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

Understand

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.