Twisted TMDs in the small-angle limit: exponentially flat and trivial bands

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Becker, Simon, Yang, Mengxuan
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866913192486109184
author Becker, Simon
Yang, Mengxuan
author_facet Becker, Simon
Yang, Mengxuan
contents Recent experiments discovered fractional Chern insulator states at zero magnetic field in twisted bilayer MoTe$_2$ [C23,Z23] and WSe$_2$ [MD23]. In this article, we study the MacDonald Hamiltonian for twisted transition metal dichalcogenides (TMDs) and analyze the low-lying spectrum in TMDs in the limit of small twisting angles. Unlike in twisted bilayer graphene Hamiltonians, we show that TMDs do not exhibit flat bands. The flatness in TMDs for small twisting angles is due to spatial confinement by a matrix-valued potential. We show that by generalizing semiclassical techniques developed by Simon [Si83] and Helffer-Sjöstrand [HS84] to matrix-valued potentials, there exists a wide range of model parameters such that the low-lying bands are of exponentially small width in the twisting angle, topologically trivial, and obey a harmonic oscillator-type spacing with explicit parameters.
format Preprint
id arxiv_https___arxiv_org_abs_2401_06078
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Twisted TMDs in the small-angle limit: exponentially flat and trivial bands
Becker, Simon
Yang, Mengxuan
Mathematical Physics
Mesoscale and Nanoscale Physics
Strongly Correlated Electrons
Analysis of PDEs
Spectral Theory
Recent experiments discovered fractional Chern insulator states at zero magnetic field in twisted bilayer MoTe$_2$ [C23,Z23] and WSe$_2$ [MD23]. In this article, we study the MacDonald Hamiltonian for twisted transition metal dichalcogenides (TMDs) and analyze the low-lying spectrum in TMDs in the limit of small twisting angles. Unlike in twisted bilayer graphene Hamiltonians, we show that TMDs do not exhibit flat bands. The flatness in TMDs for small twisting angles is due to spatial confinement by a matrix-valued potential. We show that by generalizing semiclassical techniques developed by Simon [Si83] and Helffer-Sjöstrand [HS84] to matrix-valued potentials, there exists a wide range of model parameters such that the low-lying bands are of exponentially small width in the twisting angle, topologically trivial, and obey a harmonic oscillator-type spacing with explicit parameters.
title Twisted TMDs in the small-angle limit: exponentially flat and trivial bands
topic Mathematical Physics
Mesoscale and Nanoscale Physics
Strongly Correlated Electrons
Analysis of PDEs
Spectral Theory
url https://arxiv.org/abs/2401.06078