Sum Rules for the Optical and Hall Conductivity in Graphene

Abstract

Graphene has two atoms per unit cell with quasiparticles exhibiting the Dirac-like behavior. These properties lead to interband in addition to intraband optical transitions and modify the $f$-sum rule on the longitudinal conductivity. The expected dependence of the corresponding spectral weight on the applied gate voltage $V_g$ in a field effect graphene transistor is $\sim const-|V_g{|}^{3/2}$. For $V_g=0$, its temperature dependence is $T^3$ rather than the usual $T^2$. For the Hall conductivity, the corresponding spectral weight is determined by the Hall frequency ${\omega }_H$ which is linear in the carrier imbalance density $\rho$, and hence proportional to $V_g$, and is different from the cyclotron frequency for Dirac quasiparticles.

16 pages, RevTeX4, 4 EPS figures; v2: to match PRB version

References in corpus (18)

• Electric Field Effect in Atomically Thin Carbon Films
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Two Dimensional Atomic Crystals
• Magneto-optical conductivity in Graphene
• Landau level spectroscopy of ultrathin graphite layers
• Unusual Microwave Response of Dirac Quasiparticles in Graphene
• Transport of Dirac quasiparticles in graphene: Hall and optical conductivities
• The Electronic Spectrum of Fullerenes from the Dirac Equation
• Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations
• Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations II: transport properties
• Doping dependent optical properties of Bi2Sr2CaCu2O8+d
• Infrared Imaging of the Nanometer-Thick Accumulation Layer in Organic Field-Effect Transistors
• Infrared probe of the anomalous magnetotransport of highly oriented pyrolytic graphite in the extreme quantum limit
• Sum rule for the optical Hall angle
• Magneto-optical evidence for a gapped Fermi surface in underdoped YBa2Cu3O6+x
• Optical-conductivity sum rule in cuprates and unconventional charge density waves: a short review
• Optical Sum Rule in Finite Bands

Cited by in corpus (66)

• Dyadic Green's Functions and Guided Surface Waves for a Surface Conductivity Model of Graphene
• Valley Dependent Optoelectronics from Inversion Symmetry Breaking
• Optical properties of graphene
• Optical far-infrared properties of graphene monolayer and multilayers
• The optical conductivity of graphene in the visible region of the spectrum
• Nonlinear electromagnetic response of graphene: Frequency multiplication and the self-consistent-field effects
• Non-linear electromagnetic response of graphene
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Plasmons in graphene: Recent progress and applications
• Thermal Hyperbolic Metamaterials
• Electrical Control of Plasmon Resonance with Graphene
• On the universal AC optical background in graphene
• Terahertz Science and Technology of Carbon Nanomaterials
• Optical conductivity of bilayer graphene with and without an asymmetry gap
• Semiconducting-to-metallic photoconductivity crossover and temperature-dependent Drude weight in graphene
• Optical Hall conductivity in ordinary and graphene QHE systems
• Conductivity of suspended and non-suspended graphene at finite gate voltage
• Optical conductivity, Drude weight and plasmons in twisted graphene bilayers
• Effect of electron-hole asymmetry on optical conductivity in 8-Pmmn borophene
• f-Sum Rule and Unconventional Spectral Weight Transfer in Graphene
• The quasi-normal modes of quantum criticality
• Optical evidence of surface state suppression in Bi based topological insulators
• Anisotropic longitudinal optical conductivities of tilted Dirac bands in 1T${}^{\prime }$-MoS${}_2$
• Magneto-optical conductivity in graphene including electron-phonon coupling
• Transport in a Clean Graphene Sheet at Finite Temperature and Frequency
• Dynamical current-current correlation of the hexagonal lattice and graphene
• Direction dependent giant optical conductivity in 2D \textit{semi}-Dirac materials
• Quantum plasmonic excitation in graphene and robust-to-loss propagation
• Optical properties of magnetically doped ultra-thin topological insulator slabs
• Optical conductivity of semi-Dirac and pseudospin-1 models: Zitterbewegung approach
• Valley symmetry breaking and gap tuning in graphene by spin doping
• Infrared electrodynamics and ferromagnetism in the topological semiconductors Bi${}_2$Te${}_3$ and Mn-doped Bi${}_2$Te${}_3$
• Weak momentum scattering and the conductivity of graphene
• Terahertz Dynamics of Quantum-Confined Electrons in Carbon Nanomaterials
• Spatial dispersion effects upon local excitation of extrinsic plasmons in a graphene micro-disk
• Signatures of Lifshitz transition in the optical conductivity of two-dimensional tilted Dirac materials
• Graphene as a tunable THz reservoir for shaping the Mollow triplet of an artificial atom via plasmonic effects
• Optical $N$-invariant of graphene's viscous Hall fluid
• Magneto-optics of monolayer and bilayer graphene
• Nonlinear optical conductivity of a generic two band systems, with application to doped and gapped graphene
• Plasmon anomaly in the dynamical optical conductivity of graphene
• Modified rigorous coupled-wave analysis for grating-based plasmonic structures with delta-thin conductive channel. Far- and near-field study
• Effects of heterostrain and lattice relaxation on optical conductivity of twisted bilayer graphene
• Intraband memory function and memory-function conductivity formula in doped graphene
• Robustness of the optical-conductivity sum rule in Bilayer Graphene
• Spectral singularities and tunable slab lasers with 2D material coating
• Effects of spatial dimensionality and band tilting on the longitudinal optical conductivities in Dirac bands
• Quantum magneto-optics of graphite family
• High optical absorption in graphene
• AC transport properties of single and bilayer graphene
• Time-dependent magneto-transport in a driven graphene spin valve
• Drude weight and optical conductivity of a two-dimensional heavy-hole gas with $k$-cubic spin-orbit interactions
• Unruh Effect and Takagi's Statistics Inversion in Strained Graphene
• On the convergence of the polarization tensor in space-time of three dimensions
• Effect of chiral anomaly on the circular dichroism and Hall angle in doped and tilted Weyl semimetals
• Anomalous Valley Magnetic Moment of Graphene
• Spatially dispersive dynamical response of hot carriers in doped graphene
• Sum rules, plasma frequencies and Hall phenomenology in holographic plasmas
• Microscopic quantum description of second-order nonlinearities in 2D hexagonal nanostructures beyond the Dirac cone approximation
• Modified Martin-Puplett interferometer for magneto-optical Kerr effect measurements at sub-THz frequencies
• Optical N-plasmon: Topological hydrodynamic excitations in Graphene from repulsive Hall viscosity
• Violation of f-sum Rule with Generalized Kinetic Energy
• Optical properties of biased bilayer graphene due to gap parameter effects
• Occupation Dynamics of Floquet-Volkov States and Spectral Sum Rule
• Universal absorption of two-dimensional systems
• Nanoantenna properties of graphene membrane. Quantum theory