Atomic limit and inversion-symmetry indicators for topological superconductors

Anastasiia Skurativska (UZH)

Theory of symmetry indicators has proven to be a powerful tool in identifying topologically non-trivial crystalline insulators using the symmetry representation of the Bloch states. In this talk, I will explain how this method can be extended to identify non-trivial topological phases in superconducting systems. Two main ingredients, which contribute to the topology of a superconducting state, are the symmetries of the normal metal state and of the superconducting order parameter. Based on that, I will introduce the notion of atomic limit for superconductors as a reference state for topologically-trivial superconducting phase. Then, I will define a symmetry indicator for inversion-symmetric topological superconductors with or without time-reversal symmetry, which identifies strong topological phases as well as the higher-order ones. Furthermore, I will illustrate the bulk boundary correspondence of identified phases using Dirac surface theories. This method can be used to search for topological superconductors based on first-principle calculations.