Curvatronics with bilayer graphene in an effective $4D$ spacetime

TL;DR

This paper demonstrates that bilayer graphene's low-energy excitations can be described by a 4D Dirac fermion model, where curvature influences electronic properties, enabling curvature-based control of conductivity for potential electronic applications.

Contribution

It introduces a novel effective 4D spacetime framework for bilayer graphene and shows how curvature can tune electronic band gaps, advancing the field of curvatronics.

Findings

Curvature alters the energy levels of electronic bands.

Changing curvature switches between conducting and insulating regimes.

Effective 4D Dirac fermion description emerges from bilayer graphene interactions.

Abstract

We show that in AB stacked bilayer graphene low energy excitations around the semimetallic points are described by massless, four dimensional Dirac fermions. There is an effective reconstruction of the 4 dimensional spacetime, including in particular the dimension perpendicular to the sheet, that arises dynamically from the physical graphene sheet and the interactions experienced by the carriers. The effective spacetime is the Eisenhart-Duval lift of the dynamics experienced by Galilei invariant L\'evy-Leblond spin $\frac{1}{2}$ particles near the Dirac points. We find that changing the intrinsic curvature of the bilayer sheet induces a change in the energy level of the electronic bands, switching from a conducting regime for negative curvature to an insulating one when curvature is positive. In particular, curving graphene bilayers allows opening or closing the energy gap between conduction and valence bands, a key effect for electronic devices. Thus using curvature as a tunable parameter opens the way for the beginning of curvatronics in bilayer graphene.