6247: 6180: 6171: 6157: 6114: 6073: 6064: 6052: 6043: 6029: 5970:(4): 2354–60. 5953: 5886: 5877: 5863: 5833: 5794: 5737: 5672: 5602: 5559:Rev. Mod. Phys 5549: 5506: 5479:(13): 1773–6. 5463: 5401: 5340: 5275: 5211: 5146: 5081: 5024: 4959: 4914:(10): 102001. 4894: 4832: 4808: 4755:(10): 106408. 4745:Coleman, Piers 4731: 4674: 4615: 4564: 4511:(14): 146805. 4495: 4434: 4382: 4378: 4374: 4360: 4317:Nature Physics 4306: 4255: 4246: 4232: 4205:(14): 146401. 4189: 4180: 4168: 4159: 4143: 4081: 4020: 3949: 3940: 3924: 3852: 3846: 3820: 3747: 3669: 3632:(4): 3045–67. 3612: 3543: 3498:(22): 226801. 3482: 3463:(3): 1570–81. 3447: 3392:M. Zahid Hasan 3382: 3318: 3265: 3221: 3160: 3107: 3062:(10): 106803. 3046: 3001: 2928: 2883:(14): 146802. 2863: 2818:(10): 106802. 2798: 2753:(22): 226801. 2733: 2655: 2605: 2579: 2528:Nature Physics 2514: 2479:(2): 126–143. 2459: 2406:(3): 233–239. 2386: 2341:(1): 299–324. 2321: 2247: 2187: 2119: 2082:(23): 235401. 2062: 2017:(14): 146802. 2004: 1995: 1942: 1882: 1880: 1877: 1876: 1875: 1870: 1865: 1860: 1855: 1850: 1845: 1840: 1835: 1828: 1825: 1815: 1812: 1769:Brillouin zone 1758:Main article: 1755: 1754:Classification 1752: 1737: 1732: 1717: 1716:Identification 1714: 1711: 1710: 1707: 1704: 1701: 1695: 1687: 1686: 1683: 1680: 1677: 1671: 1662: 1654: 1653: 1650: 1647: 1644: 1640: 1639: 1636: 1633: 1630: 1624: 1616: 1615: 1612: 1609: 1606: 1602: 1601: 1598: 1595: 1592: 1588: 1587: 1584: 1581: 1578: 1574: 1573: 1570: 1567: 1564: 1558: 1550: 1549: 1546: 1543: 1540: 1536: 1535: 1532: 1529: 1526: 1522: 1521: 1514: 1505: 1498: 1491: 1482: 1475: 1468: 1459: 1452: 1436: 1427: 1415: 1406: 1394: 1385: 1371: 1362: 1349: 1340: 1327: 1318: 1308: 1304: 1300: 1293: 1284: 1272: 1263: 1247: 1238: 1223: 1219: 1215: 1210: 1206: 1197: 1188: 1176: 1167: 1155: 1146: 1133: 1130: 1122: 1113: 1101: 1092: 1082: 1079: 1070: 1061: 1052: 1024: 1015: 926: 923: 914: 910: 906: 902: 898: 894: 886: 883: 879:optoelectronic 837: 832: 809: 775: 770: 759:with emergent 740: 735: 710: 705: 681: 676: 652: 647: 623: 618: 591: 588: 578: 575: 533:axion particle 521: 517: 513: 458: 454: 442: 438: 425: 421: 404: 401: 370: 365: 344:Eugene J. Mele 311: 308: 268: 245: 240: 185:band structure 131:band structure 108: 103: 81: 80: 42: 40: 33: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 7822: 7811: 7808: 7806: 7803: 7802: 7800: 7785: 7784: 7775: 7773: 7772: 7767: 7763: 7761: 7760: 7751: 7749: 7748: 7739: 7738: 7735: 7729: 7726: 7724: 7721: 7719: 7716: 7714: 7711: 7709: 7706: 7705: 7703: 7701: 7697: 7691: 7688: 7684: 7681: 7679: 7676: 7675: 7674: 7671: 7669: 7666: 7664: 7661: 7659: 7656: 7654: 7651: 7649: 7646: 7644: 7641: 7639: 7636: 7634: 7631: 7630: 7628: 7626: 7622: 7616: 7613: 7611: 7608: 7606: 7603: 7601: 7598: 7596: 7593: 7591: 7588: 7586: 7583: 7581: 7578: 7576: 7573: 7572: 7570: 7566: 7556: 7553: 7551: 7548: 7546: 7543: 7541: 7538: 7536: 7533: 7532: 7530: 7526: 7520: 7517: 7515: 7512: 7510: 7507: 7505: 7502: 7500: 7497: 7495: 7494:Semiconductor 7492: 7490: 7487: 7485: 7482: 7481: 7479: 7475: 7469: 7466: 7464: 7463:Hubbard model 7461: 7459: 7456: 7454: 7451: 7449: 7446: 7444: 7441: 7439: 7436: 7434: 7431: 7429: 7426: 7424: 7421: 7419: 7416: 7415: 7413: 7409: 7403: 7400: 7398: 7395: 7393: 7390: 7388: 7385: 7383: 7380: 7378: 7375: 7373: 7370: 7368: 7365: 7364: 7362: 7358: 7355: 7351: 7345: 7342: 7340: 7337: 7335: 7332: 7330: 7327: 7326: 7324: 7320: 7315: 7305: 7302: 7300: 7297: 7295: 7292: 7290: 7287: 7285: 7282: 7280: 7277: 7275: 7272: 7270: 7267: 7265: 7262: 7260: 7257: 7255: 7252: 7251: 7249: 7247: 7243: 7239: 7232: 7227: 7225: 7220: 7218: 7213: 7212: 7209: 7201: 7197: 7193: 7189: 7185: 7180: 7175: 7170: 7165: 7161: 7157: 7153: 7148: 7144: 7143:IEEE Spectrum 7140: 7135: 7131: 7130: 7125: 7120: 7116: 7112: 7107: 7102: 7098: 7094: 7090: 7085: 7081: 7079:9783527681594 7075: 7071: 7067: 7063: 7057: 7053: 7049: 7045: 7041: 7037: 7033: 7032: 7031:Physics World 7024: 7019: 7015: 7011: 7007: 7003: 6999: 6995: 6990: 6985: 6981: 6977: 6976: 6970: 6969: 6965: 6957: 6953: 6949: 6945: 6941: 6937: 6932: 6927: 6923: 6919: 6912: 6909: 6898: 6894: 6888: 6885: 6879: 6874: 6870: 6866: 6862: 6855: 6853: 6849: 6845: 6840: 6834: 6830: 6825: 6820: 6816: 6812: 6808: 6804: 6800: 6793: 6790: 6785: 6781: 6777: 6773: 6769: 6765: 6761: 6757: 6752: 6747: 6743: 6739: 6690: 6687: 6682: 6678: 6673: 6668: 6664: 6660: 6655: 6650: 6646: 6642: 6638: 6610: 6607: 6602: 6598: 6594: 6590: 6586: 6582: 6577: 6572: 6569:(5): 053114. 6568: 6564: 6536: 6533: 6528: 6524: 6520: 6516: 6512: 6508: 6504: 6500: 6495: 6490: 6486: 6482: 6453: 6450: 6445: 6441: 6437: 6433: 6428: 6423: 6419: 6415: 6411: 6407: 6403: 6396: 6394: 6390: 6378: 6374: 6368: 6366: 6364: 6360: 6355: 6351: 6347: 6343: 6339: 6335: 6332:(10): 17049. 6331: 6327: 6320: 6318: 6316: 6312: 6307: 6303: 6299: 6295: 6291: 6287: 6283: 6279: 6274: 6269: 6265: 6261: 6254: 6252: 6248: 6243: 6239: 6235: 6231: 6227: 6223: 6219: 6215: 6211: 6207: 6202: 6197: 6193: 6189: 6161: 6158: 6153: 6149: 6145: 6141: 6137: 6133: 6129: 6125: 6118: 6115: 6110: 6106: 6102: 6098: 6094: 6090: 6086: 6082: 6033: 6030: 6025: 6019: 6011: 6007: 6003: 5999: 5995: 5991: 5987: 5983: 5978: 5973: 5969: 5965: 5957: 5954: 5949: 5945: 5941: 5937: 5933: 5929: 5925: 5921: 5917: 5913: 5908: 5903: 5900:(9): 4711–4. 5899: 5895: 5867: 5864: 5854: 5850: 5846: 5845: 5837: 5834: 5829: 5825: 5821: 5817: 5813: 5809: 5805: 5798: 5795: 5790: 5786: 5781: 5776: 5772: 5768: 5764: 5760: 5756: 5752: 5748: 5741: 5738: 5733: 5729: 5724: 5719: 5715: 5711: 5707: 5703: 5699: 5695: 5691: 5687: 5683: 5676: 5673: 5668: 5664: 5660: 5656: 5652: 5648: 5644: 5640: 5636: 5632: 5627: 5622: 5618: 5614: 5606: 5603: 5598: 5594: 5590: 5586: 5582: 5578: 5573: 5568: 5564: 5560: 5553: 5550: 5545: 5541: 5537: 5533: 5529: 5525: 5521: 5517: 5510: 5507: 5502: 5498: 5494: 5490: 5486: 5482: 5478: 5474: 5467: 5464: 5459: 5455: 5451: 5447: 5443: 5439: 5435: 5431: 5426: 5421: 5417: 5413: 5405: 5402: 5397: 5393: 5389: 5385: 5381: 5377: 5373: 5369: 5364: 5359: 5356:(9): 094516. 5355: 5351: 5344: 5341: 5336: 5332: 5328: 5324: 5320: 5316: 5312: 5308: 5303: 5298: 5295:(9): 096407. 5294: 5290: 5286: 5279: 5276: 5271: 5267: 5262: 5257: 5253: 5249: 5244: 5239: 5235: 5231: 5227: 5220: 5218: 5216: 5212: 5207: 5203: 5199: 5195: 5191: 5187: 5183: 5179: 5174: 5169: 5166:(3): 033429. 5165: 5161: 5157: 5150: 5147: 5142: 5138: 5134: 5130: 5126: 5122: 5118: 5114: 5109: 5104: 5101:(1): 012201. 5100: 5096: 5092: 5085: 5082: 5077: 5073: 5069: 5065: 5061: 5057: 5052: 5047: 5043: 5039: 5035: 5028: 5025: 5020: 5016: 5012: 5008: 5004: 5000: 4996: 4992: 4987: 4982: 4978: 4974: 4970: 4963: 4960: 4955: 4951: 4947: 4943: 4939: 4935: 4931: 4927: 4922: 4917: 4913: 4909: 4905: 4898: 4895: 4890: 4886: 4882: 4878: 4874: 4870: 4866: 4862: 4857: 4852: 4848: 4844: 4836: 4833: 4822: 4818: 4812: 4809: 4804: 4800: 4796: 4792: 4788: 4784: 4780: 4776: 4772: 4768: 4763: 4758: 4754: 4750: 4746: 4742: 4735: 4732: 4727: 4723: 4719: 4715: 4710: 4705: 4701: 4697: 4693: 4689: 4685: 4678: 4675: 4670: 4666: 4661: 4656: 4652: 4648: 4643: 4638: 4634: 4630: 4626: 4619: 4616: 4611: 4607: 4603: 4599: 4595: 4591: 4587: 4583: 4579: 4575: 4568: 4565: 4560: 4556: 4552: 4548: 4544: 4540: 4536: 4532: 4528: 4524: 4519: 4514: 4510: 4506: 4499: 4496: 4491: 4487: 4483: 4479: 4475: 4471: 4467: 4463: 4458: 4453: 4449: 4445: 4438: 4435: 4430: 4426: 4421: 4416: 4412: 4408: 4403: 4398: 4394: 4390: 4386: 4367: 4365: 4361: 4356: 4352: 4348: 4344: 4340: 4336: 4331: 4326: 4322: 4318: 4310: 4307: 4302: 4298: 4294: 4290: 4286: 4282: 4277: 4272: 4268: 4264: 4236: 4233: 4228: 4224: 4220: 4216: 4212: 4208: 4204: 4200: 4196: 4147: 4144: 4139: 4135: 4131: 4127: 4123: 4119: 4115: 4111: 4106: 4101: 4097: 4093: 4085: 4082: 4077: 4073: 4069: 4065: 4061: 4057: 4053: 4049: 4044: 4039: 4035: 4031: 4024: 4021: 4016: 4012: 4007: 4002: 3998: 3994: 3990: 3986: 3982: 3978: 3973: 3968: 3964: 3960: 3956: 3928: 3925: 3920: 3916: 3912: 3908: 3904: 3900: 3895: 3890: 3886: 3882: 3879:(9): 1162–5. 3878: 3874: 3870: 3863: 3861: 3859: 3857: 3853: 3849: 3843: 3839: 3835: 3831: 3824: 3821: 3816: 3812: 3808: 3804: 3800: 3796: 3792: 3788: 3784: 3780: 3775: 3770: 3766: 3762: 3758: 3751: 3748: 3743: 3739: 3735: 3731: 3727: 3723: 3719: 3715: 3711: 3707: 3702: 3697: 3693: 3689: 3685: 3678: 3676: 3674: 3670: 3665: 3661: 3657: 3653: 3649: 3645: 3640: 3635: 3631: 3627: 3623: 3616: 3613: 3608: 3604: 3600: 3596: 3592: 3588: 3584: 3580: 3576: 3572: 3567: 3562: 3558: 3554: 3547: 3544: 3539: 3535: 3531: 3527: 3523: 3519: 3515: 3511: 3506: 3501: 3497: 3493: 3486: 3483: 3478: 3474: 3470: 3466: 3462: 3458: 3451: 3448: 3443: 3439: 3435: 3431: 3427: 3423: 3419: 3415: 3410: 3405: 3401: 3397: 3393: 3386: 3383: 3378: 3374: 3370: 3366: 3362: 3358: 3354: 3350: 3345: 3340: 3336: 3332: 3325: 3323: 3319: 3314: 3310: 3306: 3302: 3298: 3294: 3289: 3284: 3281:(4): 045302. 3280: 3276: 3269: 3266: 3261: 3257: 3253: 3249: 3245: 3241: 3240: 3239:Physics World 3232: 3225: 3222: 3217: 3213: 3209: 3205: 3201: 3197: 3193: 3189: 3184: 3179: 3175: 3171: 3164: 3161: 3156: 3152: 3148: 3144: 3140: 3136: 3131: 3126: 3123:(4): 045302. 3122: 3118: 3111: 3108: 3103: 3099: 3095: 3091: 3087: 3083: 3079: 3075: 3070: 3065: 3061: 3057: 3050: 3047: 3042: 3038: 3034: 3030: 3025: 3020: 3016: 3012: 3005: 3002: 2997: 2993: 2989: 2985: 2981: 2977: 2973: 2969: 2965: 2961: 2956: 2951: 2947: 2943: 2939: 2932: 2929: 2924: 2920: 2916: 2912: 2908: 2904: 2900: 2896: 2891: 2886: 2882: 2878: 2874: 2867: 2864: 2859: 2855: 2851: 2847: 2843: 2839: 2835: 2831: 2826: 2821: 2817: 2813: 2809: 2802: 2799: 2794: 2790: 2786: 2782: 2778: 2774: 2770: 2766: 2761: 2756: 2752: 2748: 2744: 2737: 2734: 2729: 2725: 2721: 2717: 2713: 2709: 2705: 2701: 2697: 2693: 2688: 2683: 2679: 2675: 2671: 2664: 2662: 2660: 2656: 2651: 2647: 2643: 2639: 2635: 2631: 2627: 2623: 2619: 2612: 2610: 2606: 2602:(4): 178–181. 2601: 2597: 2593: 2586: 2584: 2580: 2575: 2571: 2567: 2563: 2559: 2555: 2551: 2547: 2542: 2537: 2533: 2529: 2525: 2518: 2515: 2510: 2506: 2502: 2498: 2494: 2490: 2486: 2482: 2478: 2474: 2470: 2463: 2460: 2455: 2451: 2447: 2443: 2439: 2435: 2431: 2427: 2423: 2419: 2414: 2409: 2405: 2401: 2397: 2390: 2387: 2382: 2378: 2374: 2370: 2366: 2362: 2358: 2354: 2349: 2344: 2340: 2336: 2332: 2325: 2322: 2317: 2313: 2309: 2305: 2301: 2297: 2293: 2289: 2284: 2279: 2275: 2271: 2267: 2260: 2258: 2256: 2254: 2252: 2248: 2243: 2239: 2235: 2231: 2227: 2223: 2218: 2213: 2209: 2205: 2201: 2194: 2192: 2188: 2183: 2179: 2175: 2171: 2167: 2163: 2159: 2155: 2150: 2145: 2141: 2137: 2133: 2126: 2124: 2120: 2115: 2111: 2106: 2101: 2097: 2093: 2089: 2085: 2081: 2077: 2073: 2066: 2063: 2058: 2054: 2050: 2046: 2042: 2038: 2034: 2030: 2025: 2020: 2016: 2012: 2011: 1999: 1996: 1991: 1987: 1983: 1979: 1975: 1971: 1966: 1961: 1957: 1953: 1946: 1943: 1938: 1934: 1930: 1926: 1922: 1918: 1914: 1910: 1906: 1902: 1898: 1894: 1887: 1884: 1878: 1874: 1871: 1869: 1866: 1864: 1861: 1859: 1856: 1854: 1851: 1849: 1846: 1844: 1841: 1839: 1836: 1834: 1831: 1830: 1826: 1824: 1822: 1813: 1811: 1809: 1805: 1804:anti-commutes 1801: 1797: 1792: 1787: 1784: 1779: 1777: 1776:vector bundle 1772: 1770: 1766: 1761: 1753: 1751: 1735: 1715: 1708: 1705: 1702: 1689: 1688: 1684: 1681: 1678: 1656: 1655: 1651: 1648: 1645: 1642: 1641: 1637: 1634: 1631: 1618: 1617: 1613: 1610: 1607: 1604: 1603: 1599: 1596: 1593: 1590: 1589: 1585: 1582: 1579: 1576: 1575: 1571: 1568: 1565: 1552: 1551: 1547: 1544: 1541: 1538: 1537: 1533: 1530: 1527: 1524: 1523: 1499: 1476: 1453: 1450: 1449: 1443: 1421:) or p-type ( 1376: 1332: 1255: 1252: 1230: 1213: 1139: 1131: 1129: 1080: 1078: 1075: 1044: 1040: 1036: 1034: 1029: 1006: 1004: 999: 995: 990: 988: 984: 980: 976: 972: 967: 966: 962: 960: 956: 947: 943: 942: 938: 934: 932: 924: 922: 920: 892: 884: 882: 880: 876: 872: 868: 865:based on the 864: 860: 855: 853: 835: 798: 794: 790: 773: 758: 754: 738: 708: 679: 650: 621: 606: 602: 597: 589: 587: 585: 576: 574: 572: 568: 564: 559: 557: 553: 548: 546: 542: 538: 534: 530: 525: 510: 508: 504: 499: 495: 492:(ARPES). and 491: 487: 483: 479: 475: 470: 468: 464: 452: 448: 447:surface state 436: 432: 428: 416: 414: 410: 402: 400: 398: 394: 389: 385: 368: 354:in 2006. The 353: 349: 345: 341: 336: 334: 330: 326: 322: 318: 309: 307: 305: 301: 297: 292: 290: 286: 281: 243: 228: 224: 220: 219:U(1) symmetry 216: 212: 207: 205: 201: 197: 196:phase diagram 193: 192:adiabatically 188: 186: 181: 179: 175: 171: 167: 163: 159: 154: 152: 148: 144: 136: 132: 129:An idealized 127: 106: 89: 85: 77: 74: 66: 63:for details. 62: 57: 55: 51: 48: 43:This article 41: 37: 32: 31: 19: 7781: 7769: 7757: 7745: 7663:Pines' demon 7513: 7402:Kondo effect 7304:Time crystal 7199: 7159: 7155: 7142: 7127: 7096: 7092: 7061: 7038:(2): 32–36. 7035: 7029: 6979: 6973: 6921: 6917: 6911: 6900:. Retrieved 6896: 6887: 6868: 6864: 6806: 6802: 6792: 6741: 6738:Nano Letters 6737: 6689: 6644: 6640: 6609: 6566: 6562: 6535: 6487:(1): 224–9. 6484: 6480: 6452: 6409: 6405: 6381:. Retrieved 6379:. 2015-06-29 6376: 6329: 6325: 6263: 6259: 6191: 6187: 6160: 6127: 6123: 6117: 6084: 6080: 6032: 6018:cite journal 5967: 5964:Nano Letters 5963: 5956: 5897: 5894:Nano Letters 5893: 5866: 5856:, retrieved 5843: 5836: 5811: 5807: 5797: 5754: 5750: 5740: 5689: 5685: 5675: 5616: 5612: 5605: 5562: 5558: 5552: 5519: 5516:Phys. Rev. B 5515: 5509: 5476: 5472: 5466: 5415: 5411: 5404: 5353: 5349: 5343: 5292: 5288: 5278: 5233: 5229: 5163: 5159: 5149: 5098: 5094: 5084: 5041: 5037: 5027: 4976: 4972: 4962: 4911: 4907: 4897: 4846: 4842: 4835: 4824:. Retrieved 4821:Science News 4820: 4811: 4752: 4748: 4734: 4691: 4687: 4677: 4632: 4628: 4618: 4577: 4573: 4567: 4508: 4504: 4498: 4447: 4443: 4437: 4392: 4388: 4373:"Sn-doped Bi 4320: 4316: 4309: 4269:(5): 57006. 4266: 4262: 4235: 4202: 4198: 4146: 4098:(7): 546–9. 4095: 4091: 4084: 4036:(7): 541–5. 4033: 4029: 4023: 3965:(1): 27483. 3962: 3958: 3927: 3876: 3872: 3829: 3823: 3764: 3760: 3750: 3691: 3687: 3629: 3625: 3615: 3556: 3552: 3546: 3495: 3491: 3485: 3460: 3456: 3450: 3402:(9): 970–4. 3399: 3395: 3385: 3337:(1): 55–78. 3334: 3330: 3278: 3274: 3268: 3246:(2): 32–36. 3243: 3237: 3224: 3173: 3169: 3163: 3120: 3116: 3110: 3059: 3055: 3049: 3014: 3010: 3004: 2945: 2941: 2931: 2880: 2876: 2866: 2815: 2811: 2801: 2750: 2746: 2736: 2677: 2673: 2628:(2): 93–96. 2625: 2621: 2599: 2596:JETP Letters 2595: 2531: 2527: 2517: 2476: 2472: 2462: 2403: 2399: 2389: 2338: 2334: 2324: 2276:(1): 22–30. 2273: 2269: 2207: 2203: 2139: 2135: 2105:10754/315777 2079: 2075: 2065: 2014: 2008: 1998: 1955: 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