Higher-order topological superconductivity in doped topological insulators

Higher-order topological superconductors are topological states protected by spatial symmetries that exhibit gapless modes at the corners/edges of 2d/3d samples. While these phases of matter have recently attracted immense theoretical interest, experimental candidates remain scarce. This talk describes a mechanism for superconductivity in doped topological insulators which intrinsically leads to a higher order topological phase. The mechanism is effective in materials with localized orbitals, and requires a minimum doping beyond which superconductivity ensues, providing useful criteria in the search for material realizations. Mapping out the phase diagram of the Kane-Mele model with Hubbard-like interactions, we find that past a critical doping, many-body effects give rise to two possible higher-order topological states, p+iτp and s_τ, the latter of which is partially protected from disorder by a generalized Anderson theorem. Symmetry-based indicator arguments and exact diagonalization results are presented which demonstrate the resulting higher order topology. As a demonstration of the theory, microscopic modelling is presented for an artificial topological insulator based on a semiconductor heterostructure; we find that the superconducting mechanism can be enhanced by varying the depth of the quantum well.