Spin-polarized tunneling current through a thin film of topological insulator in a parallel magnetic field

We calculate the tunneling conductance \sigma between the surface states on the opposite sides of the ultra-thin film of a topological insulator in a parallel magnetic field B_y. The parallel magnetic produces a relative shift of the in-plane momenta of the two surfaces states. An overlap between the shifted Fermi circles and their spin structure define an unusual dependence of the tunneling conductance \sigma(B_y) on the magnetic field. Because the spin of the electronic surface states in topological insulators is locked with momentum, the spin-polarization of the tunneling current can be controlled by magnetic field B_y.