671:
983:, which has a radius larger than the lattice spacing. Small effective mass of electrons that is typical of semiconductors also favors large exciton radii. As a result, the effect of the lattice potential can be incorporated into the effective masses of the electron and hole. Likewise, because of the lower masses and the screened Coulomb interaction, the binding energy is usually much less than that of a hydrogen atom, typically on the order of
58:
39:
684:
5521:
2896:, called excitonium, is predicted to be the ground state. Some evidence of excitonium has existed since the 1970s but has often been difficult to discern from a Peierls phase. Exciton condensates have allegedly been seen in a double quantum well systems. In 2017 Kogar et al. found "compelling evidence" for observed excitons condensing in the three-dimensional semimetal 1
31:
2916:
contrast to ordinary (spatially direct), these spatially indirect excitons can have large spatial separation between the electron and hole, and thus possess a much longer lifetime. This is often used to cool excitons to very low temperatures in order to study Bose–Einstein condensation (or rather its two-dimensional analog).
798:. In his model the electron and the hole bound by the coulomb interaction are located either on the same or on the nearest neighbouring sites of the lattice, but the exciton as a composite quasi-particle is able to travel through the lattice without any net transfer of charge, which lead to many propositions for
2512:
of excitons. This means that spectral lines of free excitons and wide bands of self-trapped excitons can be seen simultaneously in absorption and luminescence spectra. While the self-trapped states are of lattice-spacing scale, the barrier has typically much larger scale. Indeed, its spatial scale is
2478:
Excitons are lowest excited states of the electronic subsystem of pure crystals. Impurities can bind excitons, and when the bound state is shallow, the oscillator strength for producing bound excitons is so high that impurity absorption can compete with intrinsic exciton absorption even at rather low
2465:
The hallmark of molecular excitons in organic molecular crystals are doublets and/or triplets of exciton absorption bands strongly polarized along crystallographic axes. In these crystals an elementary cell includes several molecules sitting in symmetrically identical positions, which results in the
2915:
Normally, excitons in a semiconductor have a very short lifetime due to the close proximity of the electron and hole. However, by placing the electron and hole in spatially separated quantum wells with an insulating barrier layer in between so called 'spatially indirect' excitons can be created. In
901:
exciton is invoked where the hole in a valence band is correlated with the Fermi sea of conduction electrons. In that case no bound state in a strict sense is formed, but the
Coulomb interaction leads to a significant enhancement of absorption in the vicinity of the fundamental absorption edge also
863:
Excitons give rise to spectrally narrow lines in optical absorption, reflection, transmission and luminescence spectra with the energies below the free-particle band gap of an insulator or a semiconductor. Exciton binding energy and radius can be extracted from optical absorption measurements in
2821:, the barriers are basically low. Therefore, free excitons can be seen in crystals with strong exciton-phonon coupling only in pure samples and at low temperatures. Coexistence of free and self-trapped excitons was observed in rare-gas solids, alkali-halides, and in molecular crystal of pyrene.
2023:
Monolayers of a transition metal dichalcogenide (TMD) are a good and cutting-edge example where excitons play a major role. In particular, in these systems, they exhibit a bounding energy of the order of 0.5 eV with a
Coulomb attraction between the hole and the electrons stronger than in other
2496:
results in dressing excitons with a dense cloud of virtual phonons which strongly suppresses the ability of excitons to move across the crystal. In simpler terms, this means a local deformation of the crystal lattice around the exciton. Self-trapping can be achieved only if the energy of this
1181:
4271:
Kogar, Anshul; Rak, Melinda S; Vig, Sean; Husain, Ali A; Flicker, Felix; Joe, Young Il; Venema, Luc; MacDougall, Greg J.; Chiang, Tai C.; Fradkin, Eduardo; Van Wezel, Jasper; Abbamonte, Peter (2017). "Signatures of exciton condensation in a transition metal dichalcogenide".
2014:
the exciton radius. For this potential, no general expression for the exciton energies may be found. One must instead turn to numerical procedures, and it is precisely this potential that gives rise to the nonhydrogenic
Rydberg series of the energies in 2D semiconductors.
4333:
Merkl, P.; Mooshammer, F.; Steinleitner, P.; Girnghuber, A.; Lin, K.-Q.; Nagler, P.; Holler, J.; SchĂĽller, C.; Lupton, J. M.; Korn, T.; Ovesen, S.; Brem, S.; Malic, E.; Huber, R. (2019). "Ultrafast transition between exciton phases in van der Waals heterostructures".
3822:
Madéo, Julien; Man, Michael K. L.; Sahoo, Chakradhar; Campbell, Marshall; Pareek, Vivek; Wong, E. Laine; Al-Mahboob, Abdullah; Chan, Nicholas S.; Karmakar, Arka; Mariserla, Bala Murali
Krishna; Li, Xiaoqin; Heinz, Tony F.; Cao, Ting; Dani, Keshav M. (2020-12-04).
1013:, excitons have both Wannier–Mott and Frenkel character. This is due to the nature of the Coulomb interaction between electrons and holes in one-dimension. The dielectric function of the nanotube itself is large enough to allow for the spatial extent of the
1480:
3748:
Baldini, Edoardo; Chiodo, Letizia; Dominguez, Adriel; Palummo, Maurizia; Moser, Simon; Yazdi-Rizi, Meghdad; Aubock, Gerald; Mallett, Benjamin P P; Berger, Helmuth; Magrez, Arnaud; Bernhard, Christian; Grioni, Marco; Rubio, Angel; Chergui, Majed (2017).
2491:
In crystals, excitons interact with phonons, the lattice vibrations. If this coupling is weak as in typical semiconductors such as GaAs or Si, excitons are scattered by phonons. However, when the coupling is strong, excitons can be self-trapped.
851:
of the electron and hole in a crystal are typically smaller compared to that of free electrons. Wannier-Mott excitons with binding energies ranging from a few to hundreds of meV, depending on the crystal, occur in many semiconductors including
2363:. In molecular physics, CT excitons form when the electron and the hole occupy adjacent molecules. They occur primarily in organic and molecular crystals; in this case, unlike Frenkel and Wannier excitons, CT excitons display a static
914:, the Coulomb interaction between an electron and a hole may be strong and the excitons thus tend to be small, of the same order as the size of the unit cell. Molecular excitons may even be entirely located on the same molecule, as in
823:(ii) the large radius excitons are called Wannier-Mott excitons, for which the relative motion of electron and hole in the crystal covers many unit cells. Wannier-Mott excitons are considered as hydrogen-like quasiparticles. The
1619:
in the direction perpendicular to the plane of the material. The reduced dimensionality of the system has an effect on the binding energies and radii of
Wannier excitons. In fact, excitonic effects are enhanced in such systems.
2671:
are large, and then the spatial size of the barrier is large compared with the lattice spacing. Transforming a free exciton state into a self-trapped one proceeds as a collective tunneling of coupled exciton-lattice system (an
1708:
1031:
two-photon experiments have shown. At cryogenic temperatures, many higher excitonic levels can be observed approaching the edge of the band, forming a series of spectral absorption lines that are in principle similar to
2117:
2254:
1058:
1887:
2479:
impurity concentrations. This phenomenon is generic and applicable both to the large radius (Wannier–Mott) excitons and molecular (Frenkel) excitons. Hence, excitons bound to impurities and defects possess
1340:
958:
transitions are in principle forbidden by symmetry, they become weakly-allowed in a crystal when the symmetry is broken by structural relaxations or other effects. Absorption of a photon resonant with a
886:
vector of the host lattice. The exciton energy also depends on the respective orientation of the electron and hole spins, whether they are parallel or anti-parallel. The spins are coupled by the
808:(i) The small radius excitons, or Frenkel excitons, where the electron-hole relative distance is restricted to one or only a few nearest neighbour unit cells. Frenkel excitons typically occur in
2504:
but with three essential differences. First, self-trapped exciton states are always of a small radius, of the order of lattice constant, due to their electric neutrality. Second, there exists a
2759:
2569:
2442:, and since they are found within the same molecular orbital manifold, the electron-hole state is said to be bound. Molecular excitons typically have characteristic lifetimes on the order of
2379:. Irrespective of the origin, the concept of CT exciton is always related to a transfer of charge from one atomic site to another, thus spreading the wave-function over a few lattice sites.
3257:
839:
in a crystal is much smaller and the exciton's size (radius) is much larger. This is mainly because of two effects: (a) Coulomb forces are screened in a crystal, which is expressed as a
764:, some metals, but also in certain atoms, molecules and liquids. The exciton is regarded as an elementary excitation that can transport energy without transporting net electric charge.
1375:
1027:
Often more than one band can be chosen as source for the electron and the hole, leading to different types of excitons in the same material. Even high-lying bands can be effective as
2466:
level degeneracy that is lifted by intermolecular interaction. As a result, absorption bands are polarized along the symmetry axes of the crystal. Such multiplets were discovered by
2458:) from one molecule to another. The process is strongly dependent on intermolecular distance between the species in solution, and so the process has found application in sensing and
998:. Wannier–Mott excitons are typically found in semiconductor crystals with small energy gaps and high dielectric constants, but have also been identified in liquids, such as liquid
4395:
High, A. A.; Leonard, J. R.; Hammack, A. T.; Fogler, M. M.; Butov, L. V.; Kavokin, A. V.; Campman, K. L.; Gossard, A. C. (2012). "Spontaneous coherence in a cold exciton gas".
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2147:
1568:
1237:
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to extend over a few to several nanometers along the tube axis, while poor screening in the vacuum or dielectric environment outside of the nanotube allows for large (0.4 to
1944:
3290:
Chernikov, Alexey; Berkelbach, Timothy C.; Hill, Heather M.; Rigosi, Albert; Li, Yilei; Aslan, Ozgur Burak; Reichman, David R.; Hybertsen, Mark S.; Heinz, Tony F. (2014).
1510:
715:
1206:
42:
Wannier–Mott exciton, bound electron-hole pair that is not localized at a crystal position. This figure schematically shows diffusion of the exciton across the lattice.
2799:
2669:
2629:
2609:
1992:
2701:
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1917:
1367:
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4178:
M. Furukawa, Ken-ichi Mizuno, A. Matsui, N. Tamai and I. Yamazaiu, Branching of
Exciton Relaxation to the Free and Self-Trapped Exciton States, Chemical Physics
2819:
2779:
2649:
2589:
2012:
1968:
2851:
The existence of exciton states may be inferred from the absorption of light associated with their excitation. Typically, excitons are observed just below the
3595:
783:
between the electron and the hole, a bound state is formed, akin to that of the electron and proton in a hydrogen atom or the electron and positron in
5194:
1629:
4192:
5432:
2042:
which exhibit quantum confinement effects and hence behave as quantum dots (also called 0-dimensional semiconductors), excitonic radii are given by
775:
in the valence band. Here 'hole' represents the unoccupied quantum mechanical electron state with a positive charge, an analogue in crystal of a
708:
4043:
M. Ueta, H. Kanzaki, K. Kobayashi, Y. Toyozawa, and E. Hanamura. Excitonic
Processes in Solids, Springer Series in Solid State Sciences, Vol.
2399:
Dark excitons are those where the electrons have a different momentum from the holes to which they are bound that is they are in an optically
2048:
670:
4141:
4114:
3654:
1176:{\displaystyle E(n)=-{\frac {\left({\frac {\mu }{m_{0}\varepsilon _{r}^{2}}}{\text{Ry}}\right)}{n^{2}}}\equiv -{\frac {R_{\text{X}}}{n^{2}}}}
4056:
E. I. Rashba, "Theory of Strong
Interaction of Electron Excitations with Lattice Vibrations in Molecular Crystals", Optika i Spektroskopiya
2882:
2391:
to occur, where the hole is inside the solid and the electron is in the vacuum. These electron-hole pairs can only move along the surface.
2156:
930:. Frenkel excitons are typically found in alkali halide crystals and in organic molecular crystals composed of aromatic molecules, such as
848:
817:
2451:
3041:
Monique
Combescot and Shiue-Yuan Shiau, "Excitons and Cooper Pairs: Two Composite Bosons in Many-Body Physics", Oxford University Press.
2454:) whereby if a molecular exciton has proper energetic matching to a second molecule's spectral absorbance, then an exciton may transfer (
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3971:
3271:
2344:
1720:
1242:
5330:
3687:
Ellis, D. S.; Hill, J. P.; Wakimoto, S.; Birgeneau, R. J.; Casa, D.; Gog, T.; Kim, Young-June (2008). "Charge-transfer exciton in La
3046:
701:
688:
794:
in 1931, when he described the excitation of an atomic lattice considering what is now called the tight-binding description of the
5411:
874:) describing free propagation of the electron-hole pair as a composite particle in the crystalline lattice in agreement with the
4086:
4030:
N. Schwentner, E.-E. Koch, and J. Jortner, Electronic excitations in condensed rare gases, Springer tracts in modern physics,
967:
transition leads to the creation of an electron-hole pair on a single atomic site, which can be treated as a
Frenkel exciton.
463:
3195:
Kazimierczuk, T.; Fröhlich, D.; Scheel, S.; Stolz, H.; Bayer, M. (2014). "Giant Rydberg excitons in the copper oxide Cu2O".
2497:
deformation can compete with the width of the exciton band. Hence, it should be of atomic scale, of about an electron volt.
34:
Frenkel exciton, bound electron-hole pair where the hole is localized at a position in the crystal represented by black dots
4136:. Proceedings of the International School of Physics "Enrico Fermi". Amsterdam ; New York: North-Holland. Course 96.
2375:
orbitals. Notable examples include the lowest-energy excitons in correlated cuprates or the two-dimensional exciton of TiO
2024:
traditional quantum wells. As a result, optical excitonic peaks are present in these materials even at room temperatures.
2893:
118:
5427:
4156:
I. Ya. Fugol', "Free and self-trapped excitons in cryocrystals: kinetics and relaxation processes." Advances in Physics
2706:
2516:
638:
4104:
4169:
Ch. B. Lushchik, in "Excitons," edited by E. I. Rashba, and M. D. Sturge, (North Holland, Amsterdam, 1982), p. 505.
643:
268:
5503:
2426:
to another molecular orbital, the resulting electronic excited state is also properly described as an exciton. An
771:
e.g., when a material absorbs a photon. Promoting the electron to the conduction band leaves a positively charged
4915:
2480:
2367:. CT excitons can also occur in transition metal oxides, where they involve an electron in the transition metal 3
1612:
1475:{\displaystyle r_{n}=\left({\frac {m_{0}\varepsilon _{r}a_{\text{H}}}{\mu }}\right)n^{2}\equiv a_{\text{X}}n^{2}}
533:
208:
3825:"Directly visualizing the momentum-forbidden dark excitons and their dynamics in atomically thin semiconductors"
2337:
1714:
In most 2D semiconductors, the Rytova–Keldysh form is a more accurate approximation to the exciton interaction
1033:
976:
528:
523:
49:
4733:
613:
3888:
3530:"Optical quantum confinement and photocatalytic properties in two-, one- and zero-dimensional nanostructures"
787:. Excitons are composite bosons since they are formed from two fermions which are the electron and the hole.
5545:
5471:
5106:
4467:
3263:
623:
218:
5406:
4743:
2985:"Exciton physics and device application of two-dimensional transition metal dichalcogenide semiconductors"
2508:
separating free and self-trapped states, hence, free excitons are metastable. Third, this barrier enables
2467:
2364:
813:
799:
608:
548:
518:
468:
188:
78:
2881:. If a large density of excitons is created in a material, they can interact with one another to form an
5493:
2150:
840:
809:
757:
648:
263:
248:
3111:"Magneto-optics of layered two-dimensional semiconductors and heterostructures: Progress and prospects"
2450:
emission. Molecular excitons have several interesting properties, one of which is energy transfer (see
2125:
1540:
1215:
4414:
4353:
4291:
4236:
3925:
3846:
3776:
3714:
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3455:
3370:
3313:
3214:
3169:
3132:
3083:
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2400:
1573:
887:
767:
An exciton can form when an electron from the valence band of a crystal is promoted in energy to the
238:
128:
1623:
For a simple screened Coulomb potential, the binding energies take the form of the 2D hydrogen atom
5508:
4491:
2930:
2901:
1947:
1922:
1616:
995:
911:
478:
288:
138:
5520:
3501:
Brus, Louis (1986). "Electronic wave functions in semiconductor clusters: experiment and theory".
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4404:
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4281:
4252:
4226:
3836:
3766:
3730:
3704:
3303:
3238:
3204:
3160:
Wannier, Gregory (1937). "The Structure of Electronic Excitation Levels in Insulating Crystals".
3122:
3024:
2996:
2839:
1189:
883:
618:
593:
341:
332:
4069:
E. I. Rashba, Self-trapping of excitons, in: Excitons (North-Holland, Amsterdam, 1982), p. 547.
1044:
In a bulk semiconductor, a Wannier exciton has an energy and radius associated with it, called
5488:
5401:
4880:
4625:
4552:
4430:
4369:
4307:
4217:
Eisenstein, J. P. (January 10, 2014). "Exciton Condensation in Bilayer Quantum Hall Systems".
4137:
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3559:
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3042:
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statistics in the low-density limit. In some systems, where the interactions are repulsive, a
2863:
2423:
2404:
1971:
588:
433:
323:
243:
4248:
3671:
2784:
2654:
2614:
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1977:
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3794:
3784:
3722:
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3567:
3549:
3510:
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3378:
3321:
3222:
3177:
3140:
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3006:
2329:
1520:
1209:
1010:
753:
737:
293:
258:
253:
213:
183:
153:
113:
73:
4133:
Excited-state spectroscopy in solids: Varenna on Lake Como, Villa Monastero, 9–19 July 1985
3968:
2679:
2446:, after which the ground electronic state is restored and the molecule undergoes photon or
2286:
2259:
1895:
1345:
856:
O, GaAs, other III-V and II-VI semiconductors, transition metal dichalcogenides such as MoS
5550:
5466:
5391:
5375:
5315:
4725:
4542:
4090:
3975:
2945:
2873:
Provided the interaction is attractive, an exciton can bind with other excitons to form a
991:
768:
603:
553:
423:
178:
90:
2470:
and their genesis was proposed by Alexander Davydov. It is known as 'Davydov splitting'.
4418:
4357:
4295:
4240:
3929:
3850:
3780:
3718:
3545:
3459:
3374:
3317:
3218:
3173:
3136:
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2403:
which prevents them from photon absorption and therefore to reach their state they need
5525:
5439:
5396:
5132:
4920:
4693:
4615:
4610:
4532:
3799:
3750:
3572:
3529:
3478:
3443:
2845:
2830:
2804:
2764:
2634:
2574:
2419:, or molecule, if the excitation is wandering from one cell of the lattice to another.
2348:
2333:
1997:
1953:
1523:, we have relative permittivity of 12.8 and effective electron and hole masses as 0.067
891:
836:
795:
675:
653:
633:
628:
583:
503:
438:
336:
223:
68:
57:
38:
3824:
2703:
is large, tunneling can be described by a continuum theory. The height of the barrier
2422:
When a molecule absorbs a quantum of energy that corresponds to a transition from one
5539:
5483:
5335:
5302:
5094:
5064:
4996:
4855:
4635:
4562:
4547:
4381:
4319:
4083:
3734:
3423:
Keldysh, LV (1979). "Coulomb interaction in thin semiconductor and semimetal films".
3028:
2435:
2323:
2039:
1014:
979:
tends to reduce the Coulomb interaction between electrons and holes. The result is a
927:
923:
875:
832:
791:
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761:
749:
733:
558:
364:
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327:
228:
148:
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3358:
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5011:
5001:
4991:
4752:
4703:
4645:
4567:
4522:
4442:
3950:
A. Prikhotjko, Absorption Spectra of Crystals at Low Temperatures, J. Physics USSR
3326:
3291:
3242:
2631:
is the characteristic frequency of optical phonons. Excitons are self-trapped when
898:
824:
578:
568:
538:
498:
493:
473:
318:
298:
158:
3913:
3359:"Analytic solution of a two-dimensional hydrogen atom. I. Nonrelativistic theory"
5476:
5244:
5147:
5142:
5059:
5054:
4984:
4938:
4895:
4860:
4819:
4711:
4675:
4537:
4131:
3404:
Rytova, N S. (1967). "The screened potential of a point charge in a thin film".
2834:
2443:
2311:
2033:
1703:{\displaystyle E(n)=-{\frac {R_{\text{X}}}{\left(n-{\tfrac {1}{2}}\right)^{2}}}}
1513:
1028:
784:
741:
598:
573:
543:
488:
483:
415:
3789:
3726:
3607:
3444:"Model dielectric function for 2D semiconductors including substrate screening"
5218:
5112:
5102:
5084:
4974:
4875:
4810:
4527:
4365:
3011:
2984:
931:
868:
828:
508:
350:
143:
3937:
3866:
3563:
3382:
3335:
3074:
Frenkel, J. (1931). "On the Transformation of light into Heat in Solids. I".
3020:
2407:. They can even outnumber normal bright excitons formed by absorption alone.
975:
In semiconductors, the dielectric constant is generally large. Consequently,
5360:
5350:
5320:
5213:
5179:
5172:
5049:
5039:
5034:
5006:
4774:
4557:
4303:
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2431:
935:
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563:
513:
386:
233:
133:
4434:
4373:
4311:
3874:
3808:
3581:
3487:
3343:
3234:
3181:
2415:
Alternatively, an exciton may be described as an excited state of an atom,
3390:
3095:
2848:), replacing the free electron-hole recombination at higher temperatures.
816:
with relatively narrow allowed energy bands and accordingly, rather heavy
5456:
5284:
5239:
5223:
5184:
5157:
4870:
4865:
4845:
4815:
4805:
4800:
4650:
4640:
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4620:
4595:
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4517:
3599:
3292:"Exciton Binding Energy and Nonhydrogenic Rydberg Series in MonolayerWS2"
2878:
2852:
2427:
776:
729:
123:
4426:
3554:
3514:
3226:
2112:{\displaystyle a_{\text{X}}={\frac {\varepsilon _{r}}{\mu /m_{0}}}a_{0}}
27:
Quasiparticle which is a bound state of an electron and an electron hole
17:
5365:
5355:
5279:
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5249:
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2935:
2925:
2501:
443:
428:
391:
382:
3596:"Scientists observe Hubbard exciton in strongly correlated insulators"
3468:
3145:
3110:
2343:
Hubbard excitons were observed for the first time in 2023 through the
5345:
5340:
4969:
4956:
4947:
4769:
4683:
4582:
4130:
Grassano, U. M.; Terzi, N.; SocietĂ italiana di fisica, eds. (1987).
2968:(Ed. by Seitz and Turnbul), New York, New York: Academic, v. 5, 1963.
2889:
2447:
2249:{\displaystyle \mu \equiv (m_{e}^{*}m_{h}^{*})/(m_{e}^{*}+m_{h}^{*})}
882:
and is typically parabolic for the wavevectors much smaller than the
396:
372:
103:
867:
The exciton as a quasiparticle is characterized by the momentum (or
4348:
4286:
3841:
3771:
3127:
3001:
30:
5370:
5310:
5162:
5021:
4900:
4840:
4795:
4688:
4666:
4509:
4409:
4231:
3709:
3308:
3209:
999:
401:
98:
37:
29:
2359:
An intermediate case between Frenkel and Wannier excitons is the
5137:
5069:
5029:
4605:
4600:
2500:
Self-trapping of excitons is similar to forming strong-coupling
1882:{\displaystyle V(r)=-{\frac {e^{2}}{8\epsilon _{0}r_{0}}}\left.}
946:
excitations in transition metal compounds with partially filled
772:
4456:
3442:
Trolle, Mads L.; Pedersen, Thomas G.; VĂ©niard, Valerie (2017).
1335:{\displaystyle \mu =(m_{e}^{*}m_{h}^{*})/(m_{e}^{*}+m_{h}^{*})}
2416:
2347:. Those particles have been obtained by applying a light to a
1994:
the average dielectric constant of the surrounding media, and
108:
2885:
liquid, a state observed in k-space indirect semiconductors.
4078:
S. I. Pekar, E. I. Rashba, V. I. Sheka, Soviet Physics JETP
4015:
Giant Oscillator Strengths Associated with Exciton Complexes
2019:
Example: excitons in transition metal dichalcogenides (TMDs)
897:
In metals and highly doped semiconductors a concept of the
3285:
3283:
2888:
Additionally, excitons are integer-spin particles obeying
3649:(2nd ed.). Cambridge University Press. p. 108.
2866:) is formed. These excitons are sometimes referred to as
831:, resulting in a series of energy states in analogy to a
3969:
http://ujp.bitp.kiev.ua/files/journals/53/si/53SI18p.pdf
2034:
Quantum dot § Quantum confinement in semiconductors
926:, has a typical binding energy on the order of 0.1 to 1
1676:
938:. Another example of Frenkel exciton includes on-site
805:
Excitons are often treated in the two limiting cases:
2807:
2787:
2767:
2709:
2682:
2657:
2637:
2617:
2597:
2577:
2519:
2289:
2262:
2159:
2128:
2051:
2000:
1980:
1956:
1925:
1898:
1723:
1632:
1576:
1543:
1491:
1378:
1369:
is the electron mass. Concerning the radius, we have
1348:
1245:
1218:
1192:
1061:
5420:
5384:
5301:
5262:
5232:
5206:
5193:
5125:
5093:
5020:
4955:
4946:
4937:
4833:
4788:
4760:
4751:
4742:
4724:
4702:
4674:
4665:
4581:
4508:
4499:
4490:
3673:
The Photophysics Behind Photovoltaics and Photonics
4084:http://www.jetp.ac.ru/cgi-bin/dn/e_049_01_0129.pdf
3695:probed with resonant inelastic x-ray scattering".
2813:
2793:
2773:
2754:{\displaystyle W\sim \omega ^{4}/m^{3}\gamma ^{4}}
2753:
2695:
2663:
2643:
2623:
2603:
2583:
2564:{\displaystyle r_{b}\sim m\gamma ^{2}/\omega ^{2}}
2563:
2328:Hubbard excitons are linked to electrons not by a
2302:
2275:
2248:
2141:
2111:
2006:
1986:
1962:
1938:
1911:
1881:
1702:
1595:
1562:
1504:
1474:
1361:
1342:is the reduced mass of the electron and hole, and
1334:
1231:
1200:
1175:
2256:is the reduced mass of the electron-hole system,
3893:Okinawa Institute of Science and Technology OIST
3628:: CS1 maint: bot: original URL status unknown (
3610:. Archived from the original on October 11, 2023
3262:. Oxford Master Series in Physics (2 ed.).
3063:(2nd ed.). Oxford Master Series in Physics.
2858:When excitons interact with photons a so-called
2336:. Their name derives by the English physicist
902:known as the Mahan or Fermi-edge singularity.
790:The concept of excitons was first proposed by
4468:
4000:V. L. Broude, E. I. Rashba, and E. F. Sheka,
2611:is the exciton-phonon coupling constant, and
709:
8:
4193:"New form of matter 'excitonium' discovered"
2983:Mueller, Thomas; Malic, Ermin (2018-09-10).
2510:coexistence of free and self-trapped states
2474:Giant oscillator strength of bound excitons
835:. Compared to a hydrogen atom, the exciton
5203:
5199:
4952:
4943:
4757:
4748:
4671:
4505:
4496:
4475:
4461:
4453:
716:
702:
56:
45:
4408:
4347:
4285:
4230:
4219:Annual Review of Condensed Matter Physics
3963:A. F. Prikhot'ko, Izv, AN SSSR Ser. Fiz.
3840:
3798:
3788:
3770:
3708:
3571:
3553:
3477:
3467:
3325:
3307:
3208:
3144:
3126:
3010:
3000:
2806:
2786:
2766:
2745:
2735:
2726:
2720:
2708:
2687:
2681:
2656:
2636:
2616:
2596:
2576:
2555:
2546:
2540:
2524:
2518:
2387:At surfaces it is possible for so called
2294:
2288:
2267:
2261:
2237:
2232:
2219:
2214:
2202:
2193:
2188:
2178:
2173:
2158:
2133:
2127:
2103:
2090:
2081:
2071:
2065:
2056:
2050:
1999:
1979:
1955:
1930:
1924:
1903:
1897:
1859:
1845:
1835:
1816:
1802:
1792:
1787:
1772:
1762:
1748:
1742:
1722:
1692:
1675:
1657:
1651:
1631:
1581:
1575:
1548:
1542:
1496:
1490:
1466:
1456:
1443:
1423:
1413:
1403:
1396:
1383:
1377:
1353:
1347:
1323:
1318:
1305:
1300:
1288:
1279:
1274:
1264:
1259:
1244:
1223:
1217:
1193:
1191:
1165:
1155:
1149:
1135:
1121:
1112:
1107:
1097:
1087:
1080:
1060:
4249:10.1146/annurev-conmatphys-031113-133832
4103:Kagan, Yu; Leggett, A. J. (2012-12-02).
2837:(when the characteristic thermal energy
847:significantly larger than 1 and (b) the
736:that are attracted to each other by the
3751:"Strongly bound excitons in anatase TiO
2966:Theory of excitons, Solid state physics
2957:
1239:is the (static) relative permittivity,
48:
3621:
2911:Spatially direct and indirect excitons
1052:respectively. For the energy, we have
827:of the bound state then is said to be
4106:Quantum Tunnelling in Condensed Media
3914:"Dark excitons outnumber bright ones"
990:. This type of exciton was named for
910:In materials with a relatively small
7:
4004:(Springer, New York, New York) 1985.
2978:
2976:
2974:
2829:Excitons are the main mechanism for
3509:(12). ACS Publications: 2555–2560.
2371:orbitals and a hole in the oxygen 2
1919:is the so-called screening length,
1208:is the Rydberg unit of energy (cf.
4002:Spectroscopy of molecular excitons
3991:(Plenum, New York, New York) 1971.
3755:single crystals and nanoparticles"
2591:is effective mass of the exciton,
2440:highest occupied molecular orbital
2345:Terahertz time-domain spectroscopy
25:
3889:"Dark excitons hit the spotlight"
3503:The Journal of Physical Chemistry
2989:npj 2D Materials and Applications
2452:Förster resonance energy transfer
5519:
5412:Timeline of particle discoveries
4017:, Soviet Physics Semiconductors
2349:Mott antiferromagnetic insulator
2142:{\displaystyle \varepsilon _{r}}
1563:{\displaystyle R_{\text{X}}=4.2}
1537:respectively; and that gives us
1232:{\displaystyle \varepsilon _{r}}
890:, giving rise to exciton energy
878:. The exciton energy depends on
748:. It is an electrically neutral
683:
682:
669:
3676:. Wiley-VCH Verlag. p. 82.
3357:Yang, X. L. (1 February 1991).
3109:Arora, Ashish (30 March 2021).
1596:{\displaystyle a_{\text{X}}=13}
3327:10.1103/PhysRevLett.113.076802
2243:
2207:
2199:
2166:
1733:
1727:
1642:
1636:
1613:two-dimensional (2D) materials
1329:
1293:
1285:
1252:
1071:
1065:
1:
2894:Bose–Einstein condensed state
2801:appear in the denominator of
2411:Atomic and molecular excitons
1939:{\displaystyle \epsilon _{0}}
5428:History of subatomic physics
3989:Theory of Molecular Excitons
3259:Optical Properties of Solids
3061:Optical Properties of Solids
2877:, analogous to a dihydrogen
2361:charge-transfer (CT) exciton
1505:{\displaystyle a_{\text{H}}}
779:. Because of the attractive
3670:Lanzani, Guglielmo (2012).
2430:is said to be found in the
1201:{\displaystyle {\text{Ry}}}
5567:
3790:10.1038/s41467-017-00016-6
3727:10.1103/PhysRevB.77.060501
3608:10.1038/s41567-023-02204-2
3534:Royal Society Open Science
3115:Journal of Applied Physics
2321:
2283:is the electron mass, and
2031:
269:Spin gapless semiconductor
5517:
5202:
4366:10.1038/s41563-019-0337-0
3012:10.1038/s41699-018-0074-2
2844:is less than the exciton
2833:in semiconductors at low
2487:Self-trapping of excitons
2481:giant oscillator strength
2432:lowest unoccupied orbital
1002:. They are also known as
864:applied magnetic fields.
209:Electronic band structure
5445:mathematical formulation
5040:Eta and eta prime mesons
3938:10.1063/PT.6.1.20210107a
3924:(1): 0107a. 2021-01-07.
3383:10.1103/PhysRevA.43.1186
3256:Fox, Mark (2010-03-25).
3059:Fox, Mark (2010-03-25).
1034:hydrogen spectral series
977:electric field screening
119:Bose–Einstein condensate
50:Condensed matter physics
5107:Double-charm tetraquark
4304:10.1126/science.aam6432
3859:10.1126/science.aba1029
3643:Wright, J. D. (1995) .
3296:Physical Review Letters
3264:Oxford University Press
2794:{\displaystyle \gamma }
2664:{\displaystyle \gamma }
2624:{\displaystyle \omega }
2604:{\displaystyle \gamma }
2355:Charge-transfer exciton
1987:{\displaystyle \kappa }
3602:. September 25, 2023.
3528:Edvinsson, T. (2018).
3406:Proc. MSU Phys. Astron
3182:10.1103/PhysRev.52.191
2862:(or more specifically
2815:
2795:
2775:
2755:
2697:
2665:
2645:
2625:
2605:
2585:
2565:
2365:electric dipole moment
2304:
2277:
2250:
2143:
2113:
2008:
1988:
1964:
1940:
1913:
1883:
1704:
1597:
1564:
1506:
1476:
1363:
1336:
1233:
1202:
1177:
1046:exciton Rydberg energy
814:organic semiconductors
800:optoelectronic devices
752:that exists mainly in
43:
35:
5504:Wave–particle duality
5494:Relativistic particle
4631:Electron antineutrino
3759:Nature Communications
3096:10.1103/PhysRev.37.17
2816:
2796:
2776:
2756:
2698:
2696:{\displaystyle r_{b}}
2666:
2646:
2626:
2606:
2586:
2566:
2506:self-trapping barrier
2330:Coulomb's interaction
2305:
2303:{\displaystyle a_{0}}
2278:
2276:{\displaystyle m_{0}}
2251:
2151:relative permittivity
2144:
2114:
2009:
1989:
1965:
1941:
1914:
1912:{\displaystyle r_{0}}
1884:
1705:
1598:
1565:
1507:
1477:
1364:
1362:{\displaystyle m_{0}}
1337:
1234:
1203:
1178:
841:relative permittivity
264:Topological insulator
41:
33:
4734:Faddeev–Popov ghosts
4484:Particles in physics
4060:, pp. 75, 88 (1957).
2941:Polariton superfluid
2805:
2785:
2765:
2707:
2680:
2655:
2635:
2615:
2595:
2575:
2517:
2401:forbidden transition
2287:
2260:
2157:
2126:
2049:
1998:
1978:
1954:
1923:
1896:
1721:
1630:
1574:
1541:
1489:
1376:
1346:
1243:
1216:
1190:
1059:
1024:) binding energies.
981:Wannier–Mott exciton
971:Wannier–Mott exciton
888:exchange interaction
282:Electronic phenomena
129:Fermionic condensate
5509:Particle chauvinism
5452:Subatomic particles
4427:10.1038/nature10903
4419:2012Natur.483..584H
4358:2019NatMa..18..691M
4296:2017Sci...358.1314K
4280:(6368): 1314–1317.
4241:2014ARCMP...5..159E
3930:2021PhT..2021a.107.
3851:2020Sci...370.1199M
3835:(6521): 1199–1204.
3781:2017NatCo...8...13B
3719:2008PhRvB..77f0501E
3555:10.1098/rsos.180387
3546:2018RSOS....580387E
3515:10.1021/j100403a003
3460:2017NatSR...739844T
3375:1991PhRvA..43.1186Y
3318:2014PhRvL.113g6802C
3227:10.1038/nature13832
3219:2014Natur.514..343K
3174:1937PhRv...52..191W
3137:2021JAP...129l0902A
3088:1931PhRv...37...17F
2931:Oscillator strength
2468:Antonina Prikhot'ko
2242:
2224:
2198:
2183:
1948:vacuum permittivity
1328:
1310:
1284:
1269:
1117:
1050:exciton Bohr radius
996:Nevill Francis Mott
912:dielectric constant
289:Quantum Hall effect
4197:The Times of India
4160:, pp. 1–35 (1988).
4089:2019-02-23 at the
3974:2016-03-05 at the
3646:Molecular Crystals
2811:
2791:
2771:
2751:
2693:
2661:
2641:
2621:
2601:
2581:
2561:
2300:
2273:
2246:
2228:
2210:
2184:
2169:
2139:
2109:
2004:
1984:
1960:
1936:
1909:
1879:
1700:
1685:
1593:
1560:
1502:
1472:
1359:
1332:
1314:
1296:
1270:
1255:
1229:
1198:
1173:
1103:
884:reciprocal lattice
676:Physics portal
44:
36:
5533:
5532:
5489:Massless particle
5297:
5296:
5293:
5292:
5258:
5257:
5121:
5120:
4933:
4932:
4929:
4928:
4881:Magnetic monopole
4829:
4828:
4720:
4719:
4661:
4660:
4641:Muon antineutrino
4626:Electron neutrino
4403:(7391): 584–588.
4143:978-0-444-87070-4
4116:978-0-444-60047-9
4082:, p. 251 (1979),
4021:, 807–816 (1975).
3697:Physical Review B
3656:978-0-521-47730-7
3469:10.1038/srep39844
3363:Physical Review A
3203:(7522): 343–347.
3146:10.1063/5.0042683
2864:exciton-polariton
2814:{\displaystyle W}
2774:{\displaystyle m}
2644:{\displaystyle m}
2584:{\displaystyle m}
2424:molecular orbital
2405:phonon scattering
2097:
2059:
2028:0D semiconductors
2007:{\displaystyle r}
1972:elementary charge
1963:{\displaystyle e}
1865:
1822:
1790:
1779:
1698:
1684:
1660:
1607:2D semiconductors
1584:
1551:
1499:
1459:
1433:
1426:
1196:
1171:
1158:
1141:
1124:
1119:
1040:3D semiconductors
726:
725:
434:Granular material
202:Electronic phases
16:(Redirected from
5558:
5523:
5499:Virtual particle
5270:Mesonic molecule
5204:
5200:
5045:Bottom eta meson
4953:
4944:
4916:W′ and Z′ bosons
4906:Sterile neutrino
4891:Majorana fermion
4758:
4749:
4672:
4651:Tau antineutrino
4506:
4497:
4477:
4470:
4463:
4454:
4447:
4446:
4412:
4392:
4386:
4385:
4351:
4336:Nature Materials
4330:
4324:
4323:
4289:
4267:
4261:
4260:
4234:
4214:
4208:
4207:
4205:
4203:
4189:
4183:
4182:, p. 423 (1989).
4176:
4170:
4167:
4161:
4154:
4148:
4147:
4127:
4121:
4120:
4100:
4094:
4076:
4070:
4067:
4061:
4054:
4048:
4041:
4035:
4028:
4022:
4011:
4005:
3998:
3992:
3985:
3979:
3967:, p. 499 (1948)
3961:
3955:
3954:, p. 257 (1944).
3948:
3942:
3941:
3910:
3904:
3903:
3901:
3900:
3885:
3879:
3878:
3844:
3819:
3813:
3812:
3802:
3792:
3774:
3745:
3739:
3738:
3712:
3703:(6): 060501(R).
3684:
3678:
3677:
3667:
3661:
3660:
3640:
3634:
3633:
3627:
3619:
3617:
3615:
3592:
3586:
3585:
3575:
3557:
3525:
3519:
3518:
3498:
3492:
3491:
3481:
3471:
3439:
3433:
3432:
3420:
3414:
3413:
3401:
3395:
3394:
3369:(3): 1186–1196.
3354:
3348:
3347:
3329:
3311:
3287:
3278:
3277:
3253:
3247:
3246:
3212:
3192:
3186:
3185:
3157:
3151:
3150:
3148:
3130:
3106:
3100:
3099:
3071:
3065:
3064:
3056:
3050:
3039:
3033:
3032:
3014:
3004:
2980:
2969:
2962:
2868:dressed excitons
2820:
2818:
2817:
2812:
2800:
2798:
2797:
2792:
2780:
2778:
2777:
2772:
2760:
2758:
2757:
2752:
2750:
2749:
2740:
2739:
2730:
2725:
2724:
2702:
2700:
2699:
2694:
2692:
2691:
2670:
2668:
2667:
2662:
2650:
2648:
2647:
2642:
2630:
2628:
2627:
2622:
2610:
2608:
2607:
2602:
2590:
2588:
2587:
2582:
2570:
2568:
2567:
2562:
2560:
2559:
2550:
2545:
2544:
2529:
2528:
2460:molecular rulers
2309:
2307:
2306:
2301:
2299:
2298:
2282:
2280:
2279:
2274:
2272:
2271:
2255:
2253:
2252:
2247:
2241:
2236:
2223:
2218:
2206:
2197:
2192:
2182:
2177:
2148:
2146:
2145:
2140:
2138:
2137:
2118:
2116:
2115:
2110:
2108:
2107:
2098:
2096:
2095:
2094:
2085:
2076:
2075:
2066:
2061:
2060:
2057:
2013:
2011:
2010:
2005:
1993:
1991:
1990:
1985:
1969:
1967:
1966:
1961:
1945:
1943:
1942:
1937:
1935:
1934:
1918:
1916:
1915:
1910:
1908:
1907:
1888:
1886:
1885:
1880:
1875:
1871:
1870:
1866:
1864:
1863:
1854:
1846:
1840:
1839:
1827:
1823:
1821:
1820:
1811:
1803:
1797:
1796:
1791:
1788:
1780:
1778:
1777:
1776:
1767:
1766:
1753:
1752:
1743:
1709:
1707:
1706:
1701:
1699:
1697:
1696:
1691:
1687:
1686:
1677:
1662:
1661:
1658:
1652:
1617:quantum confined
1615:, the system is
1602:
1600:
1599:
1594:
1586:
1585:
1582:
1569:
1567:
1566:
1561:
1553:
1552:
1549:
1519:For example, in
1511:
1509:
1508:
1503:
1501:
1500:
1497:
1481:
1479:
1478:
1473:
1471:
1470:
1461:
1460:
1457:
1448:
1447:
1438:
1434:
1429:
1428:
1427:
1424:
1418:
1417:
1408:
1407:
1397:
1388:
1387:
1368:
1366:
1365:
1360:
1358:
1357:
1341:
1339:
1338:
1333:
1327:
1322:
1309:
1304:
1292:
1283:
1278:
1268:
1263:
1238:
1236:
1235:
1230:
1228:
1227:
1210:Rydberg constant
1207:
1205:
1204:
1199:
1197:
1194:
1182:
1180:
1179:
1174:
1172:
1170:
1169:
1160:
1159:
1156:
1150:
1142:
1140:
1139:
1130:
1126:
1125:
1122:
1120:
1118:
1116:
1111:
1102:
1101:
1088:
1081:
1023:
1022:
1011:carbon nanotubes
989:
988:
754:condensed matter
718:
711:
704:
691:
686:
685:
678:
674:
673:
294:Spin Hall effect
184:Phase transition
154:Luttinger liquid
91:States of matter
74:Phase transition
60:
46:
21:
5566:
5565:
5561:
5560:
5559:
5557:
5556:
5555:
5536:
5535:
5534:
5529:
5513:
5467:Nuclear physics
5416:
5380:
5316:Davydov soliton
5289:
5254:
5228:
5189:
5117:
5089:
5016:
4925:
4825:
4784:
4738:
4716:
4698:
4657:
4577:
4486:
4481:
4451:
4450:
4394:
4393:
4389:
4332:
4331:
4327:
4270:
4268:
4264:
4216:
4215:
4211:
4201:
4199:
4191:
4190:
4186:
4177:
4173:
4168:
4164:
4155:
4151:
4144:
4129:
4128:
4124:
4117:
4102:
4101:
4097:
4091:Wayback Machine
4077:
4073:
4068:
4064:
4055:
4051:
4042:
4038:
4029:
4025:
4012:
4008:
3999:
3995:
3987:A. S. Davydov,
3986:
3982:
3976:Wayback Machine
3962:
3958:
3949:
3945:
3912:
3911:
3907:
3898:
3896:
3887:
3886:
3882:
3821:
3820:
3816:
3754:
3747:
3746:
3742:
3694:
3690:
3686:
3685:
3681:
3669:
3668:
3664:
3657:
3642:
3641:
3637:
3620:
3613:
3611:
3594:
3593:
3589:
3527:
3526:
3522:
3500:
3499:
3495:
3441:
3440:
3436:
3422:
3421:
3417:
3403:
3402:
3398:
3356:
3355:
3351:
3289:
3288:
3281:
3274:
3255:
3254:
3250:
3194:
3193:
3189:
3162:Physical Review
3159:
3158:
3154:
3108:
3107:
3103:
3076:Physical Review
3073:
3072:
3068:
3058:
3057:
3053:
3040:
3036:
2982:
2981:
2972:
2963:
2959:
2954:
2922:
2913:
2905:
2827:
2803:
2802:
2783:
2782:
2763:
2762:
2761:. Because both
2741:
2731:
2716:
2705:
2704:
2683:
2678:
2677:
2653:
2652:
2633:
2632:
2613:
2612:
2593:
2592:
2573:
2572:
2551:
2536:
2520:
2515:
2514:
2489:
2476:
2413:
2397:
2385:
2383:Surface exciton
2378:
2357:
2326:
2320:
2318:Hubbard exciton
2290:
2285:
2284:
2263:
2258:
2257:
2155:
2154:
2129:
2124:
2123:
2099:
2086:
2077:
2067:
2052:
2047:
2046:
2036:
2030:
2021:
1996:
1995:
1976:
1975:
1952:
1951:
1926:
1921:
1920:
1899:
1894:
1893:
1855:
1847:
1841:
1831:
1812:
1804:
1798:
1786:
1785:
1781:
1768:
1758:
1754:
1744:
1719:
1718:
1668:
1664:
1663:
1653:
1628:
1627:
1609:
1577:
1572:
1571:
1544:
1539:
1538:
1535:
1528:
1492:
1487:
1486:
1462:
1452:
1439:
1419:
1409:
1399:
1398:
1392:
1379:
1374:
1373:
1349:
1344:
1343:
1241:
1240:
1219:
1214:
1213:
1188:
1187:
1161:
1151:
1131:
1093:
1092:
1086:
1082:
1057:
1056:
1042:
1020:
1018:
1009:In single-wall
992:Gregory Wannier
986:
984:
973:
950:-shells. While
920:Frenkel exciton
908:
906:Frenkel exciton
859:
855:
846:
769:conduction band
722:
681:
668:
667:
660:
659:
658:
458:
450:
449:
448:
424:Amorphous solid
418:
408:
407:
406:
385:
367:
357:
356:
355:
344:
342:Antiferromagnet
335:
333:Superparamagnet
326:
313:
312:Magnetic phases
305:
304:
303:
283:
275:
274:
273:
203:
195:
194:
193:
179:Order parameter
173:
172:Phase phenomena
165:
164:
163:
93:
83:
28:
23:
22:
15:
12:
11:
5:
5564:
5562:
5554:
5553:
5548:
5546:Quasiparticles
5538:
5537:
5531:
5530:
5526:Physics portal
5518:
5515:
5514:
5512:
5511:
5506:
5501:
5496:
5491:
5486:
5481:
5480:
5479:
5469:
5464:
5459:
5454:
5449:
5448:
5447:
5440:Standard Model
5437:
5436:
5435:
5424:
5422:
5418:
5417:
5415:
5414:
5409:
5407:Quasiparticles
5404:
5399:
5394:
5388:
5386:
5382:
5381:
5379:
5378:
5373:
5368:
5363:
5358:
5353:
5348:
5343:
5338:
5333:
5328:
5323:
5318:
5313:
5307:
5305:
5303:Quasiparticles
5299:
5298:
5295:
5294:
5291:
5290:
5288:
5287:
5282:
5277:
5272:
5266:
5264:
5260:
5259:
5256:
5255:
5253:
5252:
5247:
5242:
5236:
5234:
5230:
5229:
5227:
5226:
5221:
5216:
5210:
5208:
5197:
5191:
5190:
5188:
5187:
5182:
5177:
5176:
5175:
5170:
5165:
5160:
5155:
5150:
5140:
5135:
5129:
5127:
5123:
5122:
5119:
5118:
5116:
5115:
5110:
5099:
5097:
5095:Exotic hadrons
5091:
5090:
5088:
5087:
5082:
5077:
5072:
5067:
5062:
5057:
5052:
5047:
5042:
5037:
5032:
5026:
5024:
5018:
5017:
5015:
5014:
5009:
5004:
4999:
4994:
4989:
4988:
4987:
4982:
4977:
4972:
4961:
4959:
4950:
4941:
4935:
4934:
4931:
4930:
4927:
4926:
4924:
4923:
4921:X and Y bosons
4918:
4913:
4908:
4903:
4898:
4893:
4888:
4883:
4878:
4873:
4868:
4863:
4858:
4853:
4848:
4843:
4837:
4835:
4831:
4830:
4827:
4826:
4824:
4823:
4813:
4808:
4803:
4798:
4792:
4790:
4786:
4785:
4783:
4782:
4777:
4772:
4766:
4764:
4755:
4746:
4740:
4739:
4737:
4736:
4730:
4728:
4722:
4721:
4718:
4717:
4715:
4714:
4708:
4706:
4700:
4699:
4697:
4696:
4694:W and Z bosons
4691:
4686:
4680:
4678:
4669:
4663:
4662:
4659:
4658:
4656:
4655:
4654:
4653:
4648:
4643:
4638:
4633:
4628:
4618:
4613:
4608:
4603:
4598:
4593:
4587:
4585:
4579:
4578:
4576:
4575:
4570:
4565:
4560:
4555:
4550:
4548:Strange (quark
4545:
4540:
4535:
4530:
4525:
4520:
4514:
4512:
4503:
4494:
4488:
4487:
4482:
4480:
4479:
4472:
4465:
4457:
4449:
4448:
4387:
4342:(7): 691–696.
4325:
4262:
4209:
4184:
4171:
4162:
4149:
4142:
4122:
4115:
4095:
4071:
4062:
4049:
4036:
4034:, p. 1 (1985).
4023:
4013:E. I. Rashba,
4006:
3993:
3980:
3956:
3943:
3905:
3880:
3814:
3752:
3740:
3692:
3688:
3679:
3662:
3655:
3635:
3587:
3520:
3493:
3434:
3415:
3396:
3349:
3279:
3273:978-0199573363
3272:
3266:. p. 97.
3248:
3187:
3152:
3101:
3066:
3051:
3034:
2970:
2956:
2955:
2953:
2950:
2949:
2948:
2943:
2938:
2933:
2928:
2921:
2918:
2912:
2909:
2903:
2846:binding energy
2831:light emission
2826:
2823:
2810:
2790:
2770:
2748:
2744:
2738:
2734:
2729:
2723:
2719:
2715:
2712:
2690:
2686:
2660:
2640:
2620:
2600:
2580:
2558:
2554:
2549:
2543:
2539:
2535:
2532:
2527:
2523:
2488:
2485:
2475:
2472:
2412:
2409:
2396:
2393:
2384:
2381:
2376:
2356:
2353:
2334:magnetic force
2322:Main article:
2319:
2316:
2297:
2293:
2270:
2266:
2245:
2240:
2235:
2231:
2227:
2222:
2217:
2213:
2209:
2205:
2201:
2196:
2191:
2187:
2181:
2176:
2172:
2168:
2165:
2162:
2136:
2132:
2120:
2119:
2106:
2102:
2093:
2089:
2084:
2080:
2074:
2070:
2064:
2055:
2029:
2026:
2020:
2017:
2003:
1983:
1959:
1933:
1929:
1906:
1902:
1890:
1889:
1878:
1874:
1869:
1862:
1858:
1853:
1850:
1844:
1838:
1834:
1830:
1826:
1819:
1815:
1810:
1807:
1801:
1795:
1784:
1775:
1771:
1765:
1761:
1757:
1751:
1747:
1741:
1738:
1735:
1732:
1729:
1726:
1712:
1711:
1695:
1690:
1683:
1680:
1674:
1671:
1667:
1656:
1650:
1647:
1644:
1641:
1638:
1635:
1608:
1605:
1592:
1589:
1580:
1559:
1556:
1547:
1533:
1526:
1495:
1483:
1482:
1469:
1465:
1455:
1451:
1446:
1442:
1437:
1432:
1422:
1416:
1412:
1406:
1402:
1395:
1391:
1386:
1382:
1356:
1352:
1331:
1326:
1321:
1317:
1313:
1308:
1303:
1299:
1295:
1291:
1287:
1282:
1277:
1273:
1267:
1262:
1258:
1254:
1251:
1248:
1226:
1222:
1184:
1183:
1168:
1164:
1154:
1148:
1145:
1138:
1134:
1129:
1115:
1110:
1106:
1100:
1096:
1091:
1085:
1079:
1076:
1073:
1070:
1067:
1064:
1041:
1038:
1004:large excitons
972:
969:
922:, named after
907:
904:
892:fine structure
857:
853:
849:Effective mass
844:
837:binding energy
818:Effective mass
796:band structure
762:semiconductors
724:
723:
721:
720:
713:
706:
698:
695:
694:
693:
692:
679:
662:
661:
657:
656:
651:
646:
641:
636:
631:
626:
621:
616:
611:
606:
601:
596:
591:
586:
581:
576:
571:
566:
561:
556:
551:
546:
541:
536:
531:
526:
521:
516:
511:
506:
501:
496:
491:
486:
481:
476:
471:
466:
460:
459:
456:
455:
452:
451:
447:
446:
441:
439:Liquid crystal
436:
431:
426:
420:
419:
414:
413:
410:
409:
405:
404:
399:
394:
389:
380:
375:
369:
368:
365:Quasiparticles
363:
362:
359:
358:
354:
353:
348:
339:
330:
324:Superdiamagnet
321:
315:
314:
311:
310:
307:
306:
302:
301:
296:
291:
285:
284:
281:
280:
277:
276:
272:
271:
266:
261:
256:
251:
249:Thermoelectric
246:
244:Superconductor
241:
236:
231:
226:
224:Mott insulator
221:
216:
211:
205:
204:
201:
200:
197:
196:
192:
191:
186:
181:
175:
174:
171:
170:
167:
166:
162:
161:
156:
151:
146:
141:
136:
131:
126:
121:
116:
111:
106:
101:
95:
94:
89:
88:
85:
84:
82:
81:
76:
71:
65:
62:
61:
53:
52:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5563:
5552:
5549:
5547:
5544:
5543:
5541:
5528:
5527:
5522:
5516:
5510:
5507:
5505:
5502:
5500:
5497:
5495:
5492:
5490:
5487:
5485:
5484:Exotic matter
5482:
5478:
5475:
5474:
5473:
5472:Eightfold way
5470:
5468:
5465:
5463:
5462:Antiparticles
5460:
5458:
5455:
5453:
5450:
5446:
5443:
5442:
5441:
5438:
5434:
5431:
5430:
5429:
5426:
5425:
5423:
5419:
5413:
5410:
5408:
5405:
5403:
5400:
5398:
5395:
5393:
5390:
5389:
5387:
5383:
5377:
5374:
5372:
5369:
5367:
5364:
5362:
5359:
5357:
5354:
5352:
5349:
5347:
5344:
5342:
5339:
5337:
5334:
5332:
5329:
5327:
5324:
5322:
5319:
5317:
5314:
5312:
5309:
5308:
5306:
5304:
5300:
5286:
5283:
5281:
5278:
5276:
5273:
5271:
5268:
5267:
5265:
5261:
5251:
5248:
5246:
5243:
5241:
5238:
5237:
5235:
5231:
5225:
5222:
5220:
5217:
5215:
5212:
5211:
5209:
5205:
5201:
5198:
5196:
5192:
5186:
5183:
5181:
5178:
5174:
5171:
5169:
5166:
5164:
5161:
5159:
5156:
5154:
5151:
5149:
5146:
5145:
5144:
5141:
5139:
5136:
5134:
5133:Atomic nuclei
5131:
5130:
5128:
5124:
5114:
5111:
5108:
5104:
5101:
5100:
5098:
5096:
5092:
5086:
5083:
5081:
5078:
5076:
5073:
5071:
5068:
5066:
5065:Upsilon meson
5063:
5061:
5058:
5056:
5053:
5051:
5048:
5046:
5043:
5041:
5038:
5036:
5033:
5031:
5028:
5027:
5025:
5023:
5019:
5013:
5010:
5008:
5005:
5003:
5000:
4998:
4997:Lambda baryon
4995:
4993:
4990:
4986:
4983:
4981:
4978:
4976:
4973:
4971:
4968:
4967:
4966:
4963:
4962:
4960:
4958:
4954:
4951:
4949:
4945:
4942:
4940:
4936:
4922:
4919:
4917:
4914:
4912:
4909:
4907:
4904:
4902:
4899:
4897:
4894:
4892:
4889:
4887:
4884:
4882:
4879:
4877:
4874:
4872:
4869:
4867:
4864:
4862:
4859:
4857:
4856:Dual graviton
4854:
4852:
4849:
4847:
4844:
4842:
4839:
4838:
4836:
4832:
4821:
4817:
4814:
4812:
4809:
4807:
4804:
4802:
4799:
4797:
4794:
4793:
4791:
4787:
4781:
4778:
4776:
4773:
4771:
4768:
4767:
4765:
4763:
4759:
4756:
4754:
4753:Superpartners
4750:
4747:
4745:
4741:
4735:
4732:
4731:
4729:
4727:
4723:
4713:
4710:
4709:
4707:
4705:
4701:
4695:
4692:
4690:
4687:
4685:
4682:
4681:
4679:
4677:
4673:
4670:
4668:
4664:
4652:
4649:
4647:
4644:
4642:
4639:
4637:
4636:Muon neutrino
4634:
4632:
4629:
4627:
4624:
4623:
4622:
4619:
4617:
4614:
4612:
4609:
4607:
4604:
4602:
4599:
4597:
4594:
4592:
4589:
4588:
4586:
4584:
4580:
4574:
4571:
4569:
4568:Bottom (quark
4566:
4564:
4561:
4559:
4556:
4554:
4551:
4549:
4546:
4544:
4541:
4539:
4536:
4534:
4531:
4529:
4526:
4524:
4521:
4519:
4516:
4515:
4513:
4511:
4507:
4504:
4502:
4498:
4495:
4493:
4489:
4485:
4478:
4473:
4471:
4466:
4464:
4459:
4458:
4455:
4444:
4440:
4436:
4432:
4428:
4424:
4420:
4416:
4411:
4406:
4402:
4398:
4391:
4388:
4383:
4379:
4375:
4371:
4367:
4363:
4359:
4355:
4350:
4345:
4341:
4337:
4329:
4326:
4321:
4317:
4313:
4309:
4305:
4301:
4297:
4293:
4288:
4283:
4279:
4275:
4266:
4263:
4258:
4254:
4250:
4246:
4242:
4238:
4233:
4228:
4224:
4220:
4213:
4210:
4198:
4194:
4188:
4185:
4181:
4175:
4172:
4166:
4163:
4159:
4153:
4150:
4145:
4139:
4135:
4134:
4126:
4123:
4118:
4112:
4108:
4107:
4099:
4096:
4092:
4088:
4085:
4081:
4075:
4072:
4066:
4063:
4059:
4053:
4050:
4046:
4040:
4037:
4033:
4027:
4024:
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3918:Physics Today
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3540:(9): 180387.
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3305:
3302:(7): 076802.
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3047:9780198753735
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2883:electron-hole
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2494:Self-trapping
2486:
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2473:
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2445:
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2436:electron hole
2433:
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2324:Hubbard model
2317:
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2091:
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2078:
2072:
2068:
2062:
2053:
2045:
2044:
2043:
2041:
2040:nanoparticles
2035:
2027:
2025:
2018:
2016:
2001:
1981:
1973:
1957:
1949:
1931:
1927:
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1055:
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1053:
1051:
1047:
1039:
1037:
1035:
1030:
1025:
1016:
1015:wave function
1012:
1007:
1005:
1001:
997:
993:
982:
978:
970:
968:
966:
962:
957:
953:
949:
945:
941:
937:
933:
929:
925:
924:Yakov Frenkel
921:
917:
913:
905:
903:
900:
895:
893:
889:
885:
881:
877:
876:Bloch theorem
873:
870:
865:
861:
850:
842:
838:
834:
833:hydrogen atom
830:
826:
821:
819:
815:
811:
806:
803:
801:
797:
793:
792:Yakov Frenkel
788:
786:
782:
781:coulomb force
778:
774:
770:
765:
763:
759:
755:
751:
750:quasiparticle
747:
743:
739:
738:Coulomb force
735:
734:electron hole
731:
719:
714:
712:
707:
705:
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497:
495:
492:
490:
487:
485:
482:
480:
477:
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472:
470:
467:
465:
464:Van der Waals
462:
461:
454:
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442:
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430:
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421:
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309:
308:
300:
297:
295:
292:
290:
287:
286:
279:
278:
270:
267:
265:
262:
260:
259:Ferroelectric
257:
255:
254:Piezoelectric
252:
250:
247:
245:
242:
240:
237:
235:
232:
230:
229:Semiconductor
227:
225:
222:
220:
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215:
212:
210:
207:
206:
199:
198:
190:
187:
185:
182:
180:
177:
176:
169:
168:
160:
157:
155:
152:
150:
149:Superfluidity
147:
145:
142:
140:
137:
135:
132:
130:
127:
125:
122:
120:
117:
115:
112:
110:
107:
105:
102:
100:
97:
96:
92:
87:
86:
80:
77:
75:
72:
70:
67:
66:
64:
63:
59:
55:
54:
51:
47:
40:
32:
19:
5524:
5325:
5195:Hypothetical
5143:Exotic atoms
5012:Omega baryon
5002:Sigma baryon
4992:Delta baryon
4744:Hypothetical
4726:Ghost fields
4712:Higgs boson
4646:Tau neutrino
4538:Charm (quark
4400:
4396:
4390:
4339:
4335:
4328:
4277:
4273:
4265:
4222:
4218:
4212:
4200:. Retrieved
4196:
4187:
4179:
4174:
4165:
4157:
4152:
4132:
4125:
4109:. Elsevier.
4105:
4098:
4079:
4074:
4065:
4057:
4052:
4044:
4039:
4031:
4026:
4018:
4014:
4009:
4001:
3996:
3988:
3983:
3964:
3959:
3951:
3946:
3921:
3917:
3908:
3897:. Retrieved
3895:. 2020-12-04
3892:
3883:
3832:
3828:
3817:
3762:
3758:
3743:
3700:
3696:
3682:
3672:
3665:
3645:
3638:
3612:. Retrieved
3590:
3537:
3533:
3523:
3506:
3502:
3496:
3451:
3447:
3437:
3428:
3424:
3418:
3409:
3405:
3399:
3366:
3362:
3352:
3299:
3295:
3258:
3251:
3200:
3196:
3190:
3165:
3161:
3155:
3118:
3114:
3104:
3079:
3075:
3069:
3060:
3054:
3037:
2992:
2988:
2965:
2964:R. S. Knox,
2960:
2914:
2897:
2887:
2872:
2867:
2857:
2850:
2838:
2828:
2509:
2505:
2499:
2493:
2490:
2477:
2464:
2459:
2455:
2421:
2414:
2398:
2395:Dark exciton
2389:image states
2388:
2386:
2372:
2368:
2360:
2358:
2342:
2338:John Hubbard
2327:
2121:
2037:
2022:
1891:
1713:
1622:
1610:
1531:
1524:
1518:
1484:
1185:
1049:
1045:
1043:
1026:
1008:
1003:
980:
974:
964:
960:
955:
951:
947:
943:
939:
919:
909:
899:Gerald Mahan
896:
879:
871:
866:
862:
825:wavefunction
822:
807:
804:
789:
766:
756:, including
745:
727:
594:von Klitzing
377:
299:Kondo effect
159:Time crystal
139:Fermi liquid
5477:Quark model
5245:Theta meson
5148:Positronium
5060:Omega meson
5055:J/psi meson
4985:Antineutron
4896:Dark photon
4861:Graviphoton
4820:Stop squark
4528:Down (quark
4225:: 159–181.
4202:10 December
3614:October 11,
2995:(1): 1–12.
2835:temperature
2825:Interaction
2676:). Because
2444:nanoseconds
2332:, but by a
2312:Bohr radius
1514:Bohr radius
1029:femtosecond
869:wavevector
785:positronium
742:bound state
740:can form a
416:Soft matter
337:Ferromagnet
5540:Categories
5219:Heptaquark
5180:Superatoms
5113:Pentaquark
5103:Tetraquark
5085:Quarkonium
4975:Antiproton
4876:Leptoquark
4811:Neutralino
4573:antiquark)
4563:antiquark)
4558:Top (quark
4553:antiquark)
4543:antiquark)
4533:antiquark)
4523:antiquark)
4492:Elementary
4349:1910.03890
4287:1611.04217
3899:2023-12-02
3842:2005.00241
3772:1601.01244
3765:(13): 13.
3168:(3): 191.
3128:2103.17110
3002:1903.02962
2952:References
2032:See also:
932:anthracene
916:fullerenes
829:hydrogenic
810:insulators
758:insulators
744:called an
559:Louis NĂ©el
549:Schrieffer
457:Scientists
351:Spin glass
346:Metamagnet
328:Paramagnet
144:Supersolid
5457:Particles
5402:Particles
5361:Polariton
5351:Plasmaron
5321:Dropleton
5214:Hexaquark
5185:Molecules
5173:Protonium
5050:Phi meson
5035:Rho meson
5007:Xi baryon
4939:Composite
4775:Gravitino
4518:Up (quark
4410:1109.0253
4382:104295452
4320:206656719
4232:1306.0584
3867:0036-8075
3735:119238654
3710:0709.1705
3564:2054-5703
3454:: 39844.
3425:JETP Lett
3336:0031-9007
3309:1403.4270
3210:1407.0691
3082:(1): 17.
3029:119537445
3021:2397-7132
2875:biexciton
2860:polariton
2789:γ
2743:γ
2718:ω
2714:∼
2674:instanton
2659:γ
2619:ω
2599:γ
2553:ω
2538:γ
2531:∼
2239:∗
2221:∗
2195:∗
2180:∗
2164:≡
2161:μ
2131:ε
2079:μ
2069:ε
1982:κ
1928:ϵ
1849:κ
1829:−
1806:κ
1760:ϵ
1740:−
1673:−
1649:−
1450:≡
1431:μ
1411:ε
1325:∗
1307:∗
1281:∗
1266:∗
1247:μ
1221:ε
1147:−
1144:≡
1105:ε
1090:μ
1078:−
936:tetracene
639:Abrikosov
554:Josephson
524:Van Vleck
514:Luttinger
387:Polariton
319:Diamagnet
239:Conductor
234:Semimetal
219:Insulator
134:Fermi gas
5433:timeline
5285:R-hadron
5240:Glueball
5224:Skyrmion
5158:Tauonium
4871:Inflaton
4866:Graviton
4846:Curvaton
4816:Sfermion
4806:Higgsino
4801:Chargino
4762:Gauginos
4621:Neutrino
4606:Antimuon
4596:Positron
4591:Electron
4501:Fermions
4435:22437498
4374:30962556
4312:29217574
4257:15776603
4087:Archived
3972:Archived
3875:33273099
3809:28408739
3624:cite web
3600:Phys.org
3582:30839677
3488:28117326
3448:Sci. Rep
3344:25170725
3235:25318523
2920:See also
2879:molecule
2853:band gap
2502:polarons
2428:electron
1570:meV and
777:positron
730:electron
689:Category
644:Ginzburg
619:Laughlin
579:Kadanoff
534:Shockley
519:Anderson
474:von Laue
124:Bose gas
18:Excitons
5421:Related
5392:Baryons
5366:Polaron
5356:Plasmon
5331:Fracton
5326:Exciton
5280:Diquark
5275:Pomeron
5250:T meson
5207:Baryons
5168:Pionium
5153:Muonium
5080:D meson
5075:B meson
4980:Neutron
4965:Nucleon
4957:Baryons
4948:Hadrons
4911:Tachyon
4886:Majoron
4851:Dilaton
4780:Photino
4616:Antitau
4583:Leptons
4443:3049881
4415:Bibcode
4354:Bibcode
4292:Bibcode
4274:Science
4237:Bibcode
4047:(1986).
3926:Bibcode
3847:Bibcode
3829:Science
3800:5432032
3777:Bibcode
3715:Bibcode
3573:6170533
3542:Bibcode
3479:5259763
3456:Bibcode
3391:9905143
3371:Bibcode
3314:Bibcode
3243:4470179
3215:Bibcode
3170:Bibcode
3133:Bibcode
3084:Bibcode
2936:Plasmon
2926:Orbiton
2438:in the
2434:and an
2310:is the
2149:is the
1970:is the
1946:is the
1530:and 0.2
1512:is the
918:. This
746:exciton
732:and an
649:Leggett
624:Störmer
609:Bednorz
569:Giaever
539:Bardeen
529:Hubbard
504:Peierls
494:Onsager
444:Polymer
429:Colloid
392:Polaron
383:Plasmon
378:Exciton
5551:Bosons
5397:Mesons
5346:Phonon
5341:Magnon
5263:Others
5233:Mesons
5126:Others
5022:Mesons
4970:Proton
4834:Others
4789:Others
4770:Gluino
4704:Scalar
4684:Photon
4667:Bosons
4510:Quarks
4441:
4433:
4397:Nature
4380:
4372:
4318:
4310:
4255:
4140:
4113:
3873:
3865:
3807:
3797:
3733:
3653:
3580:
3570:
3562:
3486:
3476:
3431:: 658.
3389:
3342:
3334:
3270:
3241:
3233:
3197:Nature
3121:(12).
3045:
3027:
3019:
2571:where
2513:about
2448:phonon
2122:where
1892:where
1485:where
1186:where
687:
654:Parisi
614:MĂĽller
604:Rohrer
599:Binnig
589:Wilson
584:Fisher
544:Cooper
509:Landau
397:Magnon
373:Phonon
214:Plasma
114:Plasma
104:Liquid
69:Phases
5385:Lists
5376:Trion
5371:Roton
5311:Anyon
5138:Atoms
4901:Preon
4841:Axion
4796:Axino
4689:Gluon
4676:Gauge
4439:S2CID
4405:arXiv
4378:S2CID
4344:arXiv
4316:S2CID
4282:arXiv
4253:S2CID
4227:arXiv
3837:arXiv
3767:arXiv
3731:S2CID
3705:arXiv
3412:: 30.
3304:arXiv
3239:S2CID
3205:arXiv
3123:arXiv
3025:S2CID
2997:arXiv
2946:Trion
1000:xenon
564:Esaki
489:Bloch
484:Debye
479:Bragg
469:Onnes
402:Roton
99:Solid
5336:Hole
5163:Onia
5070:Kaon
5030:Pion
4601:Muon
4431:PMID
4370:PMID
4308:PMID
4204:2017
4138:ISBN
4111:ISBN
3922:2021
3871:PMID
3863:ISSN
3805:PMID
3651:ISBN
3630:link
3616:2023
3578:PMID
3560:ISSN
3484:PMID
3387:PMID
3340:PMID
3332:ISSN
3268:ISBN
3231:PMID
3043:ISBN
3017:ISSN
2902:TiSe
2890:Bose
2781:and
2651:and
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1521:GaAs
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