Stable magic angle in twisted Kane-Mele materials

TL;DR

This paper demonstrates that flat bands and topological states in twisted Kane-Mele materials can be stabilized against angle disorder, with implications for robust topological phases in these systems.

Contribution

It introduces a continuum model and Wannier function analysis showing stability of flat bands and topological states in twisted Kane-Mele materials, differing from twisted bilayer graphene.

Findings

Flat bands are stabilized near the magic angle in Kane-Mele materials.

Kane-Mele spin-orbit coupling enhances fractional Chern insulator stability.

Topological flat bands are identified at large twist angles in Pt$_2$HgSe$_3$.

Abstract

We propose that flat bands and van Hove singularities near the magic angle can be stabilized against angle disorder in the twisted Kane-Mele model. With continuum model and maximally localized Wannier function approaches, we identify a quadratic dispersion relationship between the bandwidth, interaction parameters versus the twist angle, in contrast to twisted bilayer graphene (TBG). Introducing Kane-Mele spin-orbit coupling to TBG greatly reduces the fractional Chern insulator indicator and enhances the stability of fractional Chern states near the magic angle, as confirmed by exact diagonalization calculations. Moreover, in twisted bilayer Pt$_2$HgSe$_3$ with intrinsic Kane-Mele spin-orbit coupling, we identify a topological flat band at a large twist angle around 4 degrees.