Higher Landau-Level Analogs and Signatures of Non-Abelian States in Twisted Bilayer MoTe$_2$

TL;DR

This paper explores higher Landau level physics and potential non-Abelian states in twisted bilayer MoTe2, using DFT-based models and exact diagonalization, revealing signatures of non-Abelian states at certain fillings.

Contribution

The study develops a Wannier-based six-orbital model from DFT for consecutive Chern bands in twisted MoTe2, identifying non-Abelian signatures at half-filling of the second miniband.

Findings

Signatures of non-Abelian states at half-filled second miniband.

Development of a DFT-based Wannier model for Chern bands.

Identification of higher Landau level analogs in twisted MoTe2.

Abstract

Recent experimental discovery of fractional Chern insulators at zero magnetic field in moir\'e superlattices has sparked intense interests in bringing Landau level physics to flat Chern bands. In twisted MoTe$_2$ bilayers (tMoTe$_2$), recent theoretical and experimental studies have found three consecutive flat Chern bands at twist angle $\sim 2^\circ$. In this work, we investigate whether higher Landau level physics can be found in these consecutive Chern bands. At twist angles $2.00^\circ$ and $1.89^\circ$, we identify four consecutive $C = 1$ bands for the $K$ valley in tMoTe$_2$. By constructing Wannier functions directly from density functional theory (DFT) calculations, a six-orbital model is developed to describe the consecutive Chern bands, with the orbitals forming a honeycomb lattice. Exact diagonalization on top of Hartree-Fock calculations are carried out with the Wannier functions. Especially, when the second moir\'e miniband is half-filled, signatures of non-Abelian states are found. Our Wannier-based approach in modelling moir\'e superlattices is faithful to DFT wave functions and can serve as benchmarks for continuum models. The possibility of realizing non-Abelian anyons at zero magnetic field also opens up a new pathway for fault-tolerant quantum information processing.