Heavy Fermions as an Efficient Representation of Atomistic Strain and Relaxation in Twisted Bilayer Graphene

TL;DR

This paper demonstrates that the heavy fermion model effectively captures strain and relaxation effects in twisted bilayer graphene, providing a simplified yet accurate framework for understanding experimental observations.

Contribution

It introduces a heavy fermion model that efficiently incorporates strain and relaxation effects in twisted bilayer graphene, simplifying the analysis of correlated states.

Findings

Strain and relaxation are well captured by first order perturbation in the HF model.

These effects do not alter the interacting terms in the periodic Anderson model.

A minimal model with 4 symmetry-breaking terms reproduces the main effects.

Abstract

Although the strongly interacting flat bands in twisted bilayer graphene (TBG) have been approached using the minimal Bistritzer-MacDonald (BM) Hamiltonian, there is mounting evidence that strain and lattice relaxation are essential in correctly determining the order of the correlated insulator groundstates. These effects can be incorporated in an enhanced continuum model by introducing additional terms computed from the relaxation profile. To develop an analytical and physical understanding of these effects, we include strain and relaxation in the topological heavy fermion (HF) model of TBG. We find that strain and relaxation are very well captured in first order perturbation theory by projection onto the fully symmetric HF Hilbert space, and remarkably do not alter the interacting terms in the periodic Anderson model. Their effects are fully incorporated in the single-particle HF Hamiltonian, and can be reproduced in a minimal model with only 4 symmetry-breaking terms. Our results demonstrate that the heavy fermion framework of TBG is an efficient and robust representation of the perturbations encountered in experiment.