Spontaneous persistent currents in a quantum spin Hall insulator

We present a mechanism for persistent charge current. Quantum spin Hall insulators hold dissipationless spin currents in their edges so that, for a given spin orientation, a net charge current flows which is exactly compensated by the counterflow of the opposite spin. Here we show that ferromagnetic order in the edge upgrades the spin currents into persistent charge currents without applied fields. For that matter, we study the Hubbard model including Haldane-Kane-Mele spin-orbit coupling in a zigzag ribbon and consider the case of graphene. We find three electronic phases with magnetic edges that carry currents reaching 0.4 nA, comparable to persistent currents in metallic rings, for the small spin-orbit coupling in graphene. One of the phases is a valley half metal.

Impurity states in the quantum spin Hall phase in graphene

Two-dimensional insulators with time-reversal symmetry can have two topologically different phases, the quantum spin Hall and the normal phase. The former is revealed by the existence of conducting edge states that are topologically protected. Here we show that the reaction to impurity, in bulk, is radically different in the two phases and can be used as a marker for the topological phase. Within the context of the Kane-Mele model for graphene, we find that strictly normalizable in-gap impurity states only occur in the quantum spin Hall phase and carry a dissipationless current whose chirality is determined by the spin and pseudospin of the residing electron.