Quasiclassical Treatment and Odd-parity/Triplet Correspondence in Topological Superconductors

TL;DR

This paper develops a quasiclassical framework for topological superconductors with strong spin-orbit coupling, revealing that odd-parity superconductivity corresponds to spin-triplet pairing and linking zero-energy states to Andreev bound states.

Contribution

It introduces a simplified quasiclassical formalism for topological superconductors, showing the equivalence to Andreev equations and the odd-parity to triplet pairing correspondence.

Findings

Odd-parity superconductivity becomes spin-triplet in the quasiclassical limit.

Topologically-protected zero-energy states correspond to Andreev bound states.

The formalism simplifies analysis of low-energy properties in topological superconductors.

Abstract

We construct a quasiclassical framework for topological superconductors with the strong spin-orbit coupling such as CuxBi2Se3. In the manner of the quasiclassical treatment, decomposing the slowly varying component from the total quasi-particle wave function, the original massive Dirac Bogoliubov-de Gennes (BdG) Hamiltonian derived from the tight-binding model represented by 8 x 8 matrix is reduced to 4 x 4 one. The resultant equations are equivalent to Andreev-type equations of singlet or triplet superconductors, in which the apparent spin-orbit coupling vanishes. Using this formalism, we find a fact that the odd-parity superconductivity in topological superconductors turns to the spin-triplet one. % without the spin-orbit coupling through the quasiclassical treatment. Moreover, in terms of the quasiclassical treatment, we show that the topologically-protected zero-energy states in topological superconductors has the correspondence to the Andreev bound states established in a long history of studies for the unconventional superconductors. This clearly indicates that low-energy non-trivial superconducting properties in the topological superconductors can be analyzed by the established theoretical descriptions on the spin-triplet superconductors.