Abstract
Spatially uniform excitations can induce Floquet topological bandstructures within insulators which have equal characteristics to those of topological insulators. Going beyond we demonstrate in this article the evolution of Floquet topological quantum states for electromagnetically driven semiconductor bulk matter. We show the direct physical impact of the mathematical precision of the Floquet-Keldysh theory when we solve the driven system of a generalized Hubbard model with our framework of dynamical mean field theory (DMFT) in the non-equilibrium. We explain the physical consequences of the topological non-equilibrium effects in our results for correlated sysems with impact on optoelectronic applications.
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J.M. Kosterlitz, D.J. Thouless, J. Phys. C: Solid State Phys. 6, 1181 (1973)
L. Fu, C.L. Kane, E.J. Mele, Phys. Rev. Lett. 98, 106803 (2007)
M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010)
L. Fu, C.L. Kane, Phys. Rev. Lett. 100, 096407 (2008)
G. Moore, N. Read, Nucl. Phys. B 360, 362 (1991)
N. Goldmann, J. Dalibard, Phys. Rev. X 4, 031027 (2014)
I. Zuti, J. Fabian, S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004)
C. Nayak, S.H. Simon, A. Stern, M. Freedman, S. Das Sarma, Rev. Mod. Phys. 80, 1083 (2008)
M.C. Rechtsman, J.M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, Nature 496, 196 (2013)
M.A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D.N. Christodoulides, M. Khajavikhan, Science 359, eaar4005 (2018)
A. Lubatsch, R. Frank, Appl. Sci. 9, 2477 (2019)
B.A. Bernevig, T.L. Hughes, S.-C. Zhang, Science 314, 1757 (2006)
M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L.W. Molenkamp, X.-L. Qi, S.-C. Zhang, Science 318, 766 (2007)
D. Hsieh, D. Qian, L. Wray, Y. Xia, Y.S. Hor, R.J. Cava, M.Z. Hasan, Nature 452, 970 (2008)
Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y.S. Hor, R.J. Cava, M.Z. Hasan, Nat. Phys. 5, 398 (2009)
H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, S.-C. Zhang, Nat. Phys. 5, 438 (2009)
N.H. Lindner, G. Refael, V. Galitski, Nat. Phys. 7, 490 (2011)
Y. Tenenbaum Katan, D. Podolsky, Phys. Rev. Lett. 110, 016802 (2013)
T. Kitagawa, T. Oka, A. Brataas, L. Fu, E. Demler, Phys. Rev. B 84, 235108 (2011)
Z. Gu, H.A. Fertig, D.P. Arovas, A. Auerbach, Phys. Rev. Lett. 107, 216601 (2011)
Y.H. Wang, H. Steinberg, P. Jarillo-Herrero, N. Gedik, Science 342, 453 (2013)
M.S. Rudner, N.H. Lindner, E. Berg, M. Levin, Phys. Rev. X 3, 031005 (2013)
N.H. Lindner, D.L. Bergman, G. Refael, V. Galitski, Phys Rev. B 87, 235131 (2013)
L. Jiang, T. Kitagawa, J. Alicea, A.R. Akhmerov, D. Pekker, G. Refael, J.I. Cirac, E. Demler, M.D. Lukin, P. Zoller, Phys. Rev. Lett. 106, 220402 (2011)
L. D’Alessio, M. Rigol, Nat. Commun. 6, 8336 (2015)
A.G. Grushin, A. Gomez-Leon, T. Neupert, Phys. Rev. Lett. 112, 156801 (2014)
E. Bergholtz, Z. Liu, Int. J. Mod. Phys. B 27, 1330017 (2013)
G. Floquet, Ann. Sci. Éc. Norm. Supér. 12, 47 (1883)
R. Frank, Phys. Rev. B 85, 195463 (2012)
R. Frank, Ann. Phys. (Berlin) 525, 66 (2013)
F.H.M.Faisal, J.Z. Kaminski, Phys. Rev. A 56, 748 (1997)
M. Grifoni, P. Hänggi, Phys. Rep. 304, 229 (1998)
S. Restrepo, J. Cerrillo, V.M. Bastidas, D.G. Angelakis, T. Brandes, Phys. Rev. Lett. 117, 250401 (2016)
A. Eckardt, Rev. Mod. Phys. 89, 011004 (2017)
M.H. Kalthoff, G.S. Uhrig, J.K. Freericks, Phys. Rev. B 98, 035138 (2018)
M.A. Sentef, M. Claassen, A.F. Kemper, B. Moritz, T. Oka, J.K. Freericks, T.P. Devereaux, Nat. Commun. 6, 7047 (2015)
L. Yuan, S. Fan, Phys. Rev. A 92, 053822 (2015)
A. Lubatsch, J. Kroha, Ann. Phys. (Berlin) 18, 863 (2009)
A. Georges, G. Kotliar, W. Krauth, M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996)
W. Metzner, D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989)
P. Schmidt, H. Monien, https://arXiv:cond-mat/0202046 (2002)
T. Maier, M. Jarrell, T. Pruschke, M.H. Hettler, Rev. Mod. Phys. 77, 1027 (2005)
J.K. Freericks, V.M. Turkowski, V. Zlatic, Phys. Rev. Lett. 97, 266408 (2006)
N. Tsuji, T. Oka, H. Aokib, Phys. Rev. Lett. 103, 047403 (2009)
N. Lin, C.A. Marianetti, A.J. Millis, D.R. Reichman, Phys. Rev. Lett. 106, 096402 (2011)
D. Zgid, G.K.-L. Chan, J. Chem. Phys. 134, 094115 (2011)
H. Aoki, N. Tsuji, M. Eckstein, M. Kollar, T. Oka, P. Werner, Rev. Mod. Phys. 86, 779 (2014)
R. Frank, Appl. Phys. B 113, 41 (2013)
R. Frank, New J. Phys. 15, 123030 (2013)
M.E. Sorantin, A. Dorda, K. Held, E. Arrigoni, Phys. Rev. B 97, 115113 (2018)
W. Hofstetter, T. Qin, J. Phys. B: At., Mol. Opt. Phys. 51, 082001 (2018)
T. Qin, W. Hofstetter, Phys. Rev. B 97, 125115 (2018)
D.A.B. Miller, D.S. Chemla, T.C. Damen, A.C. Gossard, W. Wiegmann, T.H. Wood, C.A. Burrus, Phys. Rev. Lett. 53, 2173 (1984)
D.S. Chemla, W.H. Knox, D.A.B. Miller, S. Schmitt-Rink, J.B. Stark, R. Zimmermann, J. Luminesc. 44, 233 (1989)
M. Bukov, L. D’Alessio, A. Polkovnikov, Adv. Phys. 64, 139 (2015)
J. Zak, Phys. Rev. Lett. 62, 2747 (1989)
D. Xiao, M.-C. Chang, Q. Niu, Rev. Mod. Phys. 82, 1959 (2009)
D. Gresch, G. Autes, O.V. Yazyev, M. Troyer, D. Vanderbilt, B.A. Bernevig, A.A. Soluyanov, Phys. Rev. B 95, 075146 (2017)
P.-C. Chang, J.G. Lu, Appl. Phys. Lett. 92, 212113 (2008)
P.-C. Chang, C.-J. Chien, D. Stichtenoth, C. Ronning, J.G. Lu, Appl. Phys. Lett. 90, 113101 (2007)
F. Huang, Z. Lin, W. Lin, J. Zhang, K. Ding, Y. Wang, Q. Zheng, Z. Zhan, F. Yan, D. Chen, P. Lv, X. Wang, Chin. Sci. Bull. 59, 1235 (2014)
W.I. Park, Y.H. Jun, S.W. Jung, G.-C. Yi, Appl. Phys. Lett. 82, 964 (2003)
D. Fritsch, H. Schmidt, M. Grundmann, Appl. Phys. Lett. 88, 134104 (2006)
H. Dixit, R. Saniz, D. Lamoen, B. Partoens, J. Phys.: Condens. Matter 22, 125505 (2010)
M. Wegener,Extreme Nonlinear Optics (Springer, 2004)
R.D. King-Smith, D. Vanderbilt, Phys. Rev. B 47, 1651 (1993)
D. Vanderbilt, R.D. King-Smith, Phys. Rev. B 48, 4442 (1993)
R. Resta, Rev. Mod. Phys. 66, 899 (1994)
V. Dal Lago, M. Atala, L.E.F. Foa Torres, Phys. Rev. A 92, 023624 (2015)
E. Gull, A. Millis, A.I. Lichtenstein, A.N. Rubtsov, M. Troyer, P. Werner, Rev. Mod. Phys. 83, 349 (2011)
M. Snoek, I. Titvinidze, C. Toke, K. Byczuk, W. Hofstetter, New J. Phys. 10, 093008 (2008)
R. Peters, T. Yoshida, H. Sakakibara, N. Kawakami, Phys. Rev. B 93, 235159 (2016)
R. Peters, T. Yoshida, N. Kawakami, Phys. Rev. B 98, 075104 (2018)
S. Manmana, A.M. Essin, R.M. Noack, V. Gurarie, Phys. Rev. B 86, 205119 (2012)
S. Rachel, Rep. Prog. Phys. 81, 116501 (2018)
W. Franz, Z. Naturforsch. A 13, 484 (1958)
L.V. Keldysh, J. Exp. Theor. Phys. (USSR) 33, 994 (1957)
L.V. Keldysh, Sov. Phys. JETP 6, 763 (1958)
L.V. Keldysh, J. Exp. Theor. Phys. (USSR) 47, 1945 (1964)
L.V. Keldysh, Sov. Phys. JETP 20, 1307 (1965)
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Contribution to the Topical Issue “Non-Linear and Complex Dynamics in Semiconductors and Related Materials”, edited by Kathy Lüdge.
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Lubatsch, A., Frank, R. Evolution of Floquet topological quantum states in driven semiconductors. Eur. Phys. J. B 92, 215 (2019). https://doi.org/10.1140/epjb/e2019-100087-0
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DOI: https://doi.org/10.1140/epjb/e2019-100087-0