Dynamical preparation of Floquet Chern insulators

Nature Communications

Volumn 6, Issue , 2015, Pages

  D'Alessio, Luca ^a,b   Rigol, Marcos ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b USA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GRAPHENE;

CARBON; ELECTRIC FIELD; FUTURE PROSPECT; INSULATION; NUMERICAL MODEL; POLARIZATION; TOPOLOGY;

ADIABATICITY; ARTICLE; CHIRALITY; DYNAMICS; ELECTRIC FIELD; GEOMETRY; INSULATOR; MAGNETIC FIELD; POLARIZATION; SEMICONDUCTOR; TIME;

EID: 84943177050     PISSN: None     EISSN: 20411723     Source Type: Journal    
DOI: 10.1038/ncomms9336     Document Type: Article

References (31)

1. Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045-3067 (2010).
2. Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057-1110 (2011).
3. Knig, M. et al. The quantum spin hall effect: theory and experiment. J. Phys. Soc. Jpn 77, 031007 (2008).
4. Zhou, B., Lu, H.-Z., Chu, R.-L., Shen, S.-Q. & Niu, Q. Finite size effects on helical edge states in a quantum spin-hall system. Phys. Rev. Lett. 101, 246807 (2008).
5. Thouless, D. J., Kohmoto, M., Nightingale, M. P. & den Nijs, M. Quantized hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405-408 (1982).
6. Oka, T. & Aoki, H. Photovoltaic hall effect in graphene. Phys. Rev. B 79, 081406 (2009).
7. Kitagawa, T., Oka, T., Brataas, A., Fu, L. & Demler, E. Transport properties of nonequilibrium systems under the application of light: photoinduced quantum hall insulators without landau levels. Phys. Rev. B 84, 235108 (2011).
8. Lindner, N. H., Refael, G. & Galitski, V. Floquet topological insulator in semiconductor quantum wells. Nat. Phys. 7, 409-495 (2011).
9. Shirley, J. H. Solution of the schrödinger equation with a hamiltonian periodic in time. Phys. Rev. 138, B979-B987 (1965).
10. Zel'dovich, Y. B. The quasienergy of a quantum-mechanical system subjected to a periodic action. Sov. Phys. JETP 24, 1006 (1967).
11. Ritus, V. I. Shift and splitting of atomic energy levels by the field of an electromagnetic wave. Sov. Phys. JETP 24, 1041 (1967).
12. Reichl, L. E. The Transition to Chaos: Conservative Classical Sysstems and Quantum Manifestations (Springer, 2004).
13. Neil, W., Ashcroft, N. W. & Mermin, N. D. Solid State Physics (Saunders College, 1976).
14. Rudner, M. S., Lindner, N. H., Berg, E. & Levin, M. Anomalous edge states and the bulk-edge correspondence for periodically driven two-dimensional systems. Phys. Rev. X 3, 031005 (2013).
15. Loring, T. A. & Hastings, M. B. Disordered topological insulators via c∗-algebras. Europhys. Lett. 92, 67004 (2010).
16. Kitaev, A. Periodic table for topological insulators and superconductors. AIP Conf. Proc. 1134, 22-30 (2009).
17. Jotzu, G. et al. Experimental realization of the topological haldane model with ultracold fermions. Nature 515, 237-240 (2014).
18. Bukov, M., D'Alessio, L. & Polkovnikov, A. Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to floquet engineering. Adv. Phys. 64, 139-226 (2015).
19. Foster, M. S., Gurarie, V., Dzero, M. & Yuzbashyan, E. A. Quench-induced floquet topological p-wave superfluids. Phys. Rev. Lett. 113, 076403 (2014).
20. Foster, M. S., Dzero, M., Gurarie, V. & Yuzbashyan, E. A. Quantum quench in a p+ip superfluid: winding numbers and topological states far from equilibrium. Phys. Rev. B 88, 104511 (2013).
21. Sacramento, P. D. Fate of majorana fermions and chern numbers after a quantum quench. Phys. Rev. E 90, 032138 (2014).
22. Rigol, M. & Muramatsu, A. Free expansion of impenetrable bosons on one-dimensional optical lattices. Mod. Phys. Lett. B 19, 861-881 (2005).
23. He, K., Brown, J., Haas, S. & Rigol, M. Driven dipole oscillations and the lowest-energy excitations of strongly interacting lattice bosons in a harmonic trap. Phys. Rev. A 89, 033634 (2014).
24. Dahlhaus, J. P., Fregoso, B. M. & Moore, J. E. Magnetization signatures of light-induced quantum hall edge states. Phys. Rev. Lett. 114, 246802 (2015).
25. Bukov, M. & Polkovnikov, A. Stroboscopic versus nonstroboscopic dynamics in the floquet realization of the harper-hofstadter hamiltonian. Phys. Rev. A 90, 043613 (2014).
26. Patel, A. A., Sharma, S. & Dutta, A. Quench dynamics of edge states in 2-d topological insulator ribbons. Eur. Phys. J. B 86, 367 (2013).
27. Varney, C. N., Sun, K., Rigol, M. & Galitski, V. Interaction effects and quantum phase transitions in topological insulators. Phys. Rev. B 82, 115125 (2010).
28. D'Alessio, L. & Rigol, M. Long-time behavior of isolated periodically driven interacting lattice systems. Phys. Rev. X 4, 041048 (2014).
29. Trotter, H. F. On the product of semi-groups of operators. Proc. Amer. Math. Soc. 10, 545-551 (1959).
30. Suzuki, M. Generalized trotter's formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems. Commun. Math. Phys. 51, 183-190 (1976).
31. De Raedt, H. & De Raedt, B. Applications of the generalized trotter formula. Phys. Rev. A 28, 3575-3580 (1983).