Non-Fermi liquids and the Wiedemann-Franz law

Abstract

A general discussion of the ratio of thermal and electrical conductivities in non-Fermi liquid metals is given. In metals with sharp Drude peaks, the relevant physics is correctly organized around the slow relaxation of almost-conserved momenta. While in Fermi liquids both currents and momenta relax slowly, due to the weakness of interactions among low energy excitations, in strongly interacting non-Fermi liquids typically only momenta relax slowly. It follows that the conductivities of such non-Fermi liquids are obtained within a fundamentally different kinematics to Fermi liquids. Among these strongly interacting non-Fermi liquids we distinguish cases with only one almost-conserved momentum, which we term hydrodynamic metals, and with many patchwise almost-conserved momenta. For all these cases, we obtain universal expressions for the ratio of conductivities that violate the Wiedemann-Franz law. We further discuss the case in which long-lived `cold' quasiparticles, in general with unconventional scattering rates, coexist with strongly interacting hot spots, lines or bands. For these cases, we characterize circumstances under which non-Fermi liquid transport, in particular a linear in temperature resistivity, is and is not compatible with the Wiedemann-Franz law. We suggest the likely outcome of future transport experiments on CeCoIn5, YbRh2Si2 and Sr3Ru2O7 at their critical magnetic fields.Comment: 1+30 pages. 1 figure. 1 table. v2 shortened for increased focus and readability. v3 some material moved to appendice

Dissecting holographic conductivities

“…of the DC conductivities (1.6) still has physical meaning in terms of the DC conductivities at zero electric or heat current [11,18].…”

“…and where 11) are determined by solving the decoupled equations of motion with ingoing boundary conditions at the horizon, and contain all of the frequency dependence of the correlators. It is simple to diagonalise the matrix of correlators by defining the currents (with overall normalisation constants a ± ) 12) so that J ± J ± depends only on Θ ± , and the cross correlator J ± J ∓ = 0.…”

“…In these cases, a perturbative expansion in the (small) momentum relaxation rate Γ can be performed within the memory matrix formalism [1,2,8,10,11]. To leading order in this expansion, the conductivities are all Drude-like, with DC values determined by Γ and by the static susceptibilities χ JP and χ QP of the translationally invariant state where momentum is exactly conserved:…”

Thermo-electric transport in gauge/gravity models with momentum dissipation

“…24 We thank the referee for suggesting us this precise comparison and formulae. 25 For a recent discussion on the Wiedemann-Franz law in strongly correlated systems see [32].…”

Diffusion in inhomogeneous media

“…In this case the spatial momentum dissipation is weak. Using the memory matrix formalism [33] or holography [32] we havē…”