Generalized Dirac structure beyond the linear regime in graphene

Abstract

We show that a generalized Dirac structure survives beyond the linear regime of the low-energy dispersion relations of graphene. A generalized uncertainty principle of the kind compatible with specific quantum gravity scenarios with a fundamental minimal length (here graphene lattice spacing) and Lorentz violation (here the particle/hole asymmetry, the trigonal warping, etc.) is naturally obtained. We then show that the corresponding emergent field theory is a table-top realization of such scenarios, by explicitly computing the third order Hamiltonian, and giving the general recipe for any order. Remarkably, our results imply that going beyond the low-energy approximation does not spoil the well-known correspondence with analogue massless quantum electrodynamics phenomena (as usually believed), but rather it is a way to obtain experimental signatures of quantum-gravity-like corrections to such phenomena.

arXiv comment18 pages, 2 figures, comments added, relevant references included

References in corpus (28)

• The electronic properties of graphene
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Chiral tunneling and the Klein paradox in graphene
• Lorentz-Violating Extension of the Standard Model
• CPT Violation and the Standard Model
• Topological Materials: Weyl Semimetals
• The quantum structure of spacetime at the Planck scale and quantum fields
• A Generalized Uncertainty Principle in Quantum Gravity
• Quantum Spacetime Phenomenology
• Universality of Quantum Gravity Corrections
• Discreteness of Space from the Generalized Uncertainty Principle
• The axis of evil
• General Logarithmic Corrections to Black Hole Entropy
• The Rare Two-Dimensional Materials with Dirac Cones
• A proposal for testing Quantum Gravity in the lab
• Planck 2015 results. XVI. Isotropy and statistics of the CMB
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Discreteness of Space from GUP II: Relativistic Wave Equations
• Quantum field theory in curved graphene spacetimes, Lobachevsky geometry, Weyl symmetry, Hawking effect, and all that
• The Hawking-Unruh phenomenon on graphene
• No Existence of Black Holes at LHC Due to Minimal Length in Quantum Gravity
• Weyl-Gauge Symmetry of Graphene
• Curved Spacetimes and Curved Graphene: a status report of the Weyl-symmetry approach
• Revisiting the gauge fields of strained graphene
• Comment on "Noncommutative gauge theories and Lorentz symmetry, Phys. Rev. D {\bf 70}, 125004 (2004) by R.Banerjee, B.Chakraborty and K.Kumar"
• On the implications of the Bekenstein bound for black hole evaporation
• Green Functions of Graphene: An Analytic Approach
• Three Questions on Lorentz Violation

Cited by in corpus (32)

• GUP Modified Hawking Radiation in Bumblebee Gravity
• 30 years in: Quo vadis generalized uncertainty principle?
• Generalized Uncertainty Principle in three-dimensional gravity and the BTZ black hole
• Generalized uncertainty principle with maximal observable momentum and no minimal length indeterminacy
• (Anti-)de Sitter, Poincaré, Super symmetries, and the two Dirac points of graphene
• Torsion in quantum field theory through time-loops on Dirac materials
• Comments on the Chern-Simons photon term in the QED description of graphene
• Hunting Quantum Gravity with Analogs: the case of graphene
• Universality of minimal length
• Torsion at different scales: from materials to the Universe
• Generalized uncertainty principle in graphene
• The three "layers" of graphene monolayer and their analog generalized uncertainty principles
• Effects of discrete topology on quantum transport across a graphene $n-p-n$ junction: A quantum gravity analogue
• Turning graphene into a lab for noncommutativity
• Testing Short Distance Anisotropy in Space
• Theoretical and Observational Implications of Planck's Constant as a Running Fine Structure Constant
• A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound
• Covariant dynamics on the momentum space
• Measuring Space Deformation via Graphene under Constraints
• Derivation of the deformed Heisenberg algebra from discrete spacetime
• Generalized Uncertainty Principle from the Regularized Self-Energy
• Effective information bounds in modified quantum mechanics
• Generalized Uncertainty Principle: from the harmonic oscillator to a QFT toy model
• Emerging (2+1)D massive graviton in graphene-like systems
• Time-loops to spot torsion on bidimensional Dirac materials with dislocations
• Gamma Ray Bursters and Black Holes in the Gravity's Rainbow
• Deformation of Nanowires and Nanotubes
• Emergent GUP from Modified Hawking Radiation in Einstein-NED Theory
• Effects of underlying topology on quantum state discrimination
• GUP/BEB correspondence
• Low Energy Consequences of Loop Quantum Gravity
• Lorentz and gauge invariance of quantum space