Non-Fermi liquids and the Wiedemann-Franz law

Maissam Barkeshli; Raghu Mahajan; Sean A. Hartnoll

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Non-Fermi liquids and the Wiedemann-Franz law

Raghu Mahajan, Maissam Barkeshli, Sean A. Hartnoll

Strongly Correlated Electrons · Submitted 15 Apr 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim For all these cases, we obtain universal expressions for the ratio of conductivities that violate the Wiedemann-Franz law.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.18 · human participants 0.02 · controlled comparison 0.15 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.52 · mentions code or data availability 0.01.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

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.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A general discussion of the ratio of thermal and electrical conductivities in non-Fermi liquid metals is given.	contribution 0.86	0.70	0.05	asserted 0.89
s1	In metals with sharp Drude peaks, the relevant physics is correctly organized around the slow relaxation of almost-conserved momenta.	background 0.81	0.16	0.04	asserted 1.00
s2	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.	background 0.90	0.15	0.08	asserted 0.95
s3	It follows that the conductivities of such non-Fermi liquids are obtained within a fundamentally different kinematics to Fermi liquids.	interpretation 0.77	0.51	0.15	asserted 1.00
s4	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.	contribution 0.85	0.79	0.07	asserted 0.99
s5	For all these cases, we obtain universal expressions for the ratio of conductivities that violate the Wiedemann-Franz law.	result 0.98	0.93	0.67	asserted 1.00
s6	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.	contribution 1.00	0.38	0.04	asserted 0.73
s7	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.	result 0.56	0.83	0.14	asserted 0.88
s8	We suggest the likely outcome of future transport experiments on CeCoIn5, YbRh2Si2 and Sr3Ru2O7 at their critical magnetic fields.	future work 0.92	0.35	0.06	hedged possibility 0.99

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from argument 0.58.

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The paper

Original 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.

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References

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Cited by 10 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Holographic Q-lattices
hep-th 2013-11 conditional novelty 8.0 of 10

A linear spatial phase in a bulk complex scalar breaks translation invariance while keeping the gravitational equations one-dimensional, producing holographic metals with Drude peaks and insulators with suppressed low...
Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
cond-mat.str-el 2016-12 accept novelty 7.0 of 10

In both complex SYK models and holographic axion black branes the low-temperature Seebeck coefficient equals dS/dQ exactly, a consequence of emergent PSL(2,R) symmetry.
Thermoelectric DC conductivities from black hole horizons
hep-th 2014-06 accept novelty 7.0 of 10

The full DC thermoelectric and thermal conductivities of holographic black holes with momentum dissipation are given exactly by horizon data, and the Q-lattice ground states studied here are all thermal insulators.
Theory of universal incoherent metallic transport
cond-mat.str-el 2014-05 conditional novelty 7.0 of 10

A conjectured lower bound on charge and heat diffusion in incoherent metals reproduces the linear-in-temperature resistivity and Planckian timescale seen across cuprates, pnictides, heavy fermions and organics.
Thermal diffusivity and chaos in metals without quasiparticles
hep-th 2017-05 accept novelty 6.0 of 10

In holographic strange metals at Lifshitz or hyperscaling-violating fixed points, the thermal diffusivity equals z/(2z-2) times v_B squared times tau_L, independent of charge density, lattice strength, or magnetic field.

Show 5 more citing papers

Navier-Stokes Equations on Black Hole Horizons and DC Thermoelectric Conductivity
hep-th 2015-06 accept novelty 6.0 of 10

DC thermoelectric conductivity in holographic lattices equals the response of a forced, incompressible charged fluid on the black hole horizon, obtained by solving linearised Stokes equations there.
Dissecting holographic conductivities
hep-th 2015-05 conditional novelty 6.0 of 10

In a holographic metal with slow momentum relaxation, the thermoelectric conductivities split into a Drude part plus an intrinsic conductivity equal to the known translationally invariant value, and prior effective th...
Momentum dissipation and effective theories of coherent and incoherent transport
hep-th 2014-11 accept novelty 6.0 of 10

Heat transport in a holographic plasma without momentum conservation crosses over from sound-like to diffusive as the momentum relaxation rate grows, and at one special coupling all Green's functions are obtained in c...
Momentum relaxation in holographic massive gravity
hep-th 2013-06 accept novelty 6.0 of 10

In a holographic massive gravity model, momentum relaxes over a timescale set by the graviton mass, and the zero-temperature conductivity reduces to Drude form at small mass with computable corrections.
Holographic duality and the resistivity of strange metals
hep-th 2013-11 conditional novelty 5.0 of 10

A hydrodynamic metal with minimal viscosity and weak disorder has resistivity proportional to entropy, producing linear-in-T resistivity when the specific heat is linear.

How later papers used it

69 later papers cite it

Evidence: substantial. 60 of the citing papers share no author with it, and 14 of those carry a confident label from Pith's citation classifier.

Pith read 14 of the 105 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

2 later papers by other authors are listed below: 1 used its method or tool and 1 compared its own results with it.

Uses its method or tool 1 of 9 papers with this label

Used the memory matrix formalism from this paper, or holography, to obtain its equation, with a matrix incorporating leading order dissipation that vanishes when translation invariance is retained.

Diffusion in inhomogeneous media (2017) · 0.85 · paraphrased: the licence does not allow quoting

Compares with it 1 of 5 papers with this label

Compared its own results with expectations for fermionic systems at finite chemical potential following recent results presented in this paper.

Thermoelectric Transport Coefficients from Charged Solv and Nil Black Holes (2017) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

48 arXiv papers cite this in 76 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 54 sentences without a confident label

Builds on it 1 paper

Expanding upon earlier works such as [ref] , we provide a comprehensive and quantitative theory of the finite temperature breakdown of the WF law in metals described by Fermi liquid theory.

Electronic hydrodynamics and the breakdown of the Wiedemann-Franz and Mott laws in interacting metals · Introduction · 1.00

Uses its method or tool 5 papers

We shall employ methods similar to those used recently [ref] for the Ising-nematic quantum critical point, which was inspired by analyses of transport in holographic models of metallic states [ref] , and by Boltzmann equation studies [ref] .

DC resistivity at the onset of spin density wave order in two-dimensional metals · Introduction · 0.95
In these cases, a perturbative expansion in the (small) momentum relaxation rate $Γ$ can be performed within the memory matrix formalism [ref] .

Dissecting holographic conductivities · Introduction · 0.96
Using the memory matrix formalism [ref] or holography [ref] we have [equation] Here the matrix $L_ij$ incorporates the leading order dissipation and $L_ij→0$ when translation invariance is retained.

Diffusion in inhomogeneous media · Diffusive modes · 0.85

Compares with it 5 papers

The results in [ref] complement those obtained using the memory matrix formalism [ref] .

DC Conductivity of Magnetised Holographic Matter · Introduction · 0.96
This is a distinct mechanism to achieve a very low $L$ than that found in [ref] for coherent metals.

Theory of universal incoherent metallic transport · Experimental consequences · 0.96
We compared our results with the expectations for fermionic systems at finite chemical potential following recent results presented in [ref] .

Thermoelectric Transport Coefficients from Charged Solv and Nil Black Holes · Conclusions · 1.00

Cites it as support 2 papers

Thus, it may be intrinsic in the sense that it is not sensitive to irrelevant deformations that dissipate the momentum [ref] .

Collective diffusion and quantum chaos in holography · Discussion · 0.96
This thermal conductivity is then an intrinsic property of our infra-red theory, and is insensitive to the details of momentum relaxation[The fact that $κ$ can be insensitive to momentum relaxation at finite density has been emphasised in [ref] .].

Diffusion and Chaos from near AdS$_2$ horizons · Thermoelectric Response Coefficients · 0.97

Cites it as background 9 papers

The importance of the fate of momentum for transport has long been appreciated [ref] , but has acquired renewed relevance in the context of modern unconventional metals, e.g. [ref] .

Bad Metals from Fluctuating Density Waves · Abstract · 0.91
Typically, one assumes that strong electron-electron interactions lead to a breakdown of Fermi liquid physics and of a quasiparticle description, such that the resulting metal is a non-Fermi liquid (NFL) [ref] .

Electronic hydrodynamics and the breakdown of the Wiedemann-Franz and Mott laws in interacting metals · Introduction · 0.96
First of all, the Wiedemann-Franz ratio $κ_DC/(σ_DC T)$ (where $κ_DC = κ̅_DC-s_DC^2T/σ_DC$) is constant in temperature even though its numerical value $L_0$, [equation] depends on $β$ and in general disagrees with the Fermi-liquid prediction $L_0^(Fl) = π^2/3$ [For a recent discussion on the Wiedemann-Franz law in strongly correlated systems see [ref] ].

Thermo-electric transport in gauge/gravity models with momentum dissipation · Beyond the hydrodynamic regime · 0.90

What it cites · 55 sentences without a confident label

Uses the method or tool of 1 paper

If a quasiparticle description is apposite, this question can be addressed via the Boltzmann equation, e.g. [ref] .

Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids · The Wiedemann-Franz law · 0.83

Cites as support 1 paper

Evidence for this phenomenon can be seen in quantum oscillation experiments in e.g. Sr$_3$Ru$_2$O$_7$ [ref] .

The de Haas-van Alphen effect across the metamagnetic transition in Sr$_3$Ru$_2$O$_7$ · Non-Fermi liquids with (some) long-lived quasiparticles · 0.97

Cites as background 1 paper

Earlier work on this model includes [ref] .

Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions · Patchwise conserved momenta: Ising-nematic example · 0.99

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