Dirac fermions on a disclinated flexible surface

TL;DR

This paper develops a gauge-theory framework to model Dirac fermions on flexible elastic surfaces with disclinations, incorporating topological gauge fields and smoothing effects, and analyzes zero-mode solutions.

Contribution

It introduces a novel gauge-theory approach to describe Dirac fermions on disclinated flexible surfaces, including a natural smoothing mechanism for conical singularities.

Findings

Formulated a gauge-theory model for disclinated elastic surfaces

Incorporated topologically nontrivial gauge fields to generate conical metrics

Analyzed the existence of zero-mode solutions to the Dirac equation

Abstract

A self-consisting gauge-theory approach to describe Dirac fermions on flexible surfaces with a disclination is formulated. The elastic surfaces are considered as embeddings into R^3 and a disclination is incorporated through a topologically nontrivial gauge field of the local SO(3) group which generates the metric with conical singularity. A smoothing of the conical singularity on flexible surfaces is naturally accounted for by regarding the upper half of two-sheet hyperboloid as an elasticity-induced embedding. The availability of the zero-mode solution to the Dirac equation is analyzed.