Electronic properties of corrugated graphene, the Heisenberg principle and wormhole geometry in solid state

TL;DR

This paper develops a quantum framework for graphene's electronic properties that respects the Heisenberg principle, revealing how curvature influences electronic behavior and suggesting applications in strain engineering and analog gravity models.

Contribution

It introduces a geometric potential arising from surface curvature in graphene, integrating quantum principles with surface confinement and exploring wormhole geometries in solid state systems.

Findings

Geometric potential scales with mean curvature, affecting Fermi energy.

Curvature can be used to control electronic properties without chemical modification.

Wormhole geometries can be simulated in graphene for quantum gravity analogs.

Abstract

Adopting a purely two dimensional relativistic equation for graphene's carriers contradicts the Heisenberg uncertainty principle since it requires setting off-the-surface coordinate of a three-dimensional wavefunction to zero. Here we present a theoretical framework for describing graphene's massless relativistic carriers in accordance with this most fundamental of all quantum principles. A gradual confining procedure is used to restrict the dynamics onto a surface and normal to the surface parts and in the process the embedding of this surface into the three dimensional world is accounted for. As a result an invariant geometric potential arises in the surface part which scales linearly with the Mean curvature and shifts the Fermi energy of the material proportional to bending. Strain induced modification of the electronic properties or "straintronics" is clearly an important field of study in graphene. This opens a venue to producing electronic devices, MEMS and NEMS where the electronic properties are controlled by geometric means and no additional alteration of graphene is necessary. The appearance of this geometric potential also provides us with clues as to how quantum dynamics looks like in the curved space-time of general relativity. In this context, we explore a two-dimensional cross-section of the wormhole geometry realized with graphene as a solid state thought experiment.