Weyl-Gauge Symmetry of Graphene

Abstract

The conformal invariance of the low energy limit theory governing the electronic properties of graphene is explored. In particular, it is noted that the massless Dirac theory in point enjoys local Weyl symmetry, a very large symmetry. Exploiting this symmetry in the two spatial dimensions and in the associated three dimensional spacetime, we find the geometric constraints that correspond to specific shapes of the graphene sheet for which the electronic density of states is the same as that for planar graphene, provided the measurements are made in accordance to the inner reference frame of the electronic system. These results rely on the (surprising) general relativistic-like behavior of the graphene system arising from the combination of its well known special relativistic-like behavior with the less explored Weyl symmetry. Mathematical structures, such as the Virasoro algebra and the Liouville equation, naturally arise in this three-dimensional context and can be related to specific profiles of the graphene sheet. Speculations on possible applications of three-dimensional gravity are also proposed.

22 pages, 3 figures - two new references and few typos fixed, matches published version by Annals of Physics

References in corpus (8)

• The electronic properties of graphene
• The structure of suspended graphene sheets
• Charge inhomogeneities due to smooth ripples in graphene sheets
• Chiral Gauge Theory for Graphene
• Electron density distribution and screening in rippled graphene sheets
• Electron fractionalization for two-dimensional Dirac fermions
• Graphene with geometrically induced vorticity
• The Exact String Black-Hole behind the hadronic Rindler horizon?

Cited by in corpus (21)

• Curved Spacetimes and Curved Graphene: a status report of the Weyl-symmetry approach
• Using Weyl symmetry to make Graphene a real lab for fundamental physics
• $\mathcal{N}$-Extended $D=4$ Supergravity, Unconventional SUSY and Graphene
• Hunting Quantum Gravity with Analogs: the case of graphene
• Graphene, Dirac equation and analogue gravity
• Dark matter and dark energy induced by condensates
• Graphene and Black Holes: novel materials to reach the unreachable
• Torsion at different scales: from materials to the Universe
• Note on Hawking-Unruh effects in graphene
• Generalized Ellis-Bronnikov graphene wormhole
• The three "layers" of graphene monolayer and their analog generalized uncertainty principles
• Gravitational parameter estimation in a waveguide
• Turning graphene into a lab for noncommutativity
• Electronic states in a quantum Beltrami surface
• Quantum black holes as classical space factories
• Trace and diffeomorphism anomalies of the classical Liouville theory, Virasoro algebras, Weyl-gauging and all that
• Vortex solutions of Liouville equation and quasi spherical surfaces
• Time-loops to spot torsion on bidimensional Dirac materials with dislocations
• Electronic states in a bilayer graphene quantum ripple
• Stability of graphene hyperbolic pseudospheres under harsh conditions
• Quasiparticle picture from the Bekenstein bound