Kibble-Zurek behavior in disordered Chern insulators

Abstract

Even though no local order parameter in the sense of the Landau theory exists for topological quantum phase transitions in Chern insulators, the highly non-local Berry curvature exhibits critical behavior near a quantum critical point. We investigate the critical properties of its real space analog, the local Chern marker, in weakly disordered Chern insulators. Due to disorder, inhomogeneities appear in the spatial distribution of the local Chern marker. Their size exhibits power-law scaling with the critical exponent matching the one extracted from the Berry curvature of a clean system. We drive the system slowly through such a quantum phase transition. The characteristic size of inhomogeneities in the non-equilibrium post-quench state obeys the Kibble-Zurek scaling. In this setting, the local Chern marker thus does behave in a similar way as a local order parameter for a symmetry breaking second order phase transition. The Kibble-Zurek scaling also holds for the inhomogeneities in the spatial distribution of excitations and of the orbital polarization.

Universal Landau-Zener regimes in dynamical topological phase transitions

“…The experimental observations of a nonzero Hall drift [1,27] thus inspired a plethora of studies [15,25,26,[28][29][30][31][32][33][34][35][36][37][38][39][40][41]. Nonunitary effects, including thermal baths [28,30] and dephasing noise [34], were shown to stabilize a nearly quantized Hall conductance, in much the same way that a diagonal ensemble of unitary time evolution would predict [42,43].…”

Local Topological Markers in Odd Dimensions

“…Among the most prevalent of these topological markers is the so-called Chern marker [25]. Since the Chern marker does not require translational invariance, it has been used to probe topological phases and topological phase transitions of inhomogeneous systems [26][27][28][29][30][31][32][33]. Recent work analysed the non-equilibrium dynamics of the Chern marker for a system undergoing a quantum quench and found that topological currents arise within the system [34].…”

Self-Trapped Polarons and Topological Defects in a Topological Mott Insulator

“…We emphasize that, as in the half-filling case, the sign of C depends on the ground state symmetry breaking sector. Notice also that these local fluctuations of C, which are caused by a spontaneous breaking of translational symmetry, are reminiscent of those induced by quenched disorder in a gauge-induced Chern insulator [42].…”