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

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 show an exact mapping (with a special choice of parameters) to a noninteracting fermionic theory exhibiting Anderson localization, and the weak-coupling phase diagrams are also constructed, showing that symmetric localization can emerge regardless of other $S_z$-conserving perturbations. Our results showcase an explicit, experimentally relevant example that the edge-state two-terminal transport can yield false-negative results in identifying the $\nu_{\text{tot}}=4/3$ fractional topological insulators.