TThermodynamics of the thermoelectric working fluid close to the superconducting phase transition

Abstract

The bottleneck in state-of-the-art thermoelectric power generation and cooling is the low performance of thermoelectric materials. The main difficulty is to obtain a large thermoelectric power factor as the Seebeck coefficient and the electrical conductivity cannot be increased independently.Here, relating the thermoelastic properties of the electron gas that performs the thermoelectric energy conversion, to its transport properties, we show that the power factor can diverge in the vicinity of the metal-to-superconductor phase transition in two-dimensional systems. We provide experimental evidence of the rapid increase of the Seebeck coefficient without decreasing the electrical conductivity in a 100-nm Ba(Fe1−xCox)2As2 thin film with high structural quality, as the sample temperature approaches the critical temperature, resulting in a power factor enhancement of approximately 300. This level of performance cannot be achieved in a system with low structural quality as shown experimentally with our sample degraded by ion bombardment as defects preclude the strong enhancement of the Seebeck coefficient near the phase transition. We also theoretically discuss the thermoelectric conversion efficiency for a wide-range of model systems, and show that driving the electronic system to the vicinity of a phase transition may be an innovative path towards performance increase at the possible cost of a narrow temperature range of use of such materials.

Influence of the Anderson Transition on Thermoelectric Energy Conversion in Disordered Electronic Systems

“…We have connected the thermoelectric and thermoelastic properties of the three-dimensional Anderson model, discussing the effect of different types of electron distributions − the homogeneous ensemble and the inhomogeneous ensemble −, as well as the role of the critical exponent. In contrast with the sharp enhancement of thermoelectric conversion close to the superconducting phase transition [6], our results show a smooth, monotonously growing dependence of the thermoelectric figure of merit on temperature. Indeed, in single particle models a sharp energy-dependence of the transmission function is requested to obtain large thermoelectric efficiencies.…”

“…This is a formidable challenge, due to the interdependence of the transport coefficients, ruled by phenomenological laws such as the Wiedemann-Franz law connecting heat and electric conductivity [5]. To establish an upper bound for zT under given working conditions, it is enough to consider the thermoelectric figure of IOP Publishing doi:10.1088/1742-6596/2701/1/012018 2 merit of the conduction electron gas alone, z e T , which disregards the lattice thermal conductivity κ ph [6]:…”

“…The convective part of the heat flow, which adds to the conductive part due to electrons and phonons under open circuit conditions, can be enhanced near the critical temperature for a electronic transition [8,9]. In the literature, thermoelectric conversion was discussed for superconducting [6] and metal-insulator Anderson transition [10,11,12].…”

“…As discussed in [6,9], driving the electron gas close to a phase transition yields a significant increase of the isentropic expansion factor, which boosts the energy conversion efficiency. In the latter works, thermally driven effects, namely fluctuating Cooper pairs and nematic fluctuations, were considered in 2D systems and thin films.…”

“…Indeed, one may expect that the Seebeck coefficient may drastically increase as the system is driven away from its metallic phase as the entropy per carrier increases. Thermoelectric conversion near the Anderson transition has been studied in [10,11,12], but the link between thermoelastic and transport properties has not been yet considered, while it has been studied for the metal to superconductor phase transition [6].…”