Minimal Fractional Topological Insulator in half-filled conjugate moiré Chern bands

Motivated by recent experimental reports, we propose a "minimal" fractional topological insulator (mFTI) living in a pair of half-filled conjugate Chern bands with Chern numbers C=±1. 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 conductivity, implying the robustness of the mFTI's gapless edge state whenever time-reversal symmetry and charge conversation are present; (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 unique one that respects time-reversal symmetry. (4) the mFTI is the common descendant of multiple valley-decoupled "product TOs" with larger quantum dimensions. Similar mFTIs can be constructed for a pair of 1/q-filled conjugate Chern bands.