On topological aspects of 2D graphene like materials

TL;DR

This paper explores how curvature and magnetic fields influence the topological properties of 2D graphene-like materials, revealing how geometric variations lead to distinct topological phases.

Contribution

It introduces a curved spacetime model for multilayer graphene and links magnetic field effects to topological surface variations such as torus and sphere.

Findings

Curvature effects induce topological variations in graphene surfaces.

Magnetic fields influence geometric and topological properties.

Hexagonal tessellation relates to torus topology with genus g=1.

Abstract

We study the graphene lattice with a curvature effect. The action depicting multilayers of graphene is portrayed in curved spacetime and effective Dirac equation scopes the curvature effect. The magnetic field is responsible for the geometric variations and these changes are identified as topological aspects in graphene. By varying the geometry of the graphene one can create topologically distinct surfaces which could be remarked as torus or sphere. The 2D hexagonal tessellation induces a curvature effect and the tessellation plane is reduced to a 2-torus having genus g=1.