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

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.

References in corpus (11)

• The electronic properties of graphene
• Uniaxial Strain in Graphene by Raman Spectroscopy: G peak splitting, Gruneisen Parameters and Sample Orientation
• Energy gaps, topological insulator state and zero-field quantum Hall effect in graphene by strain engineering
• A tight-binding approach to uniaxial strain in graphene
• Optical Phonons in Carbon Nanotubes: Kohn Anomalies, Peierls Distortions and Dynamic Effects
• Graphene as an electronic membrane
• Charge inhomogeneities due to smooth ripples in graphene sheets
• Tuning electronic properties of corrugated graphene: confinement, curvature and band gap opening
• Geometry induced potential on a 2D-section of a wormhole: catenoid
• Bilayer graphene Origami: curvature-induced p-n junctions
• Quantum anticentrifugal force for wormhole geometry

Cited by in corpus (14)

• Helicoidal Graphene Nanoribbons: Chiraltronics
• Constructing spherically symmetric Einstein-Dirac systems with multiple spinors: Ansatz, wormholes and other analytical solutions
• Geometric effects in the electronic transport of deformed nanotubes
• Curvatronics with bilayer graphene in an effective $4D$ spacetime
• Graphene wormhole trapped by external magnetic field
• Fermionic vacuum currents in topologically nontrivial braneworlds: Two-brane geometry
• Current density and conductivity through modified gravity in the graphene with defects
• Fermionic currents in topologically nontrivial braneworlds
• Reverse strain-induced snake states in graphene nanoribbons
• The centripetal force law and the equation of motion for a particle on a curved hypersurface
• Generalized Centripetal Force Law and Quantization of Motion Constrained on 2D Surfaces
• General covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere
• No existence of the geometric potential for a Dirac fermion on two-dimensional curved surfaces of revolution
• RKKY interaction on curved surfaces: Different behavior of Dirac and Schrödinger carriers as interaction mediating particles