Negative-curvature spacetime solutions for graphene

Abstract

We provide a detailed analysis of the electronic properties of graphene-like materials with charge carriers living on a curved substrate, focusing in particular on constant negative-curvature spacetime. An explicit parametrization is also worked out in the remarkable case of Beltrami geometry, with an analytic solution for the pseudoparticles modes living on the curved bidimensional surface. We will then exploit the correspondent massless Dirac description, to determine how it affects the sample local density of states.

arXiv comment20 pages, 4 figures

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• Interaction between macroscopic quantum systems and gravity
• $\mathcal{N}=2$ Extended MacDowell-Mansouri Supergravity
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• Superconductors and gravity
• Electronic states in a quantum Beltrami surface
• Superconductor in static gravitational, electric and magnetic fields with vortex lattice
• Ray geodesics and wave propagation on the Beltrami surface: Optics of an optical wormhole
• Dirac equation in curved spacetime: the role of local Fermi velocity
• Vacuum currents in curved tubes
• Massless Rarita-Schwinger equations: Half and three halves spin solution
• The geometry of induced currents in two dimensional media
• Zero energy states of Dirac equation in $(2+1)$-dimensional curved spacetime
• Scalar vacuum densities on Beltrami pseudosphere