Odd-parity superconductivity from phonon-mediated pairing: Application to Cu${}_x$Bi${}_2$Se${}_3$

Abstract

Motivated by the proposed topological state in Cu${}_x$Bi${}_2$Se${}_3$, we study the possibility of phonon-mediated odd-parity superconductivity in spin-orbit coupled systems with time-reversal and inversion symmetry. For such systems, we show that, in general, pure electron-phonon coupling can never lead to a triplet state with a higher critical temperature than the leading singlet state. The Coulomb pseudopotential, which is the repulsive part of the electron-electron interaction and is typically small in weakly correlated systems, is therefore critical to stabilizing the triplet state. We introduce a chirality quantum number, which identifies the electron-phonon vertex interactions that are most favorable to the triplet channel as those that conserve chirality. Applying these results to Cu${}_x$Bi${}_2$Se${}_3$, we find that a phonon-mediated odd-parity state may be realized in the presence of weak electronic correlations if the chirality-preserving electron-phonon vertices are much stronger than the chirality-flipping vertices.

5 pages, 1 figure

References in corpus (8)

• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• Classification of topological insulators and superconductors in three spatial dimensions
• Bulk superconducting phase with a full energy gap in the doped topological insulator Cu_xBi_2Se_3
• Local Measurements of the Superconducting Pairing Symmetry in CuxBi2Se3
• Odd-Parity Pairing and Topological Superconductivity in a Strongly Spin-Orbit Coupled Semiconductor
• Unconventional superconducting pairing by conventional phonons
• Retardation effects and the Coulomb pseudopotential in the theory of superconductivity
• Unconventional superconducting pairing symmetry induced by phonons

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