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Title: Resistivity bound for hydrodynamic bad metals

Abstract

We obtain a rigorous upper bound on the resistivity ρ of an electron fluid whose electronic mean free path is short compared with the scale of spatial inhomogeneities. When such a hydrodynamic electron fluid supports a nonthermal diffusion process—such as an imbalance mode between different bands—we show that the resistivity bound becomes ρ A Γ . The coefficient A is independent of temperature and inhomogeneity lengthscale, and Γ is a microscopic momentum-preserving scattering rate. In this way, we obtain a unified mechanism—without umklapp—for ρ T 2 in a Fermi liquid and the crossover to ρ T in quantum critical regimes. This behavior is widely observed in transition metal oxides, organic metals, pnictides, and heavy fermion compounds and has presented a long-standing challenge to transport theory. Our hydrodynamic bound allows phonon contributions to diffusion constants, including thermal diffusion, to directly affect the electrical resistivity.

Authors:
;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1398834
Grant/Contract Number:  
SC0008169
Resource Type:
Published Article
Journal Name:
Proceedings of the National Academy of Sciences of the United States of America
Additional Journal Information:
Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Volume: 114 Journal Issue: 43; Journal ID: ISSN 0027-8424
Publisher:
Proceedings of the National Academy of Sciences
Country of Publication:
United States
Language:
English

Citation Formats

Lucas, Andrew, and Hartnoll, Sean A. Resistivity bound for hydrodynamic bad metals. United States: N. p., 2017. Web. doi:10.1073/pnas.1711414114.
Lucas, Andrew, & Hartnoll, Sean A. Resistivity bound for hydrodynamic bad metals. United States. doi:10.1073/pnas.1711414114.
Lucas, Andrew, and Hartnoll, Sean A. Tue . "Resistivity bound for hydrodynamic bad metals". United States. doi:10.1073/pnas.1711414114.
@article{osti_1398834,
title = {Resistivity bound for hydrodynamic bad metals},
author = {Lucas, Andrew and Hartnoll, Sean A.},
abstractNote = {We obtain a rigorous upper bound on the resistivity ρ of an electron fluid whose electronic mean free path is short compared with the scale of spatial inhomogeneities. When such a hydrodynamic electron fluid supports a nonthermal diffusion process—such as an imbalance mode between different bands—we show that the resistivity bound becomes ρ ≲ A Γ . The coefficient A is independent of temperature and inhomogeneity lengthscale, and Γ is a microscopic momentum-preserving scattering rate. In this way, we obtain a unified mechanism—without umklapp—for ρ ∼ T 2 in a Fermi liquid and the crossover to ρ ∼ T in quantum critical regimes. This behavior is widely observed in transition metal oxides, organic metals, pnictides, and heavy fermion compounds and has presented a long-standing challenge to transport theory. Our hydrodynamic bound allows phonon contributions to diffusion constants, including thermal diffusion, to directly affect the electrical resistivity.},
doi = {10.1073/pnas.1711414114},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 43,
volume = 114,
place = {United States},
year = {2017},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1073/pnas.1711414114

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Cited by: 8 works
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