Electronic properties of disclinated flexible membrane beyond the inextensional limit: Application to graphene

TL;DR

This paper develops a gauge-theory framework to analyze the electronic properties of disclinated flexible graphene membranes beyond the inextensional limit, incorporating elasticity and geometric smoothing effects.

Contribution

It introduces a novel gauge-theory approach that models disclinations on flexible membranes beyond the inextensional approximation, including a hyperboloid smoothing of the conical singularity.

Findings

Modification of Landau levels in disclinated graphene

Altered electronic density of states due to elasticity

Stabilization of the membrane theory through von Karman solutions

Abstract

Gauge-theory approach to describe Dirac fermions on a disclinated flexible membrane beyond the inextensional limit is formulated. The elastic membrane is considered as an embedding of 2D surface into R^3. The disclination is incorporated through an SO(2) gauge vortex located at the origin, which results in a metric with a conical singularity. A smoothing of the conical singularity is accounted for by replacing a disclinated rigid plane membrane with a hyperboloid of near-zero curvature pierced at the tip by the SO(2) vortex. The embedding parameters are chosen to match the solution to the von Karman equations. A homogeneous part of that solution is shown to stabilize the theory. The modification of the Landau states and density of electronic states of the graphene membrane due to elasticity is discussed.