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Dirac cone

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33: 148: 2225:
Hasan, M. Z.; Xu, S.-Y.; Neupane, M. (2015). "Chapter 4: Topological insulators, topological Dirac semimetals, topological crystalline insulators, and topological Kondo insulators". In Ortmann, Frank; Roche, Stephan; Valenzuela, Sergio O. (eds.).
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".
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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
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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".
1532:
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).
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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).
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in 1947 and experimentally observed by the Nobel Prize laureates Andre Geim and Konstantin Novoselov in 2005.
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Neupane, Madhab; Xu, Su-Yang; Sankar, Raman; Nasser, Alidoust; Bian, Guang; Liu, Chang; et al. (2014).
563: 91: 64: 124: 2241: 2187: 2133: 2023: 1949: 1884: 1811: 1748: 1691: 1619: 1551: 1480: 1403: 1346: 1281: 1216: 1159: 1096: 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: 1681: 1635: 1609: 1575: 1541: 1470: 1393: 1362: 1336: 1305: 1271: 1240: 1206: 1175: 1149: 1065: 1047: 1020: 994: 967: 933: 906: 864: 788: 762: 698: 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).
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Xu, S.-Y.; Belopolski, I.; Alidoust, N.; Neupane, M.; Bian, G.; Zhang, C.; et al. (2015).
2249: 2203: 2106: 2098: 1983: 1965: 1900: 1835: 1827: 1774: 1709: 1567: 1514: 1496: 1439: 1421: 1297: 1232: 1122: 959: 898: 890: 690: 499: 349: 157: 128: 784: 2195: 2141: 2088: 2031: 1973: 1957: 1892: 1819: 1764: 1756: 1699: 1627: 1559: 1504: 1488: 1429: 1411: 1354: 1289: 1224: 1167: 1112: 1104: 1057: 1012: 951: 882: 835: 827: 780: 682: 610: 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: 1752: 1695: 1623: 1555: 1484: 1407: 1350: 1285: 1220: 1163: 1100: 1008: 947: 878: 823: 776: 678: 606: 542: 487: 402: 337: 1978: 1927: 1769: 1728: 1509: 1458: 1434: 1381: 1117: 1084: 266: 181: 120: 2266: 2043: 1579: 1309: 1244: 1069: 1024: 290: 136: 105: 1912: 1847: 1366: 1179: 792: 622: 418: 361: 2215: 1896: 1823: 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:
Wehling, T.O.; Black-Schaffer, A.M.; Balatsky, A.V. (2014). "Dirac materials".
1563: 1061: 985:
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
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are defined by a linear dispersion relation between energy and
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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".
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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: 2219: 2200:10.1038/nmat4787 2185: 2170:Nature Materials 2158: 2156: 2154: 2149: 2114: 2096: 2094:10.1038/nmat4411 2081:Nature Materials 2069: 2067: 2065: 2047: 2021: 1992: 1991: 1981: 1947: 1923: 1917: 1916: 1882: 1858: 1852: 1851: 1809: 1789: 1783: 1782: 1772: 1724: 1718: 1717: 1707: 1689: 1657: 1651: 1650: 1648: 1646: 1617: 1602:Nature Photonics 1599: 1590: 1584: 1583: 1549: 1529: 1523: 1522: 1512: 1478: 1454: 1448: 1447: 1437: 1419: 1401: 1377: 1371: 1370: 1344: 1320: 1314: 1313: 1279: 1255: 1249: 1248: 1214: 1190: 1184: 1183: 1157: 1137: 1131: 1130: 1120: 1080: 1074: 1073: 1055: 1035: 1029: 1028: 1002: 982: 976: 975: 941: 921: 915: 914: 872: 852: 846: 845: 843: 803: 797: 796: 770: 750: 739: 738: 736: 734: 720: 714: 713: 711: 709: 672: 670:cond-mat/0509330 648: 642: 641: 639: 637: 631: 625:. 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Phys 367: 332:(3): 183–191. 312: 310: 307: 306: 305: 298: 295: 278: 277:Analog systems 275: 254: 247: 240: 229: 222: 201: 182:Dirac equation 144: 141: 131:, proposed by 121:Dirac equation 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 2285: 2274: 2271: 2270: 2268: 2257: 2251: 2247: 2243: 2238: 2233: 2229: 2223: 2222: 2217: 2213: 2209: 2205: 2201: 2197: 2193: 2189: 2184: 2179: 2175: 2171: 2167: 2162: 2161: 2148: 2143: 2139: 2135: 2131: 2127: 2123: 2118: 2117: 2112: 2108: 2104: 2100: 2095: 2090: 2086: 2082: 2078: 2073: 2072: 2060: 2059:Physics World 2056: 2051: 2050: 2045: 2041: 2037: 2033: 2029: 2025: 2020: 2015: 2011: 2007: 2002: 2001: 1997: 1989: 1985: 1980: 1975: 1971: 1967: 1963: 1959: 1955: 1951: 1946: 1941: 1937: 1933: 1929: 1922: 1919: 1914: 1910: 1906: 1902: 1898: 1894: 1890: 1886: 1881: 1876: 1873:(6): 066402. 1872: 1868: 1864: 1857: 1854: 1849: 1845: 1841: 1837: 1833: 1829: 1825: 1821: 1817: 1813: 1808: 1803: 1800:(2): 027603. 1799: 1795: 1788: 1785: 1780: 1776: 1771: 1766: 1762: 1758: 1754: 1750: 1746: 1742: 1738: 1723: 1720: 1715: 1711: 1706: 1701: 1697: 1693: 1688: 1683: 1679: 1675: 1671: 1656: 1653: 1641: 1637: 1633: 1629: 1625: 1621: 1616: 1611: 1607: 1603: 1596: 1589: 1586: 1581: 1577: 1573: 1569: 1565: 1561: 1557: 1553: 1548: 1543: 1539: 1535: 1528: 1525: 1520: 1516: 1511: 1506: 1502: 1498: 1494: 1490: 1486: 1482: 1477: 1472: 1468: 1464: 1460: 1453: 1450: 1445: 1441: 1436: 1431: 1427: 1423: 1418: 1413: 1409: 1405: 1400: 1395: 1391: 1387: 1383: 1376: 1373: 1368: 1364: 1360: 1356: 1352: 1348: 1343: 1338: 1335:(3): 031023. 1334: 1330: 1326: 1319: 1316: 1311: 1307: 1303: 1299: 1295: 1291: 1287: 1283: 1278: 1273: 1269: 1265: 1261: 1254: 1251: 1246: 1242: 1238: 1234: 1230: 1226: 1222: 1218: 1213: 1208: 1204: 1200: 1196: 1189: 1186: 1181: 1177: 1173: 1169: 1165: 1161: 1156: 1151: 1148:(1): 011029. 1147: 1143: 1136: 1133: 1128: 1124: 1119: 1114: 1110: 1106: 1102: 1098: 1094: 1090: 1086: 1079: 1076: 1071: 1067: 1063: 1059: 1054: 1049: 1045: 1041: 1034: 1031: 1026: 1022: 1018: 1014: 1010: 1006: 1001: 996: 992: 988: 981: 978: 973: 969: 965: 961: 957: 953: 949: 945: 940: 935: 931: 927: 920: 917: 912: 908: 904: 900: 896: 892: 888: 884: 880: 876: 871: 866: 862: 858: 851: 848: 842: 837: 833: 829: 825: 821: 818:(7): 075431. 817: 813: 802: 799: 794: 790: 786: 782: 778: 774: 769: 764: 760: 756: 749: 747: 745: 741: 729: 725: 719: 716: 704: 700: 696: 692: 688: 684: 680: 676: 671: 666: 662: 658: 654: 647: 644: 628: 624: 620: 616: 612: 608: 604: 599: 594: 591:(6): 063613. 590: 586: 579: 572: 569: 565: 560: 557: 552: 548: 544: 540: 536: 532: 525: 522: 509: 505: 501: 497: 493: 489: 485: 481: 477: 473: 466: 463: 459: 454: 451: 438: 434: 428: 425: 420: 416: 412: 408: 404: 400: 395: 390: 386: 382: 378: 371: 368: 363: 359: 355: 351: 347: 343: 339: 335: 331: 327: 320: 318: 314: 308: 304: 301: 300: 296: 294: 292: 291:nanophotonics 288: 284: 276: 274: 272: 268: 264: 235: 218: 214: 210: 205: 199: 195: 191: 187: 183: 179: 175: 171: 163: 159: 149: 142: 140: 138: 137:P. R. Wallace 134: 130: 126: 122: 117: 115: 111: 107: 106:nanomaterials 103: 100: 97: 93: 89: 84: 82: 78: 74: 70: 66: 62: 58: 54: 50: 42: 39:of monolayer 38: 34: 30: 19: 2227: 2173: 2169: 2151:. Retrieved 2129: 2125: 2084: 2080: 2062:. Retrieved 2058: 2009: 2005: 1935: 1931: 1921: 1870: 1866: 1856: 1797: 1793: 1787: 1744: 1740: 1722: 1677: 1673: 1655: 1643:. Retrieved 1605: 1601: 1588: 1537: 1533: 1527: 1469:(1): 11696. 1466: 1462: 1452: 1392:(1): 10735. 1389: 1385: 1375: 1332: 1328: 1324: 1318: 1267: 1263: 1253: 1202: 1198: 1188: 1145: 1141: 1135: 1092: 1088: 1078: 1043: 1039: 1033: 990: 986: 980: 929: 925: 919: 860: 856: 850: 815: 811: 801: 758: 754: 731:. Retrieved 727: 718: 706:. Retrieved 660: 656: 646: 634:. Retrieved 627:the original 588: 584: 571: 559: 534: 530: 524: 512:. Retrieved 508:the original 479: 475: 465: 453: 441:. 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Index

Dirac point
Brillouin zone in graphene
Electronic band structure
graphene
physics
electronic band structures
graphene
topological insulators
Fermi level
valence band and conduction band
conical surface
graphene
topological insulators
bismuth
antimony
thin films
nanomaterials
dispersion relation
Fermi level
Dirac equation
relativistic particles
quantum mechanics
Paul Dirac
P. R. Wallace

quantum mechanics
crossing-point which electrons avoid
lattice k-space
charge carriers
fermions

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