Quasiclassical Treatment and Odd-parity/Triplet Correspondence 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.

5 pages, no figures, to be published in J. Phys. Soc. Jpn

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Cited by in corpus (12)

• Dirac-Fermion-Induced Parity Mixing in Superconducting Topological Insulators
• Non-fragile superconductivity with nodes in the superconducting topological insulator CuxBi2Se3: Zeeman orbital field and non-magnetic impurities
• Non-magnetic impurity effects in a three-dimensional topological superconductor: From p- to s-wave behaviors
• Nematic superconductivity in Cu${}_x$Bi${}_2$Se${}_3$: The surface Andreev bound states
• Field-angle-dependent low-energy excitations around a vortex in the superconducting topological insulator CuxBi2Se3
• Effective low energy theory for surface Andreev bound states of superconducting phases in generalized Bernevig-Hughes-Zhang models
• Impurity effects in a two-dimensional topological superconductor: A link of Tc-robustness with a topological number
• Nuclear magnetic relaxation rates of unconventional superconductivity in doped topological insulators
• Multi-band Eilenberger theory of superconductivity: Systematic low-energy projection
• Inverse coherence effects in nuclear magnetic relaxation rates as a sign of topological superconductivity
• Sparse modeling approach for quasiclassical theory of superconductivity
• Possible two-component pairings in electron-doped Bi${}_2$Se${}_3$ based on a tight-binding model