Optical conductivity of a Dirac-Fermi liquid

Abstract

A Dirac-Fermi liquid (DFL)--a doped system with Dirac spectrum--is an important example of a non-Galilean-invariant Fermi liquid (FL). Real-life realizations of a DFL include, e.g., doped graphene, surface states of three-dimensional (3D) topological insulators, and 3D Dirac/Weyl metals. We study the optical conductivity of a DFL arising from intraband electron-electron scattering. It is shown that the effective current relaxation rate behaves as $1/{\tau }_J\propto \left({\omega }^2+4{\pi }^2{T}^2\right)\left(3{\omega }^2+8{\pi }^2{T}^2\right)$ for $\max \{\omega ,T\}\ll \mu$, where $\mu$ is the chemical potential, with an additional logarithmic factor in two dimensions. In graphene, the quartic form of $1/{\tau }_J$ competes with a small FL-like term, $\propto {\omega }^2+4{\pi }^2{T}^2$, due to trigonal warping of the Fermi surface. We also calculated the dynamical charge susceptibility, ${\chi }_{\mathrm{c}}(\mathbf{q},\omega )$, outside the particle-hole continua and to one-loop order in the dynamically screened Coulomb interaction. For a 2D DFL, the imaginary part of ${\chi }_{\mathrm{c}}(\mathbf{q},\omega )$ scales as $q^2\omega \ln |\omega |$ and $q^4/{\omega }^3$ for frequencies larger and smaller than the plasmon frequency at given $q$, respectively. The small-$q$ limit of $\mathrm{Im}{\chi }_{\mathrm{c}}(\mathbf{q},\omega )$ reproduces our result for the conductivity via the Einstein relation.

arXiv comment28 pages, 10 figures

References in corpus (60)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Topological Insulators
• Universal Dynamic Conductivity and Quantized Visible Opacity of Suspended Graphene
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Electronic transport in two dimensional graphene
• Giant Intrinsic Carrier Mobilities in Graphene and Its Bilayer
• Intrinsic and Extrinsic Performance Limits of Graphene Devices on SiO2
• Measurement of the Optical Conductivity of Graphene
• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• The electronic properties of bilayer graphene
• Colloquium: The transport properties of graphene: An introduction
• Controlling electron-phonon interactions in graphene at ultra high carrier densities
• Acoustic phonon scattering limited carrier mobility in 2D extrinsic graphene
• Space-time dispersion of graphene conductivity
• Hexagonal Warping Effects in the Surface States of Topological Insulator Bi${}_2$Te${}_3$
• Recent developments in transport phenomena in Weyl semimetals
• Dirac Fermions in Solids - from High Tc cuprates and Graphene to Topological Insulators and Weyl Semimetals
• Drude Conductivity of Dirac Fermions in Graphene
• Unusual Microwave Response of Dirac Quasiparticles in Graphene
• Substrate limited electron dynamics in graphene
• Limits on electron quality in suspended graphene due to flexural phonons
• Quantum critical transport in clean graphene
• Weyl Metals
• Screening induced temperature dependent transport in 2D graphene
• 3D massless Kane fermions observed in a zinc-blende crystal
• Quantum critical scaling in graphene
• Coulomb interaction, ripples, and the minimal conductivity of graphene
• Optical spectroscopy study of three dimensional Dirac semimetal ZrTe${}_5$
• Coulomb Drag in Normal Metals and Superconductors: Diagrammatic Approach
• Optical evidence for a Weyl semimetal state in pyrochlore Eu2Ir2O7
• Chiral anomaly and optical absorption in Weyl semimetals
• Quantum-critical relativistic magnetotransport in graphene
• Effect of electron-electron interactions on the conductivity of clean graphene
• Drude weight, plasmon dispersion, and a.c. conductivity in doped graphene sheets
• Conductivity of the defectless Graphene
• Anomalous density fluctuations in a strange metal
• Phenomenological study of the electronic transport coefficients of graphene
• Minimal conductivity in graphene: interaction corrections and ultraviolet anomaly
• Interband optical conductivity of the [001]-oriented Dirac semimetal Cd3As2
• Collision-dominated nonlinear hydrodynamics in graphene
• Conductivity of suspended and non-suspended graphene at finite gate voltage
• Interaction corrections to the polarization function of graphene
• Resistivity of a non-Galilean--invariant Fermi Liquid near Pomeranchuk Quantum Criticality
• Intrinsic lifetime of Dirac plasmons in graphene
• Excitonic effects in the optical conductivity of gated graphene
• First-Matsubara-frequency rule in a Fermi liquid. Part II: Optical conductivity and comparison to experiment
• First-Matsubara-frequency rule in a Fermi liquid. Part I: Fermionic self-energy
• Optical response of correlated electron systems
• 3D Dirac cone carrier dynamics in Na3Bi and Cd3As2
• Effect of Coulomb interactions on the optical properties of doped graphene
• The infrared conductivity of graphene
• The Hierarchy of Excitation Lifetimes in Two-Dimensional Fermi Gases
• Optical Conductivity of Clean Metals
• Zero temperature optical conductivity of ultra-clean Fermi liquids and superconductors
• Effect of Electron-electron Interaction on Surface Transport in Three-Dimensional Topological Insulators
• Plasmon attenuation and optical conductivity of a two-dimensional electron gas
• Dynamical susceptibility of a Fermi liquid
• Equations of motion method for triplet excitation operators in graphene
• Extracting correlation effects from Momentum-Resolved Electron Energy Loss Spectroscopy (M-EELS): Synergistic origin of the dispersion kink in Bi${}_{2.1}$Sr${}_{1.9}$CaCu${}_2$O${}_{8+x}$

Cited by in corpus (4)

• Optical Conductivity of the two dimensional Hubbard model: vertex corrections, emergent Galilean invariance and the accuracy of the single-site dynamical mean field approximation
• Collective spin modes in Fermi liquids with spin-orbit coupling
• Ballistic magnetotransport in graphene
• Electric and chiral response to a pseudoelectric field in Weyl materials