Interaction- and phonon-induced topological phase transitions in double helical liquids

TL;DR

This paper studies how electron-electron interactions and phonons influence topological superconductivity in helical liquids, revealing that phonons can induce phase transitions and affect the stability of topological zero modes.

Contribution

It provides a nonperturbative analysis showing phonons can cause topological-trivial phase transitions, challenging previous perturbative assumptions.

Findings

Electron interactions suppress nonlocal pairing, reducing topological phases.

Electron-phonon coupling can induce topological-trivial transitions.

Phonons weaken the stability of topological zero modes.

Abstract

Helical liquids, formed by time-reversal pairs of interacting electrons in topological edge channels, provide a platform for stabilizing topological superconductivity upon introducing local and nonlocal pairings through the proximity effect. Here, we investigate the effects of electron-electron interactions and phonons on the topological superconductivity in two parallel channels of such helical liquids. Interactions between electrons in different channels tend to reduce nonlocal pairing, suppressing the topological regime. Additionally, electron-phonon coupling breaks the self duality in the electronic subsystem and renormalizes the pairing strengths. Notably, while earlier perturbative calculations suggested that longitudinal phonons have no effect on helical liquids themselves to the leading order, our nonperturbative analysis shows that phonons can induce transitions between topological and trivial superconductivity, thereby weakening the stability of topological zero modes. Our findings highlight practical limitations in realizing topological zero modes in various systems hosting helical channels, including quantum spin Hall insulators, higher-order topological insulators, and their fractional counterparts recently observed in twisted bilayer systems.