33:
148:
2225:
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265:, which have doubly degenerate bands which also meet at Dirac points. Dirac semimetals contain both time reversal and spatial inversion symmetry; when one of these is broken, the Dirac points are split into two constituent
151:
Tilted Dirac cones in momentum space. From left to right, the tilt increases, from no tilt in the first cone to overtilt in the last. The three first are Type-I Weyl semimetals, the last one is a Type-II Weyl
1323:
Huang, Xiaochun; Zhao, Lingxiao; Long, Yujia; Wang, Peipei; Chen, Dong; Yang, Zhanhai; et al. (2015). "Observation of the chiral-anomaly-induced negative magnetoresistance in 3‑D Weyl semimetal Ta
1792:
Borisenko, Sergey; Gibson, Quinn; Evtushinsky, Danil; Zabolotnyy, Volodymyr; BĂĽchner, Bernd; Cava, Robert J. (2014). "Experimental realization of a three-dimensional Dirac semimetal".
116:
takes the shape of an upper conical surface for the electrons and a lower conical surface for the holes. The two conical surfaces touch each other and form a zero-band gap semimetal.
806:
GrĂĽneis, A.; Attaccalite, C.; Rubio, A.; Vyalikh, D.V.; Molodtsov, S.L.; Fink, J.; et al. (2009). "Angle-resolved photoemission study of the graphite intercalation compound KC
1038:
Singh, Bahadur; Sharma, Ashutosh; Lin, H.; Hasan, M.Z.; Prasad, R.; Bansil, A. (18 September 2012). "Topological electronic structure and Weyl semimetal in the TlBiSe2 class".
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Neupane, M.; Belopolski, I.; Hosen, Md.M.; Sanchez, D.S.; Sankar, R.; Szlawska, M.; et al. (2016). "Observation of topological nodal fermion semimetal phase in ZrSiS".
924:
Hsieh, D.; Xia, Y.; Qian, D.; Wray, L.; Dil, J.H.; Meier, F.; et al. (2009). "A tunable, topological insulator in the spin helical Dirac transport regime".
269:, and the material becomes a Weyl semimetal. In 2014, direct observation of the Dirac semimetal band structure using ARPES was conducted on the Dirac semimetal
577:
1140:
Weng, Hongming; Fang, Chen; Fang, Zhong; Bernevig, B. Andrei; Dai, Xi (2015). "Weyl semimetal phase in non-centrosymmetric transition-metal monophosphides".
193:
855:
Hsieh, D.; Qian, D.; Wray, L.; Xia, Y.; Hor, Y.S.; Cava, R.J.; Hasan, M.Z. (2008). "A topological Dirac insulator in a quantum spin Hall phase".
43:, with a zoomed inset showing the Dirac cones. There are 6 cones corresponding to the 6 vertices of the hexagonal first Brillouin zone.
2253:
2272:
172:, except at the zero dimensional Dirac points. As a result of the cones, electrical conduction can be described by the movement of
197:
2054:
1457:
Schoop, Leslie M.; Ali, Mazhar N.; StraĂźer, Carola; Topp, Andreas; Varykhalov, Andrei; Marchenko, Dmitry; et al. (2016).
1729:"Large single crystal growth, transport property, and spectroscopic characterizations of three-dimensional Dirac semimetal Cd
1380:
Zhang, Cheng-Long; Xu, Su-Yang; Belopolski, Ilya; Yuan, Zhujun; Lin, Ziquan; Tong, Bingbing; et al. (25 February 2016).
651:
Novoselov, K.S.; Geim, A.K.; Morozov, S.V.; Jiang, D.; Katsnelson, M.I.; Grigorieva, I.V.; et al. (10 November 2005).
376:
471:
72:
723:
432:
32:
626:
1258:
Xu, Su-Yang; Alidoust, Nasser; Belopolski, Ilya; Yuan, Zhujun; Bian, Guang; Chang, Tay-Rong; et al. (2015).
208:
56:
36:
457:
1727:
Sankar, R.; Neupane, M.; Xu, S.-Y.; Butler, C.J.; Zeljkovic, I.; Panneer
Muthuselvam, I.; et al. (2015).
139:
in 1947 and experimentally observed by the Nobel Prize laureates Andre Geim and
Konstantin Novoselov in 2005.
1660:
Neupane, Madhab; Xu, Su-Yang; Sankar, Raman; Nasser, Alidoust; Bian, Guang; Liu, Chang; et al. (2014).
563:
91:
64:
124:
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1949:
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1004:
943:
874:
819:
772:
674:
602:
538:
483:
398:
333:
212:
185:
109:
1085:"A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class"
2231:
2211:
2177:
2039:
2013:
1939:
1908:
1874:
1843:
1801:
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1635:
1609:
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664:
618:
592:
414:
388:
357:
165:
164:, where the energy of the valence and conduction bands are not equal anywhere in two dimensional
1459:"Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS"
1083:
Huang, S.-M.; Xu, S.-Y.; Belopolski, I.; Lee, C.-C.; Chang, G.; Wang, B.K.; et al. (2015).
1193:
Xu, S.-Y.; Belopolski, I.; Alidoust, N.; Neupane, M.; Bian, G.; Zhang, C.; et al. (2015).
2249:
2203:
2106:
2098:
1983:
1965:
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1827:
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546:
491:
406:
341:
270:
216:
189:
161:
1862:
1194:
173:
76:
1662:"Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd
2245:
2191:
2137:
2027:
1953:
1888:
1815:
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1695:
1623:
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105:
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622:
418:
361:
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1639:
971:
910:
702:
302:
1594:
147:
2035:
1016:
1382:"Signatures of the Adler–Bell–Jackiw chiral anomaly in a Weyl fermion semimetal"
113:
68:
2004:
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1563:
1061:
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Wehling, T.O.; Black-Schaffer, A.M.; Balatsky, A.V. (2014). "Dirac materials".
831:
614:
410:
1358:
1171:
652:
282:
132:
101:
2102:
1969:
1831:
1593:
Lu, Ling; Fu, Liang; Joannopoulos, John D.; SoljaÄŤic, Marin (17 March 2013).
1571:
1500:
1425:
1301:
894:
753:
Hasan, M.Z.; Moore, J.E. (2011). "Three-dimensional topological insulators".
507:
1861:
Terças, H.; Flayac, H.; Solnyshkov, D. D.; Malpuech, G. (11 February 2014).
1631:
1259:
1228:
262:
2207:
2165:
2110:
1987:
1904:
1839:
1778:
1713:
1518:
1443:
1236:
1126:
963:
902:
694:
550:
503:
353:
17:
2146:
1928:"The Emergence of Dirac points in Photonic Crystals with Mirror Symmetry"
669:
98:
87:
60:
40:
2121:
1863:"Non-Abelian Gauge Fields in Photonic Cavities and Photonic Superfluids"
1492:
1416:
955:
886:
686:
495:
1704:
1661:
1260:"Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide"
1108:
840:
177:
95:
48:
1961:
1760:
1293:
59:
that describe unusual electron transport properties of materials like
2199:
2093:
2076:
345:
286:
724:"Two-dimensional Dirac materials: Structure, properties, and rarity"
2182:
1546:
1475:
1398:
1341:
1276:
1211:
1154:
232:. However, this concept can be extended to three dimensions, where
188:, magnetoelectric effects in topological materials, and ultra high
2236:
2018:
1944:
1879:
1806:
1686:
1614:
1195:"Discovery of a Weyl Fermion semimetal and topological Fermi arcs"
1052:
999:
938:
869:
767:
597:
393:
146:
31:
207:
As an object with three dimensions, Dirac cones are a feature of
180:, a situation which is handled theoretically by the relativistic
578:"Interband tunneling near the merging transition of Dirac cones"
281:
Dirac points have been realized in many physical areas such as
236:
are defined by a linear dispersion relation between energy and
2164:
Jia, Shuang; Xu, Su-Yang; Hasan, M. Zahid (25 October 2016).
653:"Two-dimensional gas of massless Dirac fermions in graphene"
576:
Fuchs, Jean-Noël; Lim, Lih-King; Montambaux, Gilles (2012).
472:"A topological Dirac insulator in a quantum spin Hall phase"
324:
Novoselov, K.S.; Geim, A.K. (2007). "The rise of graphene".
135:. Isotropic Dirac cones in graphene were first predicted by
108:, in which the electronic energy and momentum have a linear
1595:"Weyl points and line nodes in gyroid photonic crystals"
439:. Research Highlights. Tohoku University. 29 August 2011
566:. Nobelprize.org, 5 October 2010. Retrieved 2011-12-31.
529:
Wallace, P. R. (1947). "The Band Theory of
Graphite".
2228:
Topological
Insulators: Fundamentals and Perspectives
460:. Physics World, Institute of Physics, 17 April 2012.
319:
317:
748:
746:
744:
75:take the shape of the upper and lower halves of a
2166:"Weyl semimetals, Fermi arcs, and chiral anomaly"
458:Dirac cones could exist in bismuth–antimony films
112:such that the electronic band structure near the
192:. Dirac cones were observed in 2008-2009, using
564:The Nobel Prize in Physics 2010 Press Release
435:. Advanced Institute for Materials Research.
215:between energy and the two components of the
8:
433:"Superconductors: Dirac cones come in pairs"
1926:He, Wen-Yu; Chan, C. T. (2 February 2015).
67:. In these materials, at energies near the
2235:
2181:
2145:
2092:
2017:
1977:
1943:
1878:
1805:
1768:
1703:
1685:
1613:
1545:
1508:
1474:
1433:
1415:
1397:
1340:
1275:
1210:
1153:
1116:
1051:
998:
937:
868:
839:
766:
755:Annual Review of Condensed Matter Physics
668:
596:
392:
194:angle-resolved photoemission spectroscopy
2055:"Weyl fermions are spotted at long last"
785:10.1146/annurev-conmatphys-062910-140432
184:. The massless fermions lead to various
2120:Vishwanath, Ashvin (8 September 2015).
313:
119:The name of Dirac cone comes from the
211:or surface states, based on a linear
204:and on several bismuth-based alloys.
7:
293:(microcavities, photonic crystals).
162:crossing-point which electrons avoid
25:
2053:Johnston, Hamish (23 July 2015).
27:Quantum effect in some non-metals
2075:Ciudad, David (20 August 2015).
375:Hasan, M.Z.; Kane, C.L. (2010).
73:valence band and conduction band
55:are features that occur in some
198:graphite intercalation compound
1897:10.1103/PhysRevLett.112.066402
1824:10.1103/PhysRevLett.113.027603
1:
79:, meeting at what are called
2036:10.1080/00018732.2014.927109
1017:10.1080/00018732.2014.927109
160:, Dirac cones are a kind of
2122:"Where the Weyl things are"
261:-space, this shows up as a
2289:
2273:Electronic band structures
2230:. Wiley. pp. 55–100.
1564:10.1103/PhysRevB.93.201104
1062:10.1103/PhysRevB.86.115208
832:10.1103/PhysRevB.80.075431
615:10.1103/PhysRevA.86.063613
411:10.1103/revmodphys.82.3045
57:electronic band structures
1359:10.1103/PhysRevX.5.031023
1172:10.1103/PhysRevX.5.011029
209:two-dimensional materials
196:(ARPES) on the potassium-
86:Typical examples include
37:Electronic band structure
377:"Topological Insulators"
1867:Physical Review Letters
1794:Physical Review Letters
1632:10.1038/nphoton.2013.42
1229:10.1126/science.aaa9297
1534:Physical Review B
1329:Physical Review X
1142:Physical Review X
1040:Physical Review B
812:Physical Review B
810:: A key to graphene".
585:Physical Review A
551:10.1103/PhysRev.71.622
153:
125:relativistic particles
92:topological insulators
65:topological insulators
44:
1674:Nature Communications
1463:Nature Communications
1386:Nature Communications
1089:Nature Communications
470:Hsieh, David (2008).
437:wpi-aimr.tohoku.ac.jp
150:
104:and some other novel
35:
2147:10.1103/Physics.8.84
2077:"Massless, yet real"
186:quantum Hall effects
2246:2014arXiv1406.1040Z
2192:2016NatMa..15.1140J
2138:2015PhyOJ...8...84V
2028:2014AdPhy..63....1W
2006:Advances in Physics
1954:2015NatSR...5E8186H
1889:2014PhRvL.112f6402T
1816:2014PhRvL.113b7603B
1753:2015NatSR...512966S
1696:2014NatCo...5.3786N
1624:2013NaPho...7..294L
1556:2016PhRvB..93t1104N
1493:10.1038/ncomms11696
1485:2016NatCo...711696S
1417:10.1038/ncomms10735
1408:2016NatCo...710735Z
1351:2015PhRvX...5c1023H
1286:2015NatPh..11..748X
1221:2015Sci...349..613X
1164:2015PhRvX...5a1029W
1101:2015NatCo...6.7373H
1009:2014AdPhy..63....1W
987:Advances in Physics
956:10.1038/nature08234
948:2009Natur.460.1101H
932:(7259): 1101–1105.
887:10.1038/nature06843
879:2008Natur.452..970H
824:2009PhRvB..80g5431G
777:2011ARCMP...2...55H
687:10.1038/nature04233
679:2005Natur.438..197N
607:2012PhRvA..86f3613F
543:1947PhRv...71..622W
496:10.1038/nature06843
488:2008Natur.452..970H
403:2010RvMP...82.3045H
338:2007NatMa...6..183G
213:dispersion relation
176:which are massless
110:dispersion relation
1932:Scientific Reports
1741:Scientific Reports
1705:10.1038/ncomms4786
1109:10.1038/ncomms8373
632:on 21 January 2023
154:
123:that can describe
45:
2255:978-3-527-33702-6
2176:(11): 1140–1144.
1962:10.1038/srep08186
1761:10.1038/srep12966
1540:(20): 201104(R).
1294:10.1038/nphys3437
1205:(6248): 613–617.
863:(7190): 970–974.
663:(7065): 197–200.
510:on 22 August 2023
482:(7190): 970–974.
158:quantum mechanics
129:quantum mechanics
16:(Redirected from
2280:
2259:
2239:
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2200:10.1038/nmat4787
2185:
2170:Nature Materials
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2094:10.1038/nmat4411
2081:Nature Materials
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1991:
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1602:Nature Photonics
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670:cond-mat/0509330
648:
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639:
637:
631:
625:. Archived from
600:
582:
573:
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561:
555:
554:
526:
520:
519:
517:
515:
506:. Archived from
467:
461:
455:
449:
448:
446:
444:
429:
423:
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396:
372:
366:
365:
346:10.1038/nmat1849
326:Nature Materials
321:
271:cadmium arsenide
260:
253:
246:
239:
234:Dirac semimetals
228:
221:
217:crystal momentum
190:carrier mobility
169:
21:
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1998:Further reading
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531:Physical Review
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174:charge carriers
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77:conical surface
28:
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1918:
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1652:
1608:(4): 294–299.
1585:
1524:
1449:
1372:
1315:
1270:(9): 748–754.
1264:Nature Physics
1250:
1185:
1132:
1075:
1046:(11): 115208.
1030:
977:
916:
847:
807:
798:
740:
715:
643:
568:
556:
537:(9): 622–634.
521:
462:
450:
424:
381:Rev. Mod. Phys
367:
332:(3): 183–191.
312:
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307:
306:
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298:
295:
278:
277:Analog systems
275:
254:
247:
240:
229:
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182:Dirac equation
144:
141:
131:, proposed by
121:Dirac equation
26:
24:
14:
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2059:Physics World
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