Spin injection from topological insulator into metal leads

We study theoretically helical edge and surface states of 2D and 3D topological insulators (TI) tunnel-coupled to metal leads and show that their transport properties are strongly affected by contacts as the latter play a role of a heat bath and induce damping and relaxation of electrons in the helical states of TI. A simple structure that produces a pure spin current in the external circuit is proposed. The current and the spin current delivered to the external circuit depend on the relation between characteristic lengths: decay length due to tunneling, contact length and, in case of 3D TI, mean free path and spin relaxation length caused by momentum scattering. If the decay length due to tunneling is the smallest one, then the electric and spin currents are of order of the conductance quantum in 2D TI, and of order of the conductance quantum multiplied by the ratio of the contact width to the Fermi wavelength in 3D TI. A role of electron–electron interaction is discussed in case of 2D TI, and it is shown that in contrast to the conventional Luttinger liquid picture the interaction can be treated perturbatively. The presence of interaction results in suppression of density of states at the Fermi level and hence in decrease of the electric and spin currents.