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 spin connection modifies the density of states near the origin and how this modification is altered by changing mechanical parameters. Analytical and numerical solutions reveal the emergence of asymptotically free states, but with changes in amplitude near the origin due to the modification of curvature mediated by Lamé coefficients. Upon introducing an external magnetic field, the effective potential becomes confining at large distances, producing localized Landau levels that concentrate near the deformation, thus enabling the evaluation of how mechanical coefficients affect the localization of states. 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.

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 spin connection modifies the density of states near the origin and how this modification is altered by changing mechanical parameters. Analytical and numerical solutions reveal the emergence of asymptotically free states, but with changes in amplitude near the origin due to the modification of curvature mediated by Lamé coefficients. Upon introducing an external magnetic field, the effective potential becomes confining at large distances, producing localized Landau levels that concentrate near the deformation, thus enabling the evaluation of how mechanical coefficients affect the localization of states. 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.

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 spin connection modifies the density of states near the origin and how this modification is altered by changing mechanical parameters. Analytical and numerical solutions reveal the emergence of asymptotically free states, but with changes in amplitude near the origin due to the modification of curvature mediated by Lamé coefficients. Upon introducing an external magnetic field, the effective potential becomes confining at large distances, producing localized Landau levels that concentrate near the deformation, thus enabling the evaluation of how mechanical coefficients affect the localization of states. 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.

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 spin connection modifies the density of states near the origin and how this modification is altered by changing mechanical parameters. Analytical and numerical solutions reveal the emergence of asymptotically free states, but with changes in amplitude near the origin due to the modification of curvature mediated by Lamé coefficients. Upon introducing an external magnetic field, the effective potential becomes confining at large distances, producing localized Landau levels that concentrate near the deformation, thus enabling the evaluation of how mechanical coefficients affect the localization of states. 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.