We show that an adiabatic increase of the supercurrent along a superconductor with lines of nodes of the order parameter on the Fermi surface can result in a cooling effect. The maximum cooling occurs if the supercurrent increases up to its critical value. The effect can also be observed in a mixed state of a bulk sample. An estimate of the energy dissipation shows that substantial cooling can be performed during a reasonable time even in the microkelvin regime.Although the mechanism of high temperature superconductivity still remains unclear there is strong evidence that the order parameter in high temperature superconductors has nodes on the Fermi surface [1]. Such a property is also peculiar to some superconductors with heavy fermions. In this paper we show that presence of nodes of the order parameter can lead to a cooling effect. The cooling is reached by adiabatically increasing the supercurrent around a superconducting ring or a cylinder.Currently the lowest temperature of a solid (T ∼ 1µK) is achieved by using a method of adiabatic nuclear demagnetization [2,3]. Spontaneous magnetic ordering of the nuclear magnetic moments represents the low temperature limit for nuclear refrigeration. The ordering temperature due to nuclear dipole-dipole interaction is typically a fraction of a microkelvin and, therefore, to achieve temperatures lower than 0.1µK a new refrigeration technology is needed. In our cooling mechanism the conduction electrons are cooled during the adiabatic increase of the supercurrent instead of the nuclear spin system being cooled in the nuclear demagnetization process. Further development of the idea of cooling using the phenomena of superconductivity (superfluidity) could be promising to achieve the lowest temperature of solids.
Cooling effect in clean superconductorsLet us consider a superconducting ring (or a cylinder) made from a clean high temperature superconductor. For estimates one can assume the Fermi surface to be a cylinder and the order parameter has a simple d-wave form ∆(p) = ∆ 0 cos(2φ), where φ is the polar angle in the ab crystalline plane. Taking into account the real form of the Fermi surface might change numerical coefficients, but these details are not necessary for estimating the magnitude of the cooling effect. Let the c -axis of the superconductor be parallel to the symmetry axis of the ring and the temperature of the system is T ≪ T c , where T c is the superconducting transition temperature.At low temperatures the main contribution to the electronic specific heat of the superconductor arises from quasiparticles that are activated above the gap in narrow vicinities of the nodes of the order parameter. The energy of these quasiparticles is given by