Slow quenches in two-dimensional time-reversal symmetric Z2 topological insulators

Abstract

We study the topological properties and transport in the Bernevig-Hughes-Zhang (BHZ) model undergoing a slow quench between different topological regimes. Due to the closing of the band gap during the quench, the system ends up in an excited state. For quenches governed by a Hamiltonian that preserves the symmetries present in the BHZ model (time-reversal, inversion, and conservation of spin projection), the Z2 invariant remains equal to the one evaluated in the initial state. The bulk spin Hall conductivity does change and its time average approaches that of the ground state of the final Hamiltonian. The deviations from the ground-state spin Hall conductivity as a function of the quench time follow the Kibble-Zurek scaling. We also consider the breaking of the timereversal symmetry, which restores the correspondence between the bulk invariant and the transport properties after the quench. arXiv:1802.05572v3 [cond-mat.mes-hall]

Classification of topological insulators and superconductors out of equilibrium

“…Access to coherent dynamics in cold atom experiments 17 has motivated recent studies of nonequilibrium physics in topological insulators and superconductors [18][19][20][21][22][23] . A key aspect of these studies is the behaviour of topological bulk indices after a quench between Hamiltonians.…”

Slow quenches in Chern insulator ribbons

“…In the case of two-dimensional Chern insulators, the Chern number remains well defined and is equal to the one evaluated in the initial state. 6,[12][13][14] Quenches in finite-sized systems with edges were explored less. Sudden quenches in such systems were studied in Refs.…”

“…After a quench to the topological side, the in-gap states appear and are occupied, in contrast to the bulk Chern number that remains equal to that in the initial Hamiltonian. 6,12,13 The number of generated excitations decreases as the quench becomes slow. The number of the excitations in the in-gap states scales with the quench time τ as τ −1/2 whereas the number of excitations in the bulk states scales as τ −1 .…”

Kibble-Zurek behavior in disordered Chern insulators

“…Topological systems have been realized in solid state [9][10][11][12][13][14][15] and in cold atoms [16][17][18][19][20][21][22][23]. Recently, a lot of attention has been given to dynamical critical properties after quenches across topological phase transitions in topological insulators [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38], superconductors [39][40][41] and p + ip superfluids [42,43]. An important observation of interest to this paper was made in Refs.…”

“…An important observation of interest to this paper was made in Refs. [35,38,[44][45][46] which showed that the number of excitations after a slow quench follows the Kibble-Zurek (KZ) scaling.…”