Strain effects on the electronic properties of a graphene wormhole

TL;DR

This paper investigates how strain and curvature influence the electronic behavior of a graphene wormhole, revealing effects like spin-dependent wave function damping, supersymmetric potentials, and confined Landau levels near the wormhole's throat.

Contribution

It introduces a detailed analysis of strain and curvature effects on graphene wormholes, including supersymmetric potentials and spin-dependent confinement of electronic states.

Findings

Strain causes exponential damping of wave functions without magnetic field.

Curvature induces power-law damping of the wave function.

Magnetic fields lead to spin-dependent confinement and Landau levels.

Abstract

In this work, we explore the strain and curvature effects on the electronic properties of a curved graphene structure, called the graphene wormhole. The electron dynamics is described by a massless Dirac fermion containing position--dependent Fermi velocity. In addition, the strain produces a pseudo--magnetic vector potential to the geometric coupling. For an isotropic strain tensor, the decoupled components of the spinor field exhibit a supersymmetric (SUSY) potential, depending on the centrifugal term and the external magnetic field only. In the absence of a external magnetic field, the strain yields to an exponential damped amplitude, whereas the curvature leads to a power--law damping of the wave function. The spin--curvature coupling breaks the chiral symmetry between the upper and the lower spinor component, which leads to the increasing of the wave function on either upper or lower region of the wormhole, i.e., depending on the spin number. By adding an uniform magnetic field, the effective potential exhibits an asymptotic quadratic profile and a spin--curvature barrier near the throat. As a result, the bound states (Landau levels) are confined around the wormhole throat showing an asymmetric and spin--dependent profile.