Symmetric localization of $ν_{\text{tot}}=4/3$ 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 $ν_{\text{tot}}=4/3$, consisting of two time-reversal-conjugated $ν=2/3$ 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 $ν_{\text{tot}}=4/3$ fractional topological insulators.

Figures (1)

• Figure 1: (a) The edge configuration of $\nu_{\text{tot}}=4/3$ FTI. The solid arrows indicate the charge-$e$ movers, and the dashed arrows indicate the charge-$e/3$ movers. The blue arrows can be viewed as the edge state of a spin-up $\nu=2/3$ FQH insulator; the red arrows can be viewed as the edge state of a spin-down $\nu=-2/3$ FQH insulator. (b) Illustration of the backscattering process $L^{\dagger}_{\uparrow}R_{\uparrow}L^{\dagger}_{\downarrow}R_{\uparrow}$ in $\mathcal{S}_{I,\text{loc}}$ [Eq. (\ref{['Eq:S_I_loc']})]. Note that $L^{\dagger}_{\uparrow}$ is made of three $e/3$ quasiparticles (the three red dashed lines). The interaction in $\mathcal{S}_{I,\text{loc}}$ leads to a symmetric localized state in the strong coupling limit.