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

Abstract

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 2D 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.

Role of electron-electron collisions for charge and heat transport at intermediate temperatures

“…In this section, we derive the approximate form of the collision integral given in Eq. (28) for the case of a FL in three dimensions (d = 3) [55]. Using Eq.…”

“…(17), (21)] and the Seebeck coefficient [Eq. (19)] derived using the method of Keyes acquire a simple form when the scattering rate by impurities is constant [27,28,46]…”

“…Out of these three coefficients, only κ depends on τ ee in the absence of a momentum dependence of τ ei . It is governed by the Matthiessen's rule (∼ τ −1 ei + τ −1 ee ) for two scattering rates [27,28]. For FLs at low temperatures T ≪ ǫ F , the moments of ξ p that enter the transport coefficients become ξ 2 p = π 2 T 2 /3 and ξ p = π 2 T 2 /(3ǫ F ).…”

Temperature collapse of the electric conductivity in bilayer graphene

“…In recent years, the investigation of intrinsic transport properties of two-dimensional systems has been the subject of intense interest [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Bilayer graphene (BLG) is one of the most carefully scrutinized systems within this class.…”

Stokes flow around an obstacle in viscous two-dimensional electron liquid

“…In the absence of disorder, an interacting many-body electron system can be described within the hydrodynamic framework [1][2][3] . Typical three-dimensional metals rarely enter into the hydrodynamic regime because the electron-impurity (phonon) scattering is stronger than the corresponding electron-electron interactions 4 .…”