Revisiting the electronic properties of dislocated graphene sheets

TL;DR

This paper investigates how topological defects like dislocations affect the electronic properties of graphene, using a Riemann-Cartan geometric framework linked to elasticity theory, revealing the influence of defect-induced geometry on electronic spectra.

Contribution

It introduces a Riemann-Cartan geometric approach to model dislocations in graphene, connecting elasticity parameters directly to electronic properties.

Findings

Dislocations modify the electronic spectrum of graphene.

Elastic parameters influence electronic properties through geometric modeling.

Riemann-Cartan geometry captures defect effects beyond traditional methods.

Abstract

The interplay between topological defects, such as dislocations or disclinations, and the electronic degrees of freedom in graphene has been extensively studied. In the literature, for the study of this kind of problems, it is in general used either a gauge theory or a curved spatial Riemannian geometry approach, where, in the geometric case, the information about the defects is contained in the metric and the spin-connection. However, these topological defects can also be associated to a Riemann-Cartan geometry where curvature and torsion plays an important role. In this article we study the interplay between a wedge dislocations in a planar graphene sheet and the properties of its electronic degrees of freedom. Our approach relies in its relation with elasticity theory through the so called elastic-gauge, where their typical coefficients, as for example the Poisson's ratio, appear directly in the metric, and consequently also in the electronic spectrum.