Quantum limit of thethermoelectric efficiency of heterogeneous media at low temperatures

S.A. Ktitorov, V.K.Zaitsev, M.I. Fedorov

A.F. IoffePhysico-Technical Institute, Polytekhnicheskaya ul., 26, 194021 St. Petersburg,Russia

There is a class of conductors that havelow-temperature kinetic properties, which are not specifically related to aconcrete scattering mechanism and to other nonuniversal factors. Let usconsider a polycrystal with point contacts between crystallites. These pointcontacts are really small bridges or weak links between crystallites. Largevolume of crystallites in comparison with bridges connecting them ensures theeffective thermalization. Large cross section of a crystallite makes theelectric current and heat flux densities extremely small there. Thus, we canconsider the system as a network of electric and thermal resistors andmicrothermoelements (weak links) connecting sites (crystallites), which can becharacterized by their electric potentials and temperatures . Theoreticalanalysis of the heat transport problem for the polycrystal is reduced to twodifferent ones: the first problem is to study the electric and heat transportthrough the weak link and the second is to solve the network equations for agiven distribution of links parameters. The former can be considered usingdifferent methods depending on the temperature range, the weak link geometry,and the microscopic properties of the material, while the latter is determinedexclusively by the system geometry and a distribution of parameters. It isshown in this work that the thermoelectric efficiency ZT of these structures at low enough temperatures can be expressed only interms of the fundamental constants and of the system geometry.