Signatures of localization on the edge of a fractional topological insulator

Abstract

Recent experiments in van der Waals moiré materials have reported realizations of two-dimensional fractional topological insulators (FTIs). We study transport properties of FTI edges at filling factors $ν_{\text{FTI}} = 2(1\pm 1/n)$ with integer $n \geq 2$ (even or odd), each of which supports four counter-propagating edge modes. The edge modes can undergo partial localization, leaving two of the four edge modes conducting. We identify three distinct partial-localization channels and, for each channel, determine the reduced theory describing the remaining conducting modes, from which we obtain the minimal quasiparticle charge. We further explore transport properties of each partially localized phase and in particular determine the corresponding edge conductances. We demonstrate that measurements of the conductance together with the minimal quasiparticle charge provide a fingerprint that uniquely distinguishes the three partially localized phases.