Laser-induced topological edge states in a chain with four-band energy spectrum

Document Type : Full length research Paper

Authors

Department of Physics, Faculty of Science, University of Zanjan, Zanjan 45371-38791, Iran

Abstract

Based on the theory of periodically driven quantum systems, a new pathway can be created to find topological phases by applying light on solid state systems. Here, we theoretically apply a linear laser beam to a one-dimensional lattice as a quantum wire. Using Floquet theory we study the quasi-energy of the system in a geometry with either finite or periodic boundary conditions. Topologically, the system has distinct phases depending on the laser intensity significantly. The results show that for different values of hopping dimerization and laser intensity the system hosts zero, one, two or three pairs of edge states. Furthermore, we evaluate appropriate topological invariants that for one, two, and three pairs of edge states take the values of 1, 2, and 3, respectively. Also, symmetry arguments show that there are time-reversal, particle-hole, chiral and parity symmetries. We also find that by breaking the parity symmetry, the edge states disappear resulting in this symmetry plays a key role.

Keywords

References

 
[1] K. von Klitzing, G. Dorda, M. Pepper, New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance, Physical Review Letters 45(1980) 494.
[2] D.J. Thouless, M. Kohmoto, M.P. Nightingale, M.D. Nijs, Quantized Hall Conductance in a Two-Dimensional Periodic Potential, Physical Review Letters 49 (1982) 405.
[3] M. Konig, S. Wiedmann, C. Brune, A. Roth, H. Buhmann, L.W. Molenkamp, X.L. Qi, S.C. Zhang, Quantum spin hall insulator state in HgTe quantum wells, Science 318 (2007) 766.
[4] J.E. Moore, Perspective Article The birth of topological insulators, Nature (London). 464 (2010) 194.
[5] T. Oka, H. Aoki, Photovoltaic Hall effect in graphene, Physical Review B 79 (2009) 081406.
[6] N.H. Lindner, G. Refael, V. Galitski, Floquet topological insulator in semiconductor quantum wells, Nature Physics 7 (2011) 490.
[7] A.P. Schnyder, S. Ryu, A. Furusaki, A.W.W. Ludwig, Classification of topological insulators and superconductors in three spatial dimensions, Physical Review B 78 (2008) 195125.
[8] A.Y. Kitaev, Periodic table for topological insulator and superconductors, AIP Conference Proceedings 1134 (2009) 22-30.
[9] T. Kitagawa, M.S. Rudner, E. Berg, E. Demler, Exploring topological phases with quantum walks, Physical Review A  82 (2010) 033429.
 [10] Z. Gu, H.A. Fertig, D.P. Arovas, and A. Auerbach,Spin Pumping by Parametrically Excited Exchange Magnons, Physical Review Letters 107 (2011) 216601.
[11] L. Fu, C.L. Kane, Time reversal polarization and a Z2 adiabatic spin pump, Physical Review B 74 (2006) 195312.
[12] R. Shindou,Quantum Spin Pump in S=1/2 antiferromagnetic chains -Holonomy of phase operators in sine-Gordon theory, Journal of Physics Society of Japan 74 (2005) 1214.
[13] D.J. Thouless, Quantization of particle transport, Physical Review B 27 (1983) 6083.
[14] Q. Niu and D.J. Thouless, Quantised adiabatic charge transport in the presence of substrate disorder and many-body interaction, Journal of Physics A 17 (1984) 2453.
 [15] J-I. Inoue, A. Tanaka, Photoinduced transition between conventional and topological insulators in two-dimensional electronic systems, Physical Review Letters 105 (2010) 017401.
[16] A. Gómez-León, G. Platero,  Floquet-Bloch theory and topology in periodically driven lattices, Physical Review Letters 110 (2013) 200403.

[19] H. Sambe, Steady States and Quasienergies of a Quantum-Mechanical System in an Oscillating Field, Physical Review A7 (1973) 2203.

 [17] J.H. Shirley, Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time, Physical Review B 138 (1965) 974.

[18] W.R. Salzman, Quantum mechanics of systems periodic in time, Physical Review A 10 (1974) 461.

 [20] D. Xiao, M.C. Chang, Q. Niu, Berry phase effects on electronic properties, Reviews of Modern Physics 82 (2010) 1959.

[21] S.-Q.- Shen, Topological Insulators, Hong Kong, China, (2012).

[22]T. Morimoto, A. Furusaki, Topological classification with additional symmetries from Clifford algebras,Physical Review B88 (2013) 125129.
 
[23] V. Dal Lago, M. Atala, L.E.F. Foa Torres, Floquet topological transitions in a driven one-dimensional topological insulator,Physical Review A92 (2015) 023624.
 
[24] J.K. Asboth, B. Tarasinski, P. Delplace, Chiral symmetry and bulk-boundary correspondence in periodically driven one-dimensional systems, Physical Review B 90 (2014) 125143.
Journal of Research on Many-body Systems
Volume 8, Issue 19
March 2019
Pages 83-93

Files

History

  • Receive Date: 17 August 2017
  • Revise Date: 19 June 2018
  • Accept Date: 02 July 2018

Share

How to cite

Statistics