Edge instabilities of topological superconductors

TL;DR

This paper investigates how interactions destabilize zero-energy Majorana flat bands at the edges of topological superconductors, leading to various symmetry-breaking phases, with findings supported by mean-field and quantum Monte Carlo analyses.

Contribution

It provides a detailed analysis of edge instabilities in topological superconductors, identifying specific mass terms induced by interactions and confirming results with quantum Monte Carlo simulations.

Findings

Attractive interactions induce complex mass terms including pairing and current order.

Repulsive interactions lead to ferromagnetism and spin-triplet pairing at edges.

Quantum Monte Carlo confirms instabilities even with strong quantum fluctuations.

Abstract

Nodal topological superconductors display zero-energy Majorana flat bands at generic edges. The flatness of these edge bands, which is protected by time-reversal and translation symmetry, gives rise to an extensive ground-state degeneracy. Therefore, even arbitrarily weak interactions lead to an instability of the flat-band edge states towards time-reversal and translation-symmetry-broken phases, which lift the ground-state degeneracy. We examine the instabilities of the flat-band edge states of d_{xy}-wave superconductors by performing a mean-field analysis in the Majorana basis of the edge states. The leading instabilities are Majorana mass terms, which correspond to coherent superpositions of particle-particle and particle-hole channels in the fermionic language. We find that attractive interactions induce three different mass terms. One is a coherent superposition of imaginary s-wave pairing and current order, and another combines a charge-density-wave and finite-momentum singlet pairing. Repulsive interactions, on the other hand, lead to ferromagnetism together with spin-triplet pairing at the edge. Our quantum Monte Carlo simulations confirm these findings and demonstrate that these instabilities occur even in the presence of strong quantum fluctuations. We discuss the implications of our results for experiments on cuprate high-temperature superconductors.