Kekul\'e Spiral Order from Strained Topological Heavy Fermions

TL;DR

This paper uses a topological heavy fermion model with heterostrain to explain Kekulé spiral order and symmetry-breaking phenomena in twisted bilayer graphene, aligning theoretical predictions with experimental observations.

Contribution

It introduces a framework combining heterostrain and particle-hole symmetry breaking in the THF model to analytically explain Kekulé spiral order and correlated insulator asymmetries.

Findings

Heterostrain influences the presence of incommensurate Kekulé spiral order.

Hartree-Fock method reproduces self-consistent states and predicts IKS wavevector.

The model explains stronger correlated states on the electron side, matching experiments.

Abstract

The topological heavy fermion (THF) model of twisted bilayer graphene is a framework for treating its strongly interacting topological flat bands. In this work, we employ the THF model with heterostrain and particle-hole symmetry breaking corrections to study its symmetry-broken ground states. We find that the heterostrain correction motivates a specific parent-state wavefunction which dictates the presence or absence of an incommensurate Kekul\'e spiral (IKS) at each integer filling by invoking Dirac node braiding and annihilation as a mechanism to achieve low energy gapped states. We then show that one-shot Hartree-Fock faithfully replicates the numerical results of fully self-consistent states and motivates an analytical approximation for the IKS wavevector. We can also account for the particle-hole asymmetry in the correlated insulator gaps. In particular, the THF model predicts stronger correlated states on the electron side rather than hole side in agreement with magic angle experiments, despite the electron side being more dispersive in the single-particle band structure. This work demonstrates that we can analytically explain even the more subtle symmetry breaking order properties observed in experiments where heterostrain, relaxation, and interactions together determine the ground state.