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

We calculate the tunneling conductance between the surface states on the opposite sides of an ultrathin film of a topological insulator in a parallel magnetic field. The parallel magnetic field produces a relative shift of the in-plane momenta of the two surfaces states. An overlap between the shifted Fermi circles and the spinor wave functions results in an unusual dependence of the tunneling conductance on the magnetic field. Because the spin orientation of the electronic surface states in topological insulators is locked to momentum, the spin polarization of the tunneling current can be controlled by the magnetic field.