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

Abstract

Electric, thermal and thermoelectric transport in correlated electron systems probe different aspects of the many-body dynamics, and thus provide complementary information. These are well studied in the low-and high-temperature limits, while the experimentally important intermediate regime, in which elastic and inelastic scattering are both important, is less understood. To fill this gap, we provide comprehensive solutions of the Boltzmann equation in the presence of an electric field and a temperature gradient for two different cases: First, when electron-electron collisions are treated within the relaxation-time approximation while the full momentum dependence of electron-impurity scattering is included and, second, when the electron-impurity scattering is momentum-independent, but the electron-electron collisions give rise to a momentum-dependent inelastic scattering rate of the Fermi-liquid type. We find that for Fermi-liquid as well as for Coulomb interactions, both methods give the same results for the leading temperature dependence of the transport coefficients. Moreover, the inelastic relaxation rate enters the electric conductivity and the Seebeck coefficient only when the momentum dependence of the electron-impurity collisions, analytical or non-analytical, is included. Specifically, we show that inelastic processes only mildly affect the electric conductivity, but can generate a non-monotonic dependence of the Seebeck coefficient on temperature and even a change of sign. Thermal conductivity, by contrast, always depends on the inelastic scattering rate even for a constant elastic relaxation rate.

Thermoelectric transport in a correlated electron system on the surface of liquid helium

“…Interestingly, the figure of merit ZT obtained from the above equations can significantly exceed unity. Indeed, by using the estimates S ≈ −2(k B /e) and κ ≈ (2k B T e n s τ )/m e , we obtain ZT ≈ 2(τ /τ ), which varies between about 350 and 4 for the temperature range between 0.2 and 0.6 K. Such large values of ZT are due to τ ee << τ , which corresponds to strong violation of the Weidemann-Franz law [17][18][19].…”

“…In this work, the electron-electron interaction was omitted from the discussion. However, theoretically it is expected that very fast inelastic electron-electron scattering, which is a signature of strongly-correlated electron liquid on liquid helium [16], can lead to strong violation of the Wiedemann-Franz law and significant increase of the ratio σ/κ [17][18][19]. Thus, a careful study of thermoelectric transport in this controllable disorder-free system can potentially help us to explore different regimes of thermoelectric transport for energy-conversion optimization.…”

“…According to Ref. [19] (see also an earlier work by Keyes [24]), the Boltzmann equation in the relaxation-time approximation for a many-electron system can be presented as…”

“…Following Ref. [19], it is straightforward to obtain the thermoelectric transport coefficients S, σ and κ. For the stationary state of the electron system, where no electric current flows, we obtain [26]…”

“…Our results are in good agreement with the calculations based on kinetic equations. This work provides the opportunity to study thermoelectricity in a clean model system with controllable electron-electron interaction, which can affect electric and thermal properties of the system in a nontrivial way [17][18][19]. Our simple experimental method can be readily adjusted to different configurations by choosing an appropriate electrode geometry.…”