Semiclassical analysis of two-scale electronic Hamiltonians for twisted bilayer graphene - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2023

Semiclassical analysis of two-scale electronic Hamiltonians for twisted bilayer graphene

Abstract

This paper investigates the mathematical properties of independent-electron models for twisted bilayer graphene by examining the density-of-states of corresponding single-particle Hamiltonians using tools from semiclassical analysis. This study focuses on a specific atomic-scale Hamiltonian $H_{d,\theta}$ constructed from Density-Functional Theory, and a family of moir\'e-scale Hamiltonians $H_{d,K,\theta}^{\rm eff}$ containing the Bistritzer-MacDonald model. The parameter $d$ represents the interlayer distance, and $\theta$ the twist angle. It is shown that the density-of-states of $H_{d,\theta}$ and $H_{d,K,\theta}^{\rm eff}$ admit asymptotic expansions in the twist angle parameter $\epsilon:=\sin(\theta/2)$. The proof relies on a twisted version of the Weyl calculus and a trace formula for an exotic class of pseudodifferential operators suitable for the study of twisted 2D materials. We also show that the density-of-states of $H_{d,\theta}$ admits an asymptotic expansion in $\eta:=\tan(\theta/2)$ and comment on the differences between the expansions in $\epsilon$ and $\eta$.

Dates and versions

hal-04371908 , version 1 (04-01-2024)

Identifiers

Cite

Eric Cancès, Long Meng. Semiclassical analysis of two-scale electronic Hamiltonians for twisted bilayer graphene. 2023. ⟨hal-04371908⟩
12 View
0 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More