Dirac fermions on a surface with localized strain

TL;DR

This paper investigates how localized strain deformations in a two-dimensional Dirac material affect electronic states, revealing bound states, localized Landau levels, and geometric phases through analytical and numerical methods.

Contribution

It introduces a comprehensive analysis of strain effects on Dirac fermions, including the role of spin connection and geometric potentials, which is novel in understanding strain-induced electronic phenomena.

Findings

Localized deformation induces bound states near the strain.

External magnetic fields lead to localized Landau levels.

A geometric Aharonov-Bohm phase is observed in the system.

Abstract

We study the influence of a localized Gaussian deformation on massless Dirac fermions confined to a two-dimensional curved surface. Both in-plane and out-of-plane displacements are considered within the framework of elasticity theory. These deformations couple to the Dirac spinors via the spin connection and the vielbeins, leading to a position-dependent Fermi velocity and an effective geometric potential. We show that the spin connection contributes an attractive potential centered on the deformation and explore how this influences the fermionic density of states. Analytical and numerical solutions reveal the emergence of bound states near the deformation and demonstrate how the Lam\'{e} coefficients affect curvature and state localization. Upon introducing an external magnetic field, the effective potential becomes confining at large distances, producing localized Landau levels that concentrate near the deformation. A geometric Aharonov-Bohm phase is identified through the spinor holonomy. These results contribute to the understanding of strain-induced electronic effects in Dirac materials, such as graphene.