Strain-Tuned Incommensurate Kekul\'e Spiral Order in Twisted Bilayer Graphene: a Quantum Many-Body Study

TL;DR

This study explores how strain influences the transition between Kramers intervalley coherent and incommensurate Kekulé spiral states in twisted bilayer graphene using advanced quantum many-body computational methods.

Contribution

It introduces a combined quantum Monte Carlo, exact diagonalization, and Hartree-Fock approach to analyze strain-dependent phase transitions in twisted bilayer graphene.

Findings

Identified strain-induced transition from KIVC to IKS state.

Developed an approximate sign-problem treatment in QMC for flat-band systems.

Provided insights into the phase diagram of twisted bilayer graphene.

Abstract

The understanding of quantum many-body states in twisted bilayer graphene at the magic angle has been greatly improved both in experiment and in theory. However, away from the exactly solvable chiral limit and the sign-problem-free charge neutrality point, the calculation of the ground state properties and the identification of the phase diagram are challenging due to the exponential increase in the complexity, which has rendered explanations of experimentally observed insulating and superconducting phases restricted largely to the perturbative level. Here we focus on the filling factors $\nu = \pm2$ away from charge neutrality and address the question of the strain dependence of the interacting ground state. We adjust our continuous field momentum-space quantum Monte Carlo (QMC) method to treat the sign problem approximately, and perform a quantum many-body study together with exact diagonalization (ED) and Hartree-Fock (HF) mean field. Leveraging this combined protocol of QMC, ED, and HF, we investigate the strain-tuned transition from the Kramers intervalley coherent (KIVC) state to the incommensurate Kekul\'e spiral state (IKS). Our computational protocol sheds light on the KIVC-IKS transition in a projected correlated flat-band setting, and opens the door for further understanding of the rich phase diagram of twisted bilayer graphene and other strongly-correlated flat-band systems.