Transport in a quantum spin Hall bar: Effect of in-plane magnetic field

We demonstrate theoretically that edge transport in quantum spin Hall bar can be controlled by in-plane magnetic fields. The in-plane magnetic field couples the opposite spin orientation helical edge states at the opposite edges, and induces the gaps in the energy spectrum. The hybridized electron wave functions ψ ↑ ( x , k y ) of the edge states can be destroyed with increasing the in-plane magnetic fields. When the Fermi surface is located within this energy gap induced by the in-plane magnetic field, one can expect that the conductance of the edge states becomes e2/h. By tuning the magnetic field and Fermi energy, the edge channels can be transited from opaque to transparent. This switching behavior offers us an efficient way to control the topological edge state transport.