Odd-frequency Cooper pairing in chiral symmetric systems

Odd-frequency Cooper pairs emerge at the edge of topological superconductors. We study chiral symmetric systems, where the Hamiltonian anticommutes with a chiral operator and the topological number called a winding number can be defined in the bulk. We found that the odd-frequency Cooper pair at the edge is related to an extended version of the winding number we call this relation as spectral bulk boundary correspondence (SBBC) [1]. Then the total amount of the odd-frequency Cooper pair at the edge is predicted from the bulk value through the SBBC. From the SBBC with low frequency, odd-frequency Cooper pair diverges in the topologically non-trivial phase and it is linear in the trivial phase. We will also discuss the robustness of this relation against impurity.
[1] PRB 99, 184512 (2019).