Dirac fermions in solids: From high-Tc cuprates and grapheneo opological insulators and Weyl semimetals

Annual Review of Condensed Matter Physics

Volumn 5, Issue 1, 2014, Pages 83-112

  Vafek, Oskar ^a   Vishwanath, Ashvin ^b  

^a Florida State University   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

d wave superconductors; Dirac fermions; graphene; topological insulators; Weyl semimetals

Indexed keywords

GRAPHENE; LINEAR EQUATIONS; PARTICLES (PARTICULATE MATTER); SOLIDS; SUPERCONDUCTING MATERIALS;

CONDENSED MATTER SYSTEM; D-WAVE SUPERCONDUCTORS; DIRAC FERMIONS; ELECTRONIC SYSTEMS; MASSLESS DIRAC FERMIONS; QUANTUM FIELD THEORY; RESEARCH FRONTIERS; TOPOLOGICAL INSULATORS;

ELECTRIC INSULATORS;

EID: 84896326204     PISSN: 19475454     EISSN: 19475462     Source Type: Journal    
DOI: 10.1146/annurev-conmatphys-031113-133841     Document Type: Article

References (162)

1. Dirac PAM. 1928. Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 117(778):610-24
2. Wilczek F. 2009. Nat. Phys. 5:614-8
3. Weyl H. 1929. Z. Phys. 56:330-52
4. Majorana E. 1937. Nuovo Cim. 14:171-84
5. Beenakker CWJ. 2013. Annu. Rev. Condens. Matter Phys. 4:113-36
6. Nielsen HB, Ninomiya M. 1981. Nucl. Phys. B 185:20-40
7. Itzykson C, Drouffe J-M. 1989. Statistical Field Theory, Vol. 1. Cambridge, UK: Cambridge Univ. Press, 403 pp.
8. Haldane FDM. 1988. Phys. Rev. Lett. 61:2015-8
9. Buttner B, Liu CX, Tkachov G, Novik EG, Brüne C, et al. 2011. Nat. Phys. 7:418-22
10. Maciejko J, Hughes TL, Zhang S-C. 2011. Annu. Rev. Condens. Matter Phys. 2:31-53
11. Kaplan DB. 1992. Phys. Lett. B 288:342-7
12. Kaplan DB, Sun S. 2012. Phys. Rev. Lett. 108:181807
13. Volkov BA, Pankratov OA. 1985. JETP Lett. 42:178-81
14. Fradkin E, Dagotto E, Boyanovsky D. 1986. Phys. Rev. Lett. 57:2967-70
15. Boyanovsky D, Dagotto E, Fradkin E. 1987. Nucl. Phys. B 285:340-62
16. Fu L, Kane CL, Mele EJ. 2007. Phys. Rev. Lett. 98:106803
17. Fu L, Kane CL. 2007. Phys. Rev. B 76:045302
18. Thaller B. 1992. The Dirac Equation. New York: Springer-Verlag
19. Ludwig AWW, Fisher MPA, Shankar R, Grinstein G. 1994. Phys. Rev. B 50:7526-52
20. Young AF, Kim P. 2011. Annu. Rev. Condens. Matter Phys. 2:101-20
21. Schwinger J. 1951. Phys. Rev. 82:664-79
22. Allor D, Cohen TD, McGady DA. 2008. Phys. Rev. D Part. Fields Gravit. Cosmol. 78:096009
23. Dora B, Moessner R. 2010. Phys. Rev. B 81:165431
24. Rosenstein B, Lewkowicz M, Kao HC, Korniyenko Y. 2010. Phys. Rev. B 81:041416
25. Gavrilov SP, Gitman DM, Yokomizo N. 2012. Phys. Rev. D Part. Fields Gravit. Cosmol. 86:125022
26. Brey L, Fertig HA. 2009. Phys. Rev. Lett. 103:046809
27. Castro Neto AH, Guinea F, Peres NMR, Novoselov KS, Geim AK. 2009. Rev. Mod. Phys. 81:109-62
28. MacDonald AH. 1983. Phys. Rev. B 28:2235-6
29. Lukose V, Shankar R, Baskaran G. 2007. Phys. Rev. Lett. 98:116802
30. Jackiw R, Rebbi C. 1976. Phys. Rev. D Part. Fields 13:3398-409
31. Rice MJ, Mele EJ. 1982. Phys. Rev. Lett. 49:1455-9
32. Su WP, Schrieffer JR, Heeger AJ. 1979. Phys. Rev. Lett. 42:1698-701
33. Jackiw R, Schrieffer JR. 1981. Nucl. Phys. B 190:253-65
34. Heeger AJ, Kivelson S, Schrieffer JR, Su W-P. 1988. Rev. Mod. Phys. 60:781-850
35. Jackiw R, Rossi P. 1981. Nucl. Phys. B 190:681-91
36. Weinberg EJ. 1981. Phys. Rev. D Part. Fields 24:2669-73
37. Bell JS, Jackiw R. 1969. Nuovo Cim., A 60:47-61
38. Adler SL. 1969. Phys. Rev. 177:2426-38
39. Bertlmann RA. 1996. Anomalies in Quantum Field Theory. New York: Oxford Univ. Press
40. Peskin ME, Schroeder DV. 1995. An Introduction to Quantum Field Theory. Cambridge, MA: Perseus Books, 842 pp.
41. Smythe WR. 1950. Static and Dynamic Electricity. York, Pa.: McGraw-Hill, 616 pp. 2nd ed.
42. Emelyanenko A, Boinovich L. 2008. J. Phys. Condens. Matter 20:494227
43. Wehling TO, Sasoglu E, Friedrich C, Lichtenstein AI, Katsnelson MI, Blügel S. 2011. Phys. Rev. Lett. 106:236805
44. Herbut IF. 2006. Phys. Rev. Lett. 97:146401
45. Giuliani A, Mastropietro V. 2010. Commun. Math. Phys. 293:301-46
46. Giuliani A, Mastropietro V. 2009. Phys. Rev. B 79:201403
47. Fisher MPA, Grinstein G, Girvin SM. 1990. Phys. Rev. Lett. 64:587-90
48. Herbut IF. 2001. Phys. Rev. Lett. 87:137004(4)
49. Gonzalez J, Guinea F, Vozmediano MAH. 1994. Nucl. Phys. B 424:595-618
50. Vafek O. 2007. Phys. Rev. Lett. 98:216401(4)
51. Sheehy DE, Schmalian J. 2007. Phys. Rev. Lett. 99:226-803
52. Herbut IF, Juricic V, Vafek O. 2008. Phys. Rev. Lett. 100:046403
53. Mishchenko EG. 2008. Europhys. Lett. 83:17005
54. Sheehy DE, Schmalian J. 2009. Phys. Rev. B 80:193411
55. Juricic V, Vafek O, Herbut IF. 2010. Phys. Rev. B 82:235402
56. Sodemann I, Fogler MM. 2012. Phys. Rev. B 86:115408
57. Kotov VN, Uchoa B, Casto-Neto AH. 2008. Phys. Rev. B 78:035119
58. Rosenstein B, Lewkowicz M, Maniv T. 2013. Phys. Rev. Lett. 110:066602
59. Khveshchenko DV. 2001. Phys. Rev. Lett. 87:246802
60. Leal H, Khveshchenko DV. 2004. Nucl. Phys. B 687:323-31
61. Herbut IF, Juricic V, Vafek O. 2009. Phys. Rev. B 80:075432
62. Sorella S, Tosatti E. 1992. Europhys. Lett. 19:699-704
63. Paiva T, Scalettar RT, Zheng W, Singh RRP, Oitmaa J. 2005. Phys. Rev. B 72:085123
64. Meng ZY, Lang TC, Wessel S, Assaad FF, Muramatsu A. 2010. Nature 464:847-51
65. Sorella S, Otsuka Y, Yunoki S. 2012. Sci. Rep. 2:992
66. Assaad FF, Herbut IF. 2013. arXiv:1304:6340
67. Drut JE, Lähde TA. 2009. Phys. Rev. Lett. 102:026802
68. Drut JE, Lähde TA. 2009. Phys. Rev. B 79:241405
69. Drut JE, Lähde TA. 2009. Phys. Rev. B 79:165425
70. Brower RC, Rebbi C, Schaich D. 2011. arXiv:1101.5131 [hep-lat]
71. Brower R, Rebbi C, Schaich D. 2012. arXiv:1204.5424 [hep-lat]
72. Buividovich PV, Luschevskaya EV, Pavlovsky OV, Polikarpov MI, Ulybyshev MV. 2012. Phys.Rev. B 86:045107
73. Buividovich PV, Polikarpov MI. 2012. Phys. Rev. B 86:245117
74. Ulybyshev MV, Buividovich PV, Katsnelson MI, Polikarpov MI. 2013. arXiv:1304.3660 [condmat. str-el]
75. Geim AK, MacDonald AK. 2007. Phys. Today 60:35-41
76. Slater JC, Koster GF. 1954. Phys. Rev. 94:1498-524
77. Kane CL, Mele EJ. 2005. Phys. Rev. Lett. 95:226801
78. Yao Y, Ye F, Qu X-L, Zhang S-C, Fang Z. 2007. Phys. Rev. B 75:041401
79. Min H, Hill JE, Sinitsyn NA, Sahu BR, Kleinman L, MacDonald AH. 2006. Phys. Rev. B 74:165310
80. Luttinger JM, Kohn W. 1955. Phys. Rev. 97:869-83
81. DiVincenzo DP, Mele EJ. 1984. Phys. Rev. B 29:1685-94
82. Miller DL, Kubista KD, Rutter GM, Ruan M, de Heer WA, et al. 2009. Science 324:924-7
83. Li G, Luican A, Andrei EY. 2009. Phys. Rev. Lett. 102:176804
84. Luican A, Li G, Andrei EY. 2011. Phys. Rev. B 83:041405
85. Vandecasteele N, Barreiro A, Lazzeri M, Bachtold A, Mauri F. 2010. Phys. Rev. B 82:045416
86. Nair RR, Blake P, Grigorenko AN, Novoselov KS, Booth TJ, et al. 2008. Science 320:1308
87. Li ZQ, Henriksen EA, Jiang Z, Hao Z, Martin MC, et al. 2008. Nat. Phys. 4:532-5
88. Elias DC, Gorbechev RV, Mayorov AS, Morozov SV, Zhukov AA, et al. 2011. Nat. Phys. 7:701-4
89. Guinea F, Katsnelson MI, Geim AK. 2010. Nat. Phys. 6:30-3
90. Levy N, Burke SA, Meaker KL, Panlasigui M, Zettl A, et al. 2010. Science 329:544-7
91. Vozmediano MAH, Katsnelson MI, Guinea F. 2010. Phys. Rep. 496:109-48
92. Wang Y, Wong D, Shytov AV, Brar VW, Choi S, et al. 2013. 340:737-40
93. Das Sarma S, Adam S, Hwang EH, Rossi E. 2011. Rev. Mod. Phys. 83:407-70
94. Moore JE, Balents L. 2007. Phys. Rev. B 75:121306
95. Roy R. 2009. Phys. Rev. B 79:195322
96. Zhang H, Liu C-X, Qi X-L, Dai X, Fang Z, et al. 2009. Nat. Phys. 6:438-42
97. Liu C-X, Qi X-L, Zhang H, Dai X, Fang Z, et al. 2010. Phys. Rev. B 82:045122
98. Hasan MZ, Moore JE. 2011. Annu. Rev. Condens. Matter Phys. 2:55-78
99. Harrison W. 1989. Electronic Structure and the Properties of Solids. Mineola, NY: Dover Publications, Inc
100. Ando T, Nakanishi T. 1998. J. Phys. Soc. Jpn. 67:1704-13
101. Bardarson JH, Twordzyo J, Brouwer PW, Beenakker CWJ. 2007. Phys. Rev. Lett. 99:106801
102. Nomura K, Koshino M, Ryu S. 2007. Phys. Rev. Lett. 99:146806
103. Lewenkopf CH, Mucciolo ER, Castro Neto AH. 2008. Phys. Rev. B 77:081410
104. McCann E, Kechedzhi K, Falko VI, Suzuura H, Ando T, Altshuler BL. 2006. Phys. Rev. Lett. 97:146805
105. Aleiner IL, Efetov KB. 2006. Phys. Rev. Lett. 97:236801
106. Shon NH, Ando T. 1998. J. Phys. Soc. Jpn. 67:2421-9
107. Mucciolo ER, Lewenkopf CH. 2010. J. Phys. Condens. Matter 22:273201
108. Schubert G, Fehske H, Fritz L, Vojta M. 2012. Phys. Rev. B 85:201105
109. Ostrovsky PM, Gornyi IV, Mirlin AD. 2010. Phys. Rev. Lett. 105:036803
110. Bardarson JH, Moore JE. 2012. arXiv:1209.3280 [cond-mat.mes-hall]
111. Lee DH. 2009. Phys. Rev. Lett. 103:196804
112. Vafek O. 2011. Phys. Rev. B 84:245417
113. Zhang Y-Y, Wang X-R, Xie XC. 2012. J. Phys. Condens. Matter 24:015004
114. Brüne C, Liu CX, Novik EG, Hankiewicz EM, Buhmann H, et al. 2011. Phys. Rev. Lett. 106:126803
115. Dolgopolov VT, Shashkin AA, Zhitenev NB, Dorozhkin SI. 1992. Phys. Rev. B 46:12560-7
116. Wilczek F. 1987. Phys. Rev. Lett. 58:1799-802
117. Qi X-L, Hughes TL, Zhang SC. 2008. Phys. Rev. B 78:195424
118. Franz M. 2008. Physics 1:36
119. Essin AM, Moore JE, Vanderbilt D. 2009. Phys. Rev. Lett. 102:146805
120. Van Harlingen DJ. 1995. Rev. Mod. Phys. 67:515-35
121. Kirtley JR, Tsuei CC. 2000. Rev. Mod. Phys. 72:969-1016
122. Kirtley JR, Tsuei CC, Ariando, Verwijs CJM, Harkema S, Hilgenkamp H. 2006. Nat. Phys. 2:190-4
123. Volovik GE. 1993. JETP Lett. 58:457-61
124. Wang Y, MacDonald AH. 1995. Phys. Rev. B 52:R3876-9
125. Simon SH, Lee PA. 1997. Phys. Rev. Lett. 78:1548-51
126. Yasui K, Kita T. 1999. Phys. Rev. Lett. 83:4168-71
127. Franz M, Tesanovic Z. 2000. Phys. Rev. Lett. 84:554-7
128. Marinelli L, Halperin BI, Simon SH. 2000. Phys. Rev. B 62:3488-501
129. Vafek O, Melikyan A, Franz M, Tesanovic Z. 2001. Phys. Rev. B 63:134509
130. Vishwanath A. 2001. Phys. Rev. Lett. 87:217004
131. Vafek O, Melikyan A, Tesanovic Z. 2001. Phys. Rev. B 64:224508
132. Vishwanath A. 2002. Phys. Rev. B 66:064504
133. Hussey NE, Abdel-Jawad M, Carrington A, Mackenzie AP, Balicas L. 2003. Nature 425:814-7
134. Vignolle B, Carrington A, Cooper RA, French MMJ, Mackenzie AP, et al. 2008. Nature 455:952-5
135. Melikyan A, Tesanovic Z. 2007. Phys. Rev. B 76:094509
136. Vafek O, Melikyan A. 2006. Phys. Rev. Lett. 96:167005
137. Melikyan A, Vafek O. 2008. Phys. Rev. B 78:020502
138. Melikyan A, Tesanovic Z. 2006. Phys. Rev. B 74:144501
139. Fournier D, Levy G, Pennec Y, McChesney JL, Bostwick A, et al. 2010. Nat. Phys. 6:905-18
140. Riggs SC, Vafek O, Kemper JB, Betts JB, Migliori A, et al. 2011. Nat. Phys. 7:332-5
141. Moler KA, Baar DJ, Urbach JS, Liang R, Hardy WN, Kapitulnik A. 1994. Phys. Rev. Lett. 73:2744-7
142. Wang Y, Revaz B, Erb A, Junod A. 2001. Phys. Rev. B 63:094508
143. Fisher RA, Gordon JE, Phillips N. 2007. Handbook of High-Temperature Superconductivity, ed. JR Schrieffer, JS Brooks, pp. 326-97. New York: Springer
144. Von Neumann J, Wigner E. 1929. Phys. Z. 30:467-70
145. Herring C. 1937. Phys. Rev. 52:365-73
146. Wan X, Turner AM, Vishwanath A, Savrasov SY. 2011. Phys. Rev. B 83:205101
147. Murakami S. 2007. New J. Phys. 9:356
148. Yang KY, Lu YM, Ran Y. 2011. Phys. Rev. B 84:075129
149. Delplace P, Li J, Carpentier D. 2012. Europhys. Lett. 97:67004
150. Balents L. 2011. Physics 4:36
151. Son DT, Yamamoto N. 2012. Phys. Rev. Lett. 109:181602
152. Yanagishima D, Maeno Y. 2001. J. Phys. Soc. Jpn. 70:2880-3
153. Taira N, Wakeshima M, Hinatsu Y. 2001. J. Phys. Condens. Matter 13:5527-33
154. Zhao S, Mackie JM, MacLaughlin DE, Bernal OO, Ishikawa JJ, et al. 2011. Phys. Rev. B 83:180402
155. Tafti FF, Ishikawa JJ, McCollam A, Nakatsuji S, Julian SR. 2012. Phys. Rev. B 85:205104
156. Wan X, Vishwanath A, Savrasov SY. 2012. Phys. Rev. Lett. 108:146601
157. Xu G, Weng H, Wang Z, Dai X, Fang Z. 2011. Phys. Rev. Lett. 107:186806
158. Burkov AA, Balents L. 2011. Phys. Rev. Lett. 107:127205
159. Halász G, Balents L. 2012. Phys. Rev. B 85:035103
160. Ling L, Fu L, Joannopoulos JD, Soljacic M. 2013. Nat. Photonics 7:294-9
161. Manes JL. 2012. Phys. Rev. B 85:155118
162. Turner A, Vishwanath A. 2013. arXiv:1301.0330 [cond-mat.str-el]