[1] |
Stöckmann H J 1999 Quantum Chaos: An Introduction (New York: Cambridge University Press)
|
[2] |
Gutzwiller M 1990 Chaos in Classical and Quantum Mechanics (Berlin: Springer)
|
[3] |
Haake F 2010 Quantum Signatures of Chaos (Springer)
|
[4] |
Bohigas G and Giannoni M J 1984 Mathematical and Computational Methods in Nuclear Physics, Lecture Notes in Physics, Vol. 209 (Berlin: Springer)
|
[5] |
Bohigas G, Giannoni M J and Schmit C 1984 Phys. Rev. Lett. 52 1
|
[6] |
Berry M V 1985 Proc. R. Soc. London A 400 229
|
[7] |
Weidenmüller H A and Mitchell G E 2009 Rev. Mod. Phys. 81 539
|
[8] |
A requirement for the applicability of random-matrix theory is that the system possess no geometric symmetry.
|
[9] |
Stoffregen U, Stein J, Stöckmann H J, Kuś M and Haake F 1995 Phys. Rev. Lett. 74 2666
|
[10] |
So P, Anlage S M, Ott E and Oerter R N 1995 Phys. Rev. Lett. 74 2662
|
[11] |
Beenakker C W J 2008 Rev. Mod. Phys. 80 1337
|
[12] |
Castro N A H, Guinea F, Peres N M R, Novoselov K S and Geim A K 2009 Rev. Mod. Phys. 81 109
|
[13] |
Peres N M R 2010 Rev. Mod. Phys. 82 2673
|
[14] |
Das Sarma S, Adam S, Hwang E H and Rossi E 2011 Rev. Mod. Phys. 83 407
|
[15] |
Konig M, Wiedmann S, Brune C, Roth A, Buhmann H, Molenkamp L W, Qi X L and Zhang S C 2007 Science 318 766
|
[16] |
Hsieh D, Qian D, Wray L, Xia Y, Hor Y S, Cava R J and Hasan M Z 2008 Nature 452 970
|
[17] |
Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045
|
[18] |
Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057
|
[19] |
Wurm J, Rycerz A, Adagideli I, Wimmer M, Richter K and Baranger H U 2009 Phys. Rev. Lett. 102 056806
|
[20] |
Huang L, Lai Y C, Ferry D K, Goodnick S M and Akis R 2009 Phys. Rev. Lett. 103 054101
|
[21] |
Xu H Y, Huang L, Lai Y C and Grebogi C 2013 Phys. Rev. Lett. 110 064102
|
[22] |
Yang R, Huang L, Lai Y C and Grebogi C 2011 Europhys. Lett. 94 40004
|
[23] |
Ying L, Huang L, Lai Y C and Grebogi C 2012 Phys. Rev. B 85 245448
|
[24] |
Yang R, Huang L, Lai Y C and Pecora L M 2012 Appl. Phys. Lett. 100 093105
|
[25] |
Yang R, Huang L, Lai Y C, Grebogi C and Pecora L M 2013 Chaos 23 013125
|
[26] |
Miao F, Wijeratne S, Zhang Y, Coskun U C, Bao W and Lau C N 2007 Science 317 1530
|
[27] |
Ponomarenko L A, Schedin F, Katsnelson M I, Yang R, Hill E W, Novoselov K S and Geim A K 2008 Science 320 356
|
[28] |
Stampfer C, Schurtenberger E, Molitor F, Güttinger J, Ihn T and Ensslin K 2008 Nano Lett. 8 2378
|
[29] |
Tan C L, Tan Z B, Ma L, Chen J, Yang F, Qu F M, Liu G T, Yang H F, Yang C L and Lü L 2009 Acta Phys. Sin. 58 5726 (in Chinese)
|
[30] |
Chen M, Fu Z G, Peng J P, Zheng F, Zhang H M, Feng X, Chang C Z, He K, Wang L, Zhang P, Ma X and Xue Q K 2013 arXiv:1312.4757v1[cond-mat.mes-hall]
|
[31] |
Berry M V and Mondragon R J 1987 Proc. R. Soc. London, Ser. A 412 53
|
[32] |
Neutrinos have a minuscule, but nonzero mass. See Karagiorgi G, Aguilar-Arevalo A, Conrad J M, Shaevitz M H, Whisnant K, Sorel M and Barger V 2007 Phys. Rev. D 75 013011
|
[33] |
Phatak S C, Pal S and Biswas D 1995 Phys. Rev. E 52 1333
|
[34] |
Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V and Firsov A A 2004 Science 306 666
|
[35] |
Akhmerov A R and Beenakker C W J 2007 Phys. Rev. Lett. 98 157003
|
[36] |
Xiao D, Yao W and Niu Q 2007 Phys. Rev. Lett. 99 236809
|
[37] |
Garcia-Pomar J L, Cortijo A and Nieto-Vesperinas M 2008 Phys. Rev. Lett. 100 236801
|
[38] |
Berry M V and Tabor M 1977 Proc. Roy. Soc. London, Ser. A 356 375
|
[39] |
Mehta M L 1967 Random Matrices (New York: Academic)
|
[40] |
Bohr A and Mottelson B R 1969 Nuclear Structure, Vol. 1 (New York: Benjamin) Appendix 2C, pp. 294-301
|
[41] |
Here we do not consider GSE since it is irrelevant to our studies.
|
[42] |
Dyson F J and Mehta M L 1963 J. Math. Phys. 4 701
|
[43] |
Bohigas O and Giannoni M J 1975 Ann. Phys. 89 393
|
[44] |
Liu B, Zhang G C, Ding L, Dai J H and Zhang H J 1999 Phys. Lett. A 260 406
|
[45] |
Hasegawa H, Mikeska H J and Frahm H 1988 Phys. Rev. A 38 395
|
[46] |
Li B W, Robnik M and Hu B 1998 Phys. Rev. E 57 4095
|
[47] |
Ni X, Huang L, Ying L and Lai Y C 2013 Phys. Rev. B 87 224304
|
[48] |
Ni X, Huang L, Lai Y C and Grebogi C 2012 Phys. Rev. E 86 016702
|
[49] |
Ni X, Huang L, Lai Y C and Pecora LM2012 Europhys. Lett. 98 50007
|
[50] |
Huang L, Lai Y C and Grebogi C 2011 Chaos 21 013102
|
[51] |
Saito R, Dresselhaus G and Dresselhaus M S 2000 Phys. Rev. B 61 2981
|
[52] |
Rycerz A, Tworzydło J and Beenakker C W J 2007 Nat. Phys. 3 172
|
[53] |
Cheianov V V, Fal'ko V and Altshuler B L 2007 Science 315 1252
|
[54] |
Garcia-Pomar J L, Cortijo A and Nieto-Vesperinas M 2008 Phys. Rev. Lett. 100 236801
|
[55] |
Libisch F, Stampfer C and Burgdörfer J 2009 Phys. Rev. B 79 115423
|
[56] |
Amanatidis I and Evangelou S N 2009 Phys. Rev. B 79 205420
|
[57] |
Amanatidis H, Kleftogiannis I, Katsanos D E and Evangelou S N 2013 arXiv:1302.2470 [cond-mat.dis-nn]
|
[58] |
Rycerz A 2012 Phys. Rev. B 85 245424
|
[59] |
Reich S, Maultzsch J, Thomsen C and Ordejon P 2002 Phys. Rev. B 66 035412
|
[60] |
Son Y W, Cohen M L and Louie S G 2006 Phys. Rev. Lett. 97 216803
|
[61] |
Lanczos C 1950 J. Res. Natl. Bur. Stand. 45 255
|
[62] |
Chen J H, Jang C, Adam S, Fuhrer M S, Williams E D and Ishigami M 2008 Nat. Phys. 4 377
|
[63] |
Huang L, Lai Y C and Grebogi C 2010 Phys. Rev. E 81 055203
|
[64] |
Berry M V and Robnik M 1986 J. Phys. A: Math. Gen. 19 649
|
[65] |
The magnetic field can be scaled down for larger confinements to yield similar effects.
|
[66] |
Brey L and Fertig H A 2006 Phys. Rev. B 73 235411
|
[67] |
Suzuura H and Ando T 2002 Phys. Rev. Lett. 89 266603
|
[68] |
Robnik M and Berry M V 1986 J. Phys. A: Math. Gen. 19 669
|
[69] |
Robnik M 1986 Quantum Chaos and Statistical Nuclear Physics, Lecture Notes in Physcs, Vol. 263 (Berlin: Springer-Verlag)
|
[70] |
Alhassid Y and Lewenkopf C H 1995 Phys. Rev. Lett. 75 3922
|
[71] |
Robnik M and Berry M V 1985 J. Phys. A 18 1361
|
[72] |
Robnik M 1986 Nonlinear Phenomena and Chaos, Malvern Physics Series (Bristol: Adam-Hilger)
|
[73] |
Robnik M 1986 J. Phys. A 19 3619
|
[74] |
Wimmer M, Akhmerov A R and Guinea F 2010 Phys. Rev. B 82 045409
|
[75] |
Bell R J and Dean P 1970 Discuss. Faraday Soc. 50 55
|
[76] |
Bell R J 1972 Rep. Prog. Phys. 35 1315
|
[77] |
Fujita M, Wakabayashi K, Nakada K and Kusakabe K 1996 J. Phys. Soc. Jpn. 65 1920
|
[78] |
Wimmer M, Adagideli I, Berber S and Tománek D and Richter K 2008 Phys. Rev. Lett. 100 177207
|
[79] |
Nomura K, Koshino M and Ryu S 2007 Phys. Rev. Lett. 99 146806
|
[80] |
Ryu S, Mudry C, Obuse H and Furusaki A 2007 Phys. Rev. Lett. 99 116601
|
[81] |
Ostrovsky P M, Gornyi I V and Mirlin A D 2007 Phys. Rev. Lett. 98 256801
|
[82] |
Bena C 2008 Phys. Rev. Lett. 100 076601
|
[83] |
Brihuega I, Mallet P, Bena C, Bose S, Michaelis C, Vitali L, Varchon F, Magaud L, Kern K and Veuillen J Y 2008 Phys. Rev. Lett. 101 206802
|
[84] |
Ando T, Nakanishi T and Saito R 1998 J. Phys. Soc. Jpn. 67 2857
|
[85] |
Morozov S V, Novoselov K S, Katsnelson M I, Schedin F, Ponomarenko L A, Jiang D and Geim A K 2006 Phys. Rev. Lett. 97 016801
|
[86] |
McCann E, Kechedzhi K, Fal'ko V I, Suzuura H, Ando T and Altshuler B L 2006 Phys. Rev. Lett. 97 146805
|
[87] |
Morpurgo A F and Guinea F 2006 Phys. Rev. Lett. 97 196804
|
[88] |
Wu X, Li X, Song Z, Berger C and de Heer W A 2007 Phys. Rev. Lett. 98 136801
|
[89] |
Kharitonov M Y and Efetov K B 2008 Phys. Rev. B 78 033404
|
[90] |
Klein D J 1994 Chem. Phys. Lett. 217 261
|
[91] |
Wakabayashi K, Okada S, Tomita R, Fujimoto S and Natsume Y 2010 J. Phys. Soc. Jpn. 79 034706
|
[92] |
Lewenkopf C H, Mucciolo E R, Castro Neto A H 2008 Phys. Rev. B 77 081410
|
[93] |
Mucciolo E R, Castro Neto A H and Lewenkopf C H 2009 Phys. Rev. B 79 075407
|
[94] |
Carmier P and Ullmo D 2008 Phys. Rev. B 77 245413
|
[95] |
Carmier P, Lewenkopf C and Ullmo D 2010 Phys. Rev. B 81 241406
|
[96] |
Rycerz A 2013 Phys. Rev. B 87 195431
|
[97] |
Ergün G 2012 Computational Complexity 2012 2549
|
[98] |
It should be noted that the representation here is different than the energy representation, in which the Hamiltonian is diagonalized and is real.
|
[99] |
Leyvraz F, Schmit C and Seligman T H 1996 J. Phys. A: Math. Gen. 29 L575
|
[100] |
Dembowski C, Gräf H D, Heine A, Rehfeld H, Richter A and Schmit C 2000 Phys. Rev. E 62 R4516
|