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Theory of universal incoherent metallic transport


The anomalous transport of important materials such as high-temperature superconductors and other ‘bad metals’ is not well understood theoretically. In an incoherent metal, transport is controlled by the collective diffusion of energy and charge rather than by quasiparticle or momentum relaxation. Here, we explore the possibility of a universal bound D νF2/(kBT) on the underlying diffusion constants in an incoherent metal. Such a bound is loosely motivated by results from holographic duality, the uncertainty principle and measurements of diffusion in strongly interacting non-metallic systems. Metals close to saturating this bound are shown to have a linear-in-temperature resistivity with an underlying dissipative timescale matching that recently deduced from experimental data on a wide range of metals. This bound may therefore be responsible for the ubiquitous appearance of high-temperature regimes in metals with T-linear resistivity. To establish this calls for direct measurements of diffusive processes and of charge susceptibilities in incoherent metals.

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Figure 1: Quasiparticle bounds versus incoherent bounds.
Figure 2: Lorenz ratio as a function of temperature.


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I have benefited greatly from discussions with A. Kapitulnik, G. Kotliar, B. Laughlin, A. Mackenzie, R. McKenzie, V. Oganesyan, J. Orenstein, B. Spivak and especially S. Kivelson. S.A.H. is partially financially supported by a DOE Early Career Award and by a Sloan fellowship.

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Correspondence to Sean A. Hartnoll.

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Hartnoll, S. Theory of universal incoherent metallic transport. Nature Phys 11, 54–61 (2015).

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