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Register a new userNonequilibrium quasiparticles and electron cooling by normal metal - superconductor tunnel junctions
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We consider a model NISIN system with two junctions in series, where N is a normal metal, S is a superconductor and I is an insulator. We assume that the resistance of the first junction is high, while the resistance of the second one is low. In this case the first junction cools the left normal electrode, while the second junction partially removes excited quasiparticles from the superconductor. We consider cooling properties of this double junction structure. It is shown that the cooling power depends strongly on the ratio of the resistances of the two junctions. In conclusion, we derive a generalized expression for the cooling power of a NIS tunnel junction taking into account charge imbalance effects.
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We investigate heat and charge transport in NNIS tunnel junctions in the diffusive limit. Here N and S are massive normal and superconducting electrodes (reservoirs), N is a normal metal strip, and I is an insulator. The flow of electric current in such structures at subgap bias is accompanied by heat transfer from the normal metal into the superconductor, which enables refrigeration of electrons in the normal metal. We show that the two-particle current due to Andreev reflection generates Joule heating, which is deposited in the N electrode and dominates over the single-particle cooling at low enough temperatures. This results in the existence of a limiting temperature for refrigeration. We consider different geometries of the contact: one-dimensional and planar, which is commonly used in the experiments. We also discuss the applicability of our results to a double-barrier SINIS microcooler.
We demonstrate both theoretically and experimentally two limiting factors in cooling electrons using biased tunnel junctions to extract heat from a normal metal into a superconductor. Firstly, when the injection rate of electrons exceeds the internal relaxation rate in the metal to be cooled, the electrons do no more obey the Fermi-Dirac distribution, and the concept of temperature cannot be applied as such. Secondly, at low bath temperatures, states within the gap induce anomalous heating and yield a theoretical limit of the achievable minimum temperature.
We discuss the theoretical framework to describe quasiparticle electric and heat currents in NIS tunnel junctions in the dirty limit. The approach is based on quasiclassical Keldysh-Usadel equations. We apply this theory to diffusive NISS tunnel junctions. Here N and S are respectively normal metal and superconductor reservoirs, I is an insulator layer and S is a nonequilibrium superconducting lead. We calculate the quasiparticle electric and heat currents in such structures and consider the effect of inelastic relaxation in the S lead. We find that in the absence of strong relaxation the electric current and the cooling power for voltages $eV < Delta$ are suppressed. The value of this suppression scales with the diffusive transparency parameter. We ascribe this suppression to the effect of backtunneling of nonequilibrium quasiparticles into the normal metal.
We investigate heat and charge transport through a diffusive SIF1F2N tunnel junction, where N (S) is a normal (superconducting) electrode, I is an insulator layer and F1,2 are two ferromagnets with arbitrary direction of magnetization. The flow of an electric current in such structures at subgap bias is accompanied by a heat transfer from the normal metal into the superconductor, which enables refrigeration of electrons in the normal metal. We demonstrate that the refrigeration efficiency depends on the strength of the ferromagnetic exchange field h and the angle {alpha} between the magnetizations of the two F layers. As expected, for values of h much larger than the superconducting order parameter Delta, the proximity effect is suppressed and the efficiency of refrigeration increases with respect to a NIS junction. However, for h sim Delta the cooling power (i.e. the heat flow out of the normal metal reservoir) has a non-monotonic behavior as a function of h showing a minimum at h approx Delta. We also determine the dependence of the cooling power on the lengths of the ferromagnetic layers, the bias voltage, the temperature, the transmission of the tunneling barrier and the magnetization misalignment angle {alpha}.
The point-contact spectra of tantalum in the superconducting state, with $Ta$, $Cu$, and $Au$ counterelectrodes, have been studied. We discovered some new distinctive features, whose position on the $eV$ axis is determined by the critical power required for the injection of nonequilibriumquasiparticles. At this level of power the band gap $Delta $ decreases abruptly in the vicinity of the contact. A correction to the point-contact spectrum, with the sign opposite to that of the usual correction, arises in the region of phonon energies. The maxima in the $Ta$ spectrum become sharper and their position on the energy axis becomes stabilized near the values $e{{V}_{ph}}=7.0$, 11.3, 15.5, and 18 $meV$, which correspond to low phonon group velocities $partial omega /partial qsimeq 0$ in $Ta$. This is confirmed by the existence of corresponding flattenings on the dispersion relations $omega (q)$ of lattice vibrations. Slow phonons are created near the $N-S$ interface in quasiparticle recombination and relaxation processes and cause a decrease in $Delta $ and an increase in the differential resistance in the vicinity of $e{{V}_{ph}}$. An excess quasiparticle charge is accumulated in the region of the contact, producing a correction to the resistance, which decreases as $eV$, $T$, and $H$ increase. These mechanisms are particularly effective in dirty contacts, thus permitting phonon spectroscopy in the superconducting state even when the current flow occurs in a nearly thermal mode.
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