Thermopower in superconductors: Temperature dependence of magnetic flux in a bimetallic loop

Abstract

The thermopower of superconductors measured via the magnetic flux in a bimetallic loop is evaluated. It is shown that by a standard matching of the electrostatic potential, known as the Bernoulli potential, one explains the experimentally observed amplitude and the divergence in the vicinity of the critical temperature.The thermopower is a widely used tool to study electronic properties of conductive materials. An exception are superconductors, where the supercurrent cancels any diffusive current so that the zero net current or voltage are observed. This feature is known from 1935 and since then there were a number of attempts to access diffusive currents in an indirect way. 1 Already in 1944 Ginzburg noticed that in inhomogeneous systems like bimetallic loops, the counter-flowing supercurrent creates a magnetic flux. 2 The boom in this field came 30 years later. In 1974 Garland and Van Harlingen proposed a simple phenomenological theory 3 and Gal'perin, Gurevich, and Kozub published a microscopic treatment 4 based on the Boltzmann-type approach. These theories predicted fluxes of similar amplitudes and temperature dependences.In the same year Zavaritskii presented experimental data 5 and he was soon followed by others. 6-8 Experimental results were a surprise. Zavaritskii 5 and Falco 7 observed the expected temperature dependence, but Pegrum, Guénault, and Pickett 6 and Van Harlingen and Garland 8 monitored a thermally induced magnetic flux by five orders of magnitude larger. Moreover, the theory predicts that close to T c the flux ⌽ diverges as d⌽ / dT ϰ ͑T c − T͒ −1 , while a steeper divergence d⌽ / dT ϰ ͑T c − T͒ −3/2 was observed. 6,8 The experimental situation in the late 1970s is reviewed in Ref. 9.The giant flux stimulated a number of theoretical studies 10-15 that explored various additional components ranging from a trapped flux, over impurities, over interfaces, to an influence of supercurrent flow. Most of these ingredients bring only a minor correction to the original prediction. It was speculated, that the only sizable contribution can come from the trapped flux, which increasingly leaks into the ring as the temperature approaches its critical value.All these speculations were terminated by measurements of Van Harlingen, Heidel, and Garland. 16 To avoid the penetration of the external magnetic field they used the toroidal geometry and convincingly demonstrated that the large magnetic flux with the d⌽ / dT ϰ ͑T c − T͒ −3/2 divergence is a genuine effect. By comparing a number of samples they could conclude that the flux is proportional to the thermopower in the normal state and therefore that it is indeed caused by the thermal diffusion of electrons. The lack of at least a qualitative theory has discouraged further measurements in this direction and the thermopower joined the family of puzzling transport properties in superconductors.Alternative measurements of the thermopower via the superconducting fountain effect 17 or the charge imbalance in the conversion region 18 confirmed the theory of Gal...

Thermopower oscillations in mesoscopic Andreev interferometers

“…The origin of this "giant flux" puzzle remains debated. 10,11 Mesoscopic systems provide an altogether different way to probe the thermoelectric phenomena in the presence of superconductivity. The superconducting correlations can penetrate the normal-metal part of the system due to a process known as Andreev reflection.…”

Flux-induced Nernst effect in a superconducting loop

“…Our study differs from those in [41][42][43][44][45] since we consider a uniform material and from that in [47] since we consider a uniform cross section. where the integration is along the wire.…”

“…A case with ring topology that has been studied experimentally [41,42] and theoretically [43][44][45] is that of a bimetallic loop. A related effect, which has been reviewed in [46], is the appearance of magnetic flux when a temperature gradient is present in a nonuniform loop.…”

A Fermi liquid approach to an explanation of the thermoelectric effects experimentally observed in superconductors

“…The unperturbed function n 0 (ε p ) appearing in equation ( 3) is regarded here as a local equilibrium distribution function equal to the Fermi function (with replacing ε p → ε p when v s = 0, see equations (10) and ( 11)):…”

“…Koláček and Lipavský [10] have presented a descriptive examination of the superconductive thermopower based on a speculative introduction of the so-called Bernoulli potential. In spite of an approximation to the experimental results of Van Harlingen et al [5], such an ad hoc approach is unlikely to be considered as a rigorous theory.…”