Electronic hydrodynamics and the breakdown of the WiedemannFranz and Mott laws in interacting metals
Abstract
We present the theory of thermoelectric transport in metals with longlived quasiparticles, carefully addressing the interplay of electronelectron scattering as well as electronimpurity scattering, but neglecting electronphonon scattering. In Fermi liquids with a large Fermi surface and weak electronimpurity scattering, we provide universal and simple formulas for the behavior of the thermoelectric conductivities across the ballistictohydrodynamic crossover. In this regime, the electrical conductivity is relatively unchanged by hydrodynamic effects. In contrast, the thermal conductivity can be parametrically smaller than predicted by the WiedemannFranz law. A less severe violation of the Mott law arises. We quantitatively compare the violations of the WiedemannFranz law arising from (i) momentumconserving electronelectron scattering in the collision integral, (ii) hydrodynamic modifications of the electronimpurity scattering rate, and (iii) thermal broadening of the Fermi surface, and show that (i) is generally the largest effect. We present simple formulas for electrical and thermal magnetoconductivity across the ballistictohydrodynamic limit, along with a more complicated formula for the thermoelectric magnetoconductivity. In a finite magnetic field, the Lorenz number may be smaller or larger than predicted by the WiedemannFranz law, and the crossover between these behaviors is a clear prediction for experiments. The arbitrarily strong violation of the WiedemannFranz law found in our work arises entirely from electronelectron interaction effects within the Fermiliquid paradigm, and does not imply any nonFermiliquid behavior. We predict clear experimental signatures of bulk hydrodynamics in highmobility twodimensional GaAs semiconductor structures, where a spectacular failure of the WiedemannFranz law should persist down to very low temperatures in highquality and lowdensity samples.
 Publication:

Physical Review B
 Pub Date:
 June 2018
 DOI:
 10.1103/PhysRevB.97.245128
 arXiv:
 arXiv:1804.00665
 Bibcode:
 2018PhRvB..97x5128L
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 21+8 pages