Dynamical competition between Quantum Hall and Quantum Spin Hall effects

Abstract

In this paper we investigate the occurrence of quantum phase transitions in topological systems out of equi- librium. More specifically, we consider graphene with a sizable spin-orbit coupling, irradiated by circularly- polarized light. In the absence of light, the spin-orbit coupling drives a quantum spin Hall phase where edge currents with opposite spins counter-propagate. On the other hand, the light generates a time-dependent vector potential, which leads to a hopping parameter with staggered time-dependent phases around the benzene ring. The model is a dynamical version of the Haldane model, which considers a static staggered flux with zero total flux through each plaquette. Since the light breaks time-reversal symmetry, a quantum Hall phase protected by an integer topological invariant arises. By numerically solving the complete problem, with spin-orbit coupling and light, and investigating different values of the driving frequency ω, we show that the spectrum exhibits non-trivial gaps not only at zero energy, but also at ω/2. This additional gap is created by photon resonances between the valence and conduction band of graphene, and the symmetry of the spectrum forces it to lie at ω/2. By increasing the intensity of the irradiation, the topological state in the zero energy gap undergoes a dynamical phase transition from a quantum spin Hall to a quantum Hall phase, whereas the gap around ω/2 remains in the quantum Hall regime.

6 pages, 3 figures

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Cited by in corpus (10)

• Experimental observation of anomalous topological edge modes in a slowly-driven photonic lattice
• Out of equilibrium electrons and the Hall conductance of a Floquet topological insulator
• Driving protocol for a Floquet topological phase without static counterpart
• Genesis of the Floquet Hofstadter butterfly
• Floquet Quantum Spin Hall Insulator in Cold Atomic Systems
• Bandwidth-resonant Floquet states in honeycomb optical lattices
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• Non-adiabatic bulk-surface oscillations in driven topological insulators
• Topologically trivial and nontrivial edge bands in graphene induced by irradiation
• Edge states and phase diagram for graphene under polarized light