Unconventional pairing in three-dimensional topological insulators with a warped surface state

We study the effect of the Fermi surface anisotropy (hexagonal warping) on the superconducting pair potential, induced in a three-dimensional topological insulator (TI) by proximity with an s-wave superconductor (S) in presence of a magnetic moment of a nearby ferromagnetic insulator (FI). In the previous studies, similar problem was treated with a simplified Hamiltonian, describing an isotropic Dirac cone dispersion. This approximation is only valid near the Dirac point. However, in topological insulators, the chemical potential often lies well above this point, where the Dirac cone is strongly anisotropic and its constant energy contour has a snowflake shape. Taking into account this shape, we show that a very exotic pair potential is induced on the topological insulator surface. Based on the symmetry arguments we also discuss the possibility of a supercurrent flowing along the S/FI interface, when an S/FI hybrid structure is formed on the TI surface.