Phase-Slip Centers as Cooling Engines

Abstract

Based on time-dependent Ginzburg-Landau system of equations, Éliashberg’s kinetic equations and finite element modeling, we analyze phonon emission by the phase-slip centers in superconducting filaments. Our results show that in the dissipative regime with these centers, thin superconducting filaments can be effective in originating not only positive but also negative thermal fluxes, i.e., they both generate and absorb phonons. In a stationary oscillatory regime, at a given moment of time, this generation and absorption of phonons reveals itself as positive and negative spectrum of phonons at different spectral ranges. Moreover, at a given spectral range, the emission reverses its sign during the period of oscillation. This fact is associated with the reciprocation of the energy emission and absorption at different spectral intervals during the oscillation period of the phase-slip center. The integral value of energy over the whole spectral range is time-dependent, being positive for some part of the period and negative for the rest of it. Its time integral over the period reveals a positive value, which corresponds to the total energy released in this dissipative state of superconducting filament. In a simple case, when the filament is embedded in a thermal heat bath (substrates typically play that role), this energy dissipates, elevating locally the temperature of filament’s environment. However, in a more sophisticated design, the positive and negative fluxes may become separated. This can be achieved by using the thermal diode effect (the Kapitza boundaries can play the role of such diodes). Such a separation may yield to the net cooling of some part of the filament environment, while the other part will serve as a heat sink. Thus, with an appropriate design of their thermal surroundings, the phase-slip centers can serve as effective solid-state cooling engines. They may be effective for reducing further the cryostat cold finger temperature; for example, from 1 K to sub-K temperatures.