Cascade of topological phase transitions and revival of topological zero modes in imperfect double helical liquids

TL;DR

This paper investigates how imperfections, interactions, and disorder influence topological phases and zero modes in double helical liquids, revealing a cascade of phase transitions and the revival of Majorana zero modes.

Contribution

It demonstrates how realistic imperfections and disorder can induce topological phase transitions and revive Majorana zero modes in proximitized double helical liquids.

Findings

Topological phase transitions depend on pairing and interaction asymmetries.

Disorder can be used to tune and reshape topological superconductivity.

Revival of Majorana zero modes occurs through cascades of topological phases.

Abstract

Two parallel helical edge channels hosting interacting electrons, when proximitized by local and nonlocal pairings, can host time-reversal-invariant pairs of topological zero modes at the system corners. Here we show that realistic imperfections substantially enrich the physics of such proximitized double helical liquids. Specifically, we analyze this platform and its fractional counterparts in the presence of pairing and interaction asymmetries between the two channels, as well as random spin-flip terms arising from either magnetic disorder or coexisting charge disorder and external magnetic fields. Using renormalization-group analysis, we determine how Coulomb interactions, pairings, and magnetic disorder collectively influence the transport behavior and topological properties of the double helical liquid. As the system transitions from class DIII to class BDI, an additional topological phase supporting a single Majorana zero mode per corner emerges. We further show how additional pairing or Coulomb asymmetry influences the stability of various topological phases and uncovers a revival of Majorana zero modes and cascades of transitions through topological phases characterized by a $\mathbb {Z}$ invariant, which are accessible through controlling the electrical screening effect. We also analyze the spatial structure of the zero modes and the bulk gap closing through channel-resolved density profiles. In contrast to conventional understanding, disorder is not merely detrimental, as it in general allows for a tuning knob that qualitatively reshapes the topological superconductivity in imperfect helical liquids.