Long Wavelength Correlations and Transport in a Marginal Fermi Liquid

Abstract

Marginal Fermi liquid was originally introduced as a phenomenological description of the cuprates in a part of the metallic doping range which appears to be governed by fluctuations due to a quantum-critical point. An essential result due to the form of the assumed fluctuation spectra is that the large inelastic quasiparticle relaxation rate near the Fermi-surface is proportional to the energy measured from the chemical potential, ${\tau }_i^{-1}\propto \epsilon$. We present a microscopic long-wavelength derivation of the hydrodynamic properties in such a situation by an extension of the procedure that Eliashberg used for the derivation of the hydrodynamic properties of a Landau-Fermi-liquid. In particular, the density-density and the current-current correlations and the relation between the two are derived, and the connection to microscopic calculations of the frequency dependence of the optical conductivity with an additional fermi-liquid correction factor shown to follow. The method used here may be necessary, quite generally, for the correct hydrodynamic theory for any problem of quantum-critical fluctuations in fermions.

5 pages

References in corpus (9)

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• Magnetic order in the pseudogap phase of high-$T_C$ superconductors
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• Hall effect in the marginal Fermi liquid regime of high-Tc superconductors
• Universality of the single-particle spectra of cuprate superconductors

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• Loop current fluctuations and quantum critical transport
• Non-quasiparticle transport and resistivity saturation: A view from the large-N limit
• Optical conductivity of a two-dimensional metal at the onset of spin-density-wave order
• Quantum Criticality in Quasi-Two Dimensional Itinerant Antiferromagnets
• Quantum Interference of Hydrodynamic Modes in a Dirty Marginal Fermi Liquid
• Superconducting critical temperature in the extended diffusive SYK model
• Collective Modes in the Loop Current Ordered Phase of Cuprates
• Dynamic structure function of some singular Fermi-liquids
• Quantum-critical transport in marginal Fermi liquids
• Incoherent transport in a classical spin liquid
• Thermalization of dipole oscillations in confined systems by rare collisions