Twist-tuned quantum criticality in moir\'e bilayer graphene

TL;DR

This paper predicts a tunable quantum phase transition in moiré bilayer graphene from a semimetal to an insulator, characterized by symmetry breaking, and provides a theoretical framework for experimental verification.

Contribution

It introduces a detailed theoretical analysis of a twist-angle-driven quantum critical point in bilayer graphene, linking it to the Gross-Neveu-XY universality class.

Findings

Identifies a continuous quantum phase transition controlled by twist angle.

Characterizes the transition as belonging to the Gross-Neveu-XY universality class.

Provides a testable theoretical framework for experimental observation.

Abstract

We argue that moir\'e bilayer graphene at charge neutrality hosts a continuous semimetal-to-insulator quantum phase transition that can be accessed experimentally by tuning the twist angle between the two layers. For small twist angles near the first magic angle, the system realizes a Kramers intervalley-coherent insulator, characterized by circulating currents and spontaneously broken time reversal and U(1) valley symmetries. For larger twist angles above a critical value, the spectrum remains gapless down to the lowest temperatures, with a fully symmetric Dirac semimetal ground state. Using self-consistent Hartree-Fock theory applied to a realistic model of twisted bilayer graphene, based on the Bistritzer-MacDonald Hamiltonian augmented by screened Coulomb interactions, we find that the twist-tuned quantum phase transition is continuous. We argue that the quantum critical behavior belongs to the relativistic Gross-Neveu-XY universality class, and we characterize it through an effective field theory analysis. Our theoretical predictions can be directly tested using current experimental setups incorporating the recently developed quantum twisting microscope.