Thermoelectric effects in superconducting nanostructures

Abstract

We study thermoelectric effects in superconducting nanobridges and demonstrate that the magnitude of these effects can be comparable or even larger than that for a macroscopic circuit. It is shown that a large gradient of the electron temperature can be realistically created on nanoscale and masking effects of spurious magnetic fields are minimal in nanostructures. For these reasons nanodevices are favorable for studying the thermoelectric effect in superconductors.

Resolving thermoelectric “paradox” in superconductors

“…The theory of thermoelectric quasiparticle current, I q , was developed by Galperin et al ( 3 ), Guénault and Webster ( 16 ), and Van Harlingen et al ( 4 ); however, calculation of the superconducting circulating current, I cs , which generates the thermoelectric magnetic flux, was not attempted. Here, we proceed with the calculation using minimization of the total energy of the superconducting loop, W , with respect to I cs , as suggested by Gurevich et al ( 13 ); see the Supplementary Materials for details.…”

“…The measured quasiparticle current ( 10 ) was orders of magnitude smaller than the supercurrent and agreed well with the theory ( 11 ). No plausible explanations for the observations and no experimentally supported analysis have been offered to date, and the paradox remained unresolved [see Galperin et al ( 12 ) and Gurevich et al ( 13 ) and references therein].…”

“…Theoretically, we deduce a new formula connecting the thermoelectric magnetic flux and the current circulating in the loop in the presence of a temperature gradient. For calculations, we use a method suggested recently ( 13 ), taking into account the energy balance in the system. Our proof-of-principle experiments agree well with the new theory.…”

“…To precisely determine and control the k value in such large loops as well as measure the period of oscillations, one had to control the absolute magnitude of magnetic field with a precision of about 10 −9 T, an extremely difficult task that was never done. Consequently, separation of the genuine thermoelectric flux has not been completed, leaving the puzzling discrepancy between the theory and the experiment unexplained ( 1 , 12 , 13 ). The conceptual and technological advance reported here is based on highly sensitive hybrid quantum interferometers ( 14 , 15 ) coupled to the bimetallic loops fabricated using modern nanolithography with areas up to five orders of magnitude smaller than those measured previously.…”

Thermopower oscillations in mesoscopic Andreev interferometers

“…From Eqs. (11) we find the current energy densities j e (ε), j Q (ε) in the parameterization of Eqs. (5,7) as…”