2018/04/02 by Andrew Lucas, Sankar Das Sarma, S. Das Sarma
Materials Science · Physics and Astronomy · #Advanced Thermoelectric Materials and Devices #Condensed matter physics #Electron #Fermi gas #Fermi liquid theory #Fermi surface #Phonon #Phonon scattering #Physics #Quantum and electron transport phenomena #Quantum mechanics #Quasiparticle #Scattering #Superconductivity #Thermal conductivity #Thermal properties of materials #Wiedemann–Franz law #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.97.245128
published as Phys. Rev. B 97, 245128 (2018) · 21+8 pages
arxiv created 2018/04/02 · openalex publication_date 2018/06/18 · arxiv updated 2018/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present the theory of thermoelectric transport in metals with long-lived quasiparticles, carefully addressing the interplay of electron-electron scattering as well as electron-impurity scattering, but neglecting electron-phonon scattering. In Fermi liquids with a large Fermi surface and weak electron-impurity scattering, we provide universal and simple formulas for the behavior of the thermoelectric conductivities across the ballistic-to-hydrodynamic 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 Wiedemann-Franz law. A less severe violation of the Mott law arises. We quantitatively compare the violations of the Wiedemann-Franz law arising from (i) momentum-conserving electron-electron scattering in the collision integral, (ii) hydrodynamic modifications of the electron-impurity 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 ballistic-to-hydrodynamic 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 Wiedemann-Franz law, and the crossover between these behaviors is a clear prediction for experiments. The arbitrarily strong violation of the Wiedemann-Franz law found in our work arises entirely from electron-electron interaction effects within the Fermi-liquid paradigm, and does not imply any non-Fermi-liquid behavior. We predict clear experimental signatures of bulk hydrodynamics in high-mobility two-dimensional GaAs semiconductor structures, where a spectacular failure of the Wiedemann-Franz law should persist down to very low temperatures in high-quality and low-density samples.