Tuning electronic properties of corrugated graphene: confinement, curvature and band gap opening

Abstract

It is shown that for monolayer graphene electrons are confined on a perfect two dimensional surface. The implications for the electronic properties of corrugated graphene are discussed in view of a derivation of the constrained relativistic dynamics for the massless carriers in two dimensions. Surface curvature is related to a series of phenomena with practical applications such as curvature induced p-n junctions, band gap opening and decoherence. We also establish a bending free energy by treating graphene as a soft electronic membrane.

8 pages, 5 figures

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• Helicoidal Graphene Nanoribbons: Chiraltronics
• Electronic properties of corrugated graphene, the Heisenberg principle and wormhole geometry in solid state
• Disordered graphene and boron nitride in a microwave tight-binding analog
• Geometric effects in the electronic transport of deformed nanotubes
• Electronic properties of bilayer graphene catenoid bridge
• Pauli Equation on a Curved Surface and Rashba Splitting on a Corrugated Surface
• Analogies in electronic properties of graphene wormhole and perturbed nanocylinder
• Landau levels, self-adjoint extensions and Hall conductivity on a cone
• Optical conductivity of curved graphene
• Electronic properties of a nanotorus
• Geometric Potential Resulting from Dirac Quantization
• Generalized Ellis-Bronnikov graphene wormhole
• Position-dependent mass effects on a bilayer graphene catenoid bridge
• Pseudo-Hermitian Dirac operator on the torus for massless fermions under the action of external fields
• Two-dimensional electron gas under the effect of constrained potential and magnetic field in curved space
• General covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere
• Band Gap Modulation of Graphene on SiC
• Electronic states in quantum wires on a Möbius strip
• Geometrodynamics of a 2D Curved Surface due to a Constrained Quantum Particle via its Gravitational Dual: ${\mathcal{S}}^2$ Analytical Model Calculations
• Electronic states in a bilayer graphene quantum ripple