Quantum Field Theory in Graphene

Abstract

This is a short non-technical introduction to applications of the Quantum Field Theory methods to graphene. We derive the Dirac model from the tight binding model and describe calculations of the polarization operator (conductivity). Later on, we use this quantity to describe the Quantum Hall Effect, light absorption by graphene, the Faraday effect, and the Casimir interaction.

12pp, based on a talk at QFEXT 11, v2: references added

References in corpus (17)

• The electronic properties of graphene
• Universal Dynamic Conductivity and Quantized Visible Opacity of Suspended Graphene
• Unconventional Integer Quantum Hall effect in graphene
• Universal dynamical conductance in graphite
• Optical far-infrared properties of graphene monolayer and multilayers
• The optical conductivity of graphene in the visible region of the spectrum
• Unusual Microwave Response of Dirac Quasiparticles in Graphene
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• On the universal AC optical background in graphene
• Finite temperature Casimir effect for graphene
• Dynamical polarization, screening, and plasmons in gapped graphene
• Chiral Gauge Theory for Graphene
• Lifshitz-type formulas for graphene and single-wall carbon nanotubes: van der Waals and Casimir interations
• Many-body effects in van der Waals-Casimir interaction between graphene layers
• Casimir interactions in graphene systems
• Manifestations of topological effects in graphene
• Planar QED at finite temperature and density: Hall conductivity, Berry's phases and minimal conductivity of graphene

Cited by in corpus (32)

• Enhanced Casimir effect for doped graphene
• Faraday rotation in graphene
• The quest for Casimir repulsion between Chern-Simons surfaces
• Landau-Khalatnikov-Fradkin transformations in Reduced Quantum Electrodynamics
• Surface plasmons for doped graphene
• Polarization operator in the 2+1 dimensional quantum electrodynamics with a nonzero fermion density in a constant uniform magnetic field
• Electric conductivity in graphene: Kubo model versus a nonlocal quantum field theory model
• Quantum Dirac fermions in half space and their interaction with electromagnetic field
• Graphene through the looking glass of QFT
• Superconducting phase transitions induced by chemical potential in (2+1)-dimensional four-fermion quantum field theory
• Magnetic catalysis effect in (2+1)-dimensional Gross--Neveu model with Zeeman interaction
• Radiation from electrons in graphene in strong electric field
• Charge density and conductivity of disordered Berry-Mondragon graphene nanoribbons
• Network model for periodically strained graphene
• Graphene transparency in weak magnetic fields
• Electronic transport in bent carbon nanotubes
• Optical Transparency in an effective model for Graphene
• The low temperature behavior the Casimir-Polder energy for conductive plane
• New class of spin projection operators for 3D models
• Optical Conductivity in an effective model for Graphene: Finite temperature corrections
• To gap or not to gap? Mass distortions and edge modes in graphene armchair nanoribbons
• Quantum Holonomies in Graphene Wormholes
• Zeroes of combinations of Bessel functions and mean charge of graphene nanodots
• Casimir-Lifshitz force with graphene: theory versus experiment, role of spatial non-locality and of losses
• Chiral magnetic effect at finite temperature in a field-theoretic approach
• Redshift as a stretching factor in rotating graphene wormholes
• Dispersion Forces Between Fields Confined to Half Spaces
• Candidate entanglement invariants for two Dirac spinors
• Temperature Dependence of the Response Functions of Graphene: Impact on Casimir and Casimi-Polder Forces in and out of Thermal Equilibrium
• Low degree Lorentz invariant polynomials as potential entanglement invariants for multiple Dirac spinors
• Comment on "Electric conductivity of graphene: Kubo model versus a nonlocal quantum field theory model (arXiv:2403.02279v3)"
• Hall conductivity of strained $Z_2$ crystals