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

Abstract: We propose a "minimal" fractional topological insulator (mFTI), motivated by the recent experimental report on the signatures of FTI at total filling factor $\nu_{\rm tot} = 3$ in a transition metal dichalcogenide (TMD) moir\'{e} system. The observed FTI at $\nu_{\rm tot} = 3$ is likely given by a topological state living in a pair of half-filled conjugate Chern bands with Chern numbers $C=\pm 1$ on top of another pair of fully-filled conjugate Chern bands. We propose the mFTI as a strong 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 with 32 Abelian anyons (including the electron); (2) the minimally-charged anyon carries electric charge $e^\ast = e/2$, together with the spin-Hall conductivity, implying that the mFTI's robust edge state remains gapless 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 topological order's complexity) within all the topological orders that can potentially be realized at the same electron filling of the system and with the same Hall transports; (4) the mFTI is the common descendant of multiple valley-decoupled "product topological orders" with larger quantum dimensions. It is also a symmetry-enriched topological order promoted from multiple symmetry-protected topological states, after gauging part of their symmetries.