Symmetric localization of $\nu_{\text{tot}}=4/3$ fractional topological insulator edges

TL;DR

This paper develops a theory for the edges of a fractional topological insulator at total filling 4/3, revealing multiple phases, conductance values, and conditions under which edge states become insulating, challenging simple transport-based identification.

Contribution

It introduces a disordered interacting edge theory for the 4/3 fractional topological insulator, identifying distinct phases and the impact of spin-changing perturbations on edge states.

Findings

Three distinct phases with different conductance values identified.

Interaction-induced insulating edge states can form without symmetry breaking.

Edge-state transport alone may not reliably identify the topological phase.

Abstract

Motivated by the recent twisted MoTe$_2$ experiment [arXiv:2601.18508], we develop a disordered interacting edge theory of a fractional topological insulator at $\nu_{\text{tot}}=4/3$, consisting of two time-reversal-conjugated $\nu=2/3$ fractional quantum Hall states. For an $S_z$-conserving edge, we uncover three distinct phases with two possible conductance values per edge in the long-edge limit: $\frac{2}{3}\frac{e^2}{h}$ and $\frac{4}{3}\frac{e^2}{h}$. In the presence of $S_z$-changing perturbations (e.g., Rashba spin-orbit coupling), an interaction-induced insulating edge state can emerge without breaking time-reversal or charge-conservation symmetry, corresponding to the absence of a topologically protected edge state. We further provide an exact mapping to a noninteracting fermionic theory exhibiting Anderson localization. Our results showcase an explicit, experimentally relevant example that the edge-state two-terminal transport is insufficient to identify the $\nu_{\text{tot}}=4/3$ fractional topological insulators.