Zero temperature optical conductivity of ultra-clean Fermi liquids and superconductors

Abstract

We calculate the low-frequency optical conductivity sigma(w) of clean metals and superconductors at zero temperature neglecting the effects of impurities and phonons. In general, the frequency and temperature dependences of sigma have very little in common. For small Fermi surfaces in three dimensions (but not in 2D) we find for example that Re sigma(w>0)=const. for low w which corresponds to a scattering rate Gamma proportional to w^2 even in the absence of Umklapp scattering when there is no T^2 contribution to Gamma. In the main part of the paper we discuss in detail the optical conductivity of d-wave superconductors in 2D where Re sigma(w>0) \propto w^4 for the smallest frequencies and the Umklapp processes typically set in smoothly above a finite threshold w_0 smaller than twice the maximal gap Delta. In cases where the nodes are located at (pi/2, pi/2), such that direct Umklapp scattering among them is possible, one obtains Re sigma(w) \propto w^2.

arXiv comment7 pages, 3 figures

References in corpus (7)

• Phenomenological Models for the Gap Anisotropy of Bi-2212 as Measured by ARPES
• d-Wave Model for Microwave Response of High-Tc Superconductors
• Conductivity of a clean one-dimensional wire
• Thermal Conductivity of Spin-1/2 Chains
• Infrared conductivity of a d_{x^2-y^2}-wave superconductor with impurity and spin-fluctuation scattering
• Microwave conductivity of YBa${}_2$Cu${}_3$O${}_{6.99}$ including inelastic scattering
• Optical spectral weight distribution in d-wave superconductors

Cited by in corpus (27)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Electrodynamics of Correlated Electron Materials
• Collision-dominated nonlinear hydrodynamics in graphene
• Mixed-valence insulators with neutral Fermi surfaces
• First-Matsubara-frequency rule in a Fermi liquid. Part II: Optical conductivity and comparison to experiment
• Optical response of correlated electron systems
• Optical spectroscopy shows that the normal state of URu${}_2$Si${}_2$ is an anomalous Fermi liquid
• Optical Conductivity of Clean Metals
• Microwave spectroscopy on heavy-fermion systems: probing the dynamics of charges and magnetic moments
• Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids
• Effect of Electron-electron Interaction on Surface Transport in Three-Dimensional Topological Insulators
• Optical conductivity of a two-dimensional metal at the onset of spin-density-wave order
• Microwave conductivity of heavy fermions in UPd2Al3
• Optical conductivity of a two-dimensional metal near a quantum-critical point: the status of the "extended Drude formula"
• Optical Conductivity of the two dimensional Hubbard model: vertex corrections, emergent Galilean invariance and the accuracy of the single-site dynamical mean field approximation
• Optical conductivity of a metal near an Ising-nematic quantum critical point
• Separated transport relaxation scales and interband scattering in SrRuO${}_3$, CaRuO${}_3$, and Sr${}_2$RuO${}_4$ thin films
• Fermi Surface Geometry and Optical Conductivity of a 2D Electron Gas near an Ising-Nematic Quantum Critical Point
• Unconventional scaling of resistivity in two-dimensional Fermi liquids
• Many-body effects in nodal-line semimetals: correction to the optical conductivity
• Signatures of phase transitions in the microwave response of YbRh2Si2
• Microwave Conductivity Distinguishes Between Different d-wave States: Umklapp Scattering in Unconventional Superconductors
• Quantum criticality and optical conductivity in a two-valley system
• Magnetoconductivity due to electron-electron interaction in a non-Galilean-invariant Fermi liquid
• Collective excitations and stability of a non-Fermi liquid state near a quantum-critical point of a metal
• Probing the Quantum Geometry of Correlated Metals using Optical Conductivity
• Optical conductivity of a Dirac-Fermi liquid