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

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