Transport in helical Luttinger liquids in the fractional quantum Hall regime

TL;DR

This paper studies transport in helical domain walls within fractional quantum Hall systems, revealing current redistribution among modes and the emergence of spin modes crucial for fractional topological superconductivity.

Contribution

It provides experimental and theoretical insights into transport in helical domain walls at fractional quantum Hall states, highlighting the role of spin-non-conserving processes.

Findings

Current carried by helical domain walls is smaller than naive predictions.

Luttinger liquid theory explains current redistribution among modes.

Spin modes are essential for fractional topological superconductivity.

Abstract

Domain walls in fractional quantum Hall ferromagnets are gapless helical one-dimensional channels formed at the boundaries of topologically distinct quantum Hall (QH) liquids. Na\"{i}vely, these helical domain walls (hDWs) constitute two counter-propagating chiral states with opposite spins. Coupled to an s-wave superconductor, helical channels are expected to lead to topological superconductivity with high order non-Abelian excitations. Here we investigate transport properties of hDWs in the $\nu=2/3$ fractional QH regime. Experimentally we found that current carried by hDWs is substantially smaller than the prediction of the na\"{i}ve model. Luttinger liquid theory of the system reveals redistribution of currents between quasiparticle charge, spin and neutral modes, and predicts the reduction of the hDW current. Inclusion of spin-non-conserving tunneling processes reconciles theory with experiment. The theory confirms emergence of spin modes required for the formation of fractional topological superconductivity.