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

We construct a quasiclassical framework for topological superconductors with a strong spin-orbit coupling such as CuxBi2Se3. In a manner of the quasiclassical treatment, by decomposing the slowly varying component from a total quasiparticle wave function, the original massive Dirac Bogoliubov-de Gennes (BdG) Hamiltonian derived from a tight-binding model represented by an 8 X 8 matrix is reduced to a 4 X 4 matrix. 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 that the odd-parity superconductivity in topological superconductors turns to the spin-triplet one. Moreover, in terms of quasiclassical treatment, we show that the topologically-protected zero-energy states in topological superconductors have correspond to the Andreev bound states established in a long history of studies of unconventional superconductors. This clearly indicates that low-energy nontrivial superconducting properties in the topological superconductors can be analyzed using established theoretical descriptions of the spin-triplet superconductors.