Generalized Ellis-Bronnikov graphene wormhole

TL;DR

This paper explores how the geometry of a generalized Ellis-Bronnikov graphene wormhole influences electron behavior, revealing the impact of curvature and shape parameters on bound states and probability densities.

Contribution

It introduces a detailed analysis of electron dynamics on a curved graphene surface with a generalized wormhole shape, highlighting the role of geometric parameters.

Findings

Geometry significantly affects bound state energies.

Orbital angular momentum influences electron probability density.

Shape parameter $n$ alters the electronic properties.

Abstract

In this paper, we investigate the spinless stationary Schr\"odinger equation for the electron when it is permanently bound to a generalized Ellis-Bronnikov graphene wormhole-like surface. The curvature gives rise to a geometric potential affecting thus the electronic dynamics. The geometry of the wormhole's shape is controlled by the parameter $n$ which assumes even values. We discuss the role played by the parameter $n$ and the orbital angular momentum on bound states and probability density for the electron.