Odd-Parity Topological Superconductors: Theory and Application to Cu$_x$Bi$_2$Se$_3$

TL;DR

This paper introduces a simple criterion for identifying odd-parity topological superconductors and applies it to Cu$_x$Bi$_2$Se$_3$, proposing a pairing model and experimental tests for its topological phase.

Contribution

It provides a straightforward method to identify odd-parity topological superconductors and models the pairing mechanism in Cu$_x$Bi$_2$Se$_3$ as a topological superconductor.

Findings

Inter-orbital triplet pairing with odd parity is favored in Cu$_x$Bi$_2$Se$_3$.

The proposed model predicts a topological superconductor phase.

Experimental tests are suggested to verify the pairing symmetry.

Abstract

Topological superconductors have been theoretically predicted as a new class of time-reversal-invariant superconductors which are fully gapped in the bulk but have protected gapless surface Andreev bound states. In this work, we provide a simple criterion that directly identifies this topological phase in \textit{odd-parity} superconductors. We next propose a two-orbital $U-V$ pairing model for the newly discovered superconductor Cu$_x$Bi$_2$Se$_3$%. Due to its peculiar three-dimensional Dirac band structure, we find that an inter-orbital triplet pairing with odd-parity is favored in a significant part of the phase diagram, and therefore gives rise to a topological superconductor phase. Finally we propose sharp experimental tests of such a pairing symmetry.