Interaction-driven first-order and higher-order topological superconductivity

TL;DR

This paper explores various topological superconducting states in the Rashba-Hubbard model, revealing new first- and second-order topological phases with Majorana edge and corner modes, using a combined fRG and MFT approach.

Contribution

It introduces a novel combined fRG+MFT methodology to identify and analyze multiple topological superconducting phases, including higher-order states, in a model relevant to real materials.

Findings

Discovery of cascade of topological superconducting states with different pairing symmetries.

Identification of first-order topological states with Majorana edge modes.

Prediction of second-order topological states with Majorana corner modes.

Abstract

We investigate topological superconductivity in the Rashba-Hubbard model, describing heavy-atom superlattice and van der Waals materials with broken inversion. We focus in particular on fillings close to the van Hove singularities, where a large density of states enhances the superconducting transition temperature. To determine the topology of the superconducting gaps and to analyze the stability of their surface states in the presence of disorder and residual interactions, we employ an fRG+MFT approach, which combines the unbiased functional renormalization group (fRG) with a real-space mean-field theory (MFT). Our approach uncovers a cascade of topological superconducting states, including $A_1$ and $B_1$ pairings, whose wave functions are of dominant $p$- and $d$-wave character, respectively, as well as a time-reversal breaking $A_1 + i B_1$ pairing. While the $A_1$ and $B_1$ states have first order topology with helical and flat-band Majorana edge states, respectively, the $A_1 + i B_1$ pairing exhibits second-order topology with Majorana corner modes. We investigate the disorder stability of the bulk superconducting states, analyze interaction-induced instabilites of the edge states, and discuss implications for experimental systems.