Bilayer graphene with parallel magnetic field and twisting: Phases and phase transitions in a highly tunable Dirac system

TL;DR

This paper investigates how twisting and parallel magnetic fields in bilayer graphene create a highly tunable Dirac system, revealing new phases, phase transitions, and the effects of additional perpendicular fields.

Contribution

It introduces a comprehensive effective theory for bilayer graphene under combined twisting and magnetic fields, analyzing phase transitions and symmetry transformations.

Findings

Sizable in-plane magnetic fields simplify the low-energy Dirac points.

Multiple fully gapped states can emerge with strong interactions.

Quantum critical behavior of phase transitions is characterized.

Abstract

The effective theory for bilayer graphene (BLG), subject to parallel/in-plane magnetic fields, is derived. With a sizable magnetic field the trigonal warping becomes irrelevant, and one ends up with two Dirac points in the vicinity of each valley in the low-energy limit, similar to the twisted BLG. Combining twisting and parallel field thus gives rise to a Dirac system with tunable Fermi velocity and cutoff. If the interactions are sufficiently strong, several fully gapped states can be realized in these systems, in addition to the ones in a pristine setup. Transformations of the order parameters under various symmetry operations are analyzed. The quantum critical behavior of various phase transitions driven by the twisting and the magnetic field is reported. The effects of an additional perpendicular fields, and possible ways to realize the new massive phases is highlighted.