Tuning between a fractional topological insulator and competing phases at $\nu_\mathrm{T}=2/3$

TL;DR

This paper investigates a spinful Landau level model at filling fraction 2/3, revealing various phases including a fractional topological insulator, influenced by short-range interactions, relevant for moiré transition metal dichalcogenides.

Contribution

It identifies and characterizes multiple competing phases in a spinful Landau level system, highlighting the role of short-range pseudopotentials in phase stability.

Findings

Discovery of a fractional topological insulator phase.

Identification of phase separation and spin-polarized quantum Hall states.

Dependence of phase behavior on pseudopotential parity.

Abstract

We study a spinful, time-reversal symmetric lowest Landau level model for a flatband quantum spin Hall system at total filling fraction $\nu_\mathrm{T}=2/3$. Such models are relevant, e.g. for spin-valley locked moir\'e transition metal dichalcogenides. The opposite Chern number of the two spins hinders the formation of a quantum Hall ferromagnet, instead favouring other phases. We study the phase diagram in dependence on different short-range Haldane pseudopotentials $V_m$ and uncover several phases: A fractional topological insulator, a phase separated state, a spin-polarized fractional quantum Hall state, and the partially particle-hole transformed Halperin (111) state. The effect of the pseudopotentials $V_m$ depends on the parity of $m$, the relative angular momentum.