Minimal Fractional Topological Insulator in Half-Filled Conjugate Moiré Chern Bands

We propose a “minimal” fractional topological insulator (mFTI), motivated by the recent experimental report on the fractional quantum spin-Hall effect in a transition metal dichalcogenide moiré system. The observed effect suggests the possibility of a topological state living in a pair of half-filled conjugate Chern bands with Chern numbers C=±1. We propose the mFTI as a novel candidate topological state in the half-filled conjugate Chern bands. The mFTI is characterized by the following features. (1) It is a fully gapped topological order (TO) with 16 Abelian anyons if the electron is considered trivial (32 including electrons), (2) the minimally charged anyon carries electric charge e*=e/2, together with the fractional quantum spin-Hall conductance, implying the robustness of the mFTI’s gapless edge state whenever time-reversal symmetry and charge conservation are present, and (3) the mFTI is minimal in the sense that it has the smallest total quantum dimension (a metric for the TO’s complexity) within all the TOs that can potentially be realized at the same electron filling and with the same Hall transports; the mFTI is also the minimal TO that respects time-reversal symmetry. (4) The mFTI is the common descendant of multiple valley-decoupled “product TOs” with larger quantum dimensions. It can also be viewed as the result of gauging multiple symmetry-protected topological states. Similar mFTIs are classified and constructed for a pair of 1/q-filled conjugate Chern bands. We further classify the mFTIs via the stability of the gapless interfaces between them.