Twisted bilayer graphene in a parallel magnetic field

TL;DR

This paper investigates how an in-plane magnetic field influences the electronic band structure of twisted bilayer graphene, revealing the formation of quadratic band crossing points and changes in Dirac point behavior at and near magic angles.

Contribution

It provides a detailed analysis of the magnetic field effects on the non-interacting band structure of twisted bilayer graphene using the continuum model, highlighting new phenomena like QBCPs.

Findings

Quadratic band crossing points form at the magic angle under a parallel magnetic field.

Magnetic fields can induce qualitative changes in the Dirac points near charge neutrality.

The overall dispersion remains invariant over a range of magnetic field strengths.

Abstract

We study the effect of an in-plane magnetic field on the non-interacting dispersion of twisted bilayer graphene. Our analysis is rooted in the chirally symmetric continuum model, whose zero-field band structure hosts exactly flat bands and large energy gaps at the magic angles. At the first magic angle, the central bands respond to a parallel field by forming a quadratic band crossing point (QBCP) at the Moire Brillouin zone center. Over a large range of fields, the dispersion is invariant with an overall scale set by the magnetic field strength. For deviations from the magic angle and for realistic interlayer couplings, the motion and merging of the Dirac points lying near charge neutrality are discussed in the context of the symmetries, and we show that small magnetic fields are able to induce a qualitative change in the energy spectrum. We conclude with a discussion on the possible ramifications of our study to the interacting ground states of twisted bilayer graphene systems.