Electrically controllable spin filtering based on superconducting helical states

The magnetoelectric effects in the surface states of the three-dimensional (3D) topological insulator (TI) are extremely strong due to the full spin-momentum locking. Here the microscopic theory of S/3D TI bilayer structures in terms of quasiclassical Green's functions is developed. On the basis of the developed formalism it is shown that the DOS in the S/TI bilayer manifests giant magnetoelectric behavior and, as a result, S/3D TI heterostructures can work as nonmagnetic fully electrically controllable spin filters. It is shown that due to the full spin-momentum locking the amplitudes of the odd-frequency singlet and triplet components of the condensate wave function are equal. The same is valid for the even frequency singlet and triplet components. We unveil the connection between the odd-frequency pairing in S/3D TI heterostructures and magnetoelectric effects in the DOS.