Andreev Current-Induced Dissipation in a Hybrid Superconducting Tunnel Junction

Abstract

We have studied hybrid superconducting micro-coolers made of a double SuperconductorInsulator-Normal metal tunnel junction. Under subgap conditions, the Andreev current is found to dominate the single-particle tunnel current. We show that the Andreev current introduces additional dissipation in the normal metal equivalent to Joule heating. By analyzing quantitatively the heat balance in the system, we provide a full description of the evolution of the electronic temperature with the voltage. The dissipation induced by the Andreev current is found to dominate the quasiparticle tunneling-based cooling over a large bias range.PACS numbers: 74.50.+r, 74.45.+c In a tunnel junction between a normal metal (N) and a superconductor (S), the charge transfer occurs mainly through two different mechanisms. The tunneling of a single quasi-particle is possible for electrons or holes with an energy E (compared to the Fermi level E F ) larger than the superconductor gap ∆. At low energy, the charge transfer occurs through the Andreev reflection [1,2]. In the normal metal, an electron (a hole) impinging on the superconducting interface is reflected as a hole (an electron), enabling the transfer of a Cooper pair into (out of) the superconductor. As the energies of the involved electron and hole are located symmetrically around E F , the Andreev reflection does not carry heat through the interface at zero bias. The probability for an incident quasi-particle to follow an Andreev reflection, a specular reflection or a tunnel transfer is given in the ballistic regime (no disorder) by the BTK theory [3]. For a N-I-S tunnel junction with an insulator (I) of intermediate or low transparency, the Andreev reflection probability is predicted to be vanishingly small. Taking into account the quasi-particles confinement in the vicinity of the interface, this is no longer true. This confinement can be induced by the disorder or the presence of a second barrier in the normal metal. A single quasiparticle then experiences several collisions with the interface [4,5]. The actual Andreev reflection transmission coefficient corresponds to the coherent addition of many individual transmission probabilities. Therefore, the Andreev sub-gap current significantly exceeds the ballistic case prediction [6,7] and can be modulated by a magnetic flux [8].A quasi-particle current in a N-I-S junction indeed carries both a charge current and a heat current. With a voltage bias smaller than the gap ∆/e, the tunnel current is selectively made out of high-energy electrons (or holes); this cools the electronic population of the normal metal [9]. In this way, (S-I-N-I-S) micro-coolers based on a double tunnel junction provide a significant temperature reduction which reaches an optimum at a voltage bias just below the gap. At a very low temperature, the thermal transport in such N-I-S tunnel junctions appears to be still little understood. For instance, an apparent reversal of the normal metal temperature evolution was observed in various experiments [10,11] and r...

Experimental realization of a Coulomb blockade refrigerator

“…3(b) indicates 3 pA, which we have chosen as a biasing current for the temperature probe. This value is in the temperature sensitive region, not influenced by the Andreev current leakage [30][31][32] that appears as a constant slope at low bias values in Fig. 3(b).…”

“…These problems can be resolved in the future by improving filtering and thermometry. Increased resistance of the NIS junctions would reduce the magnitude of the Andreev current and the heat it produces, which is significant towards low temperatures [31]. Alternative thermometry can be used as well.…”

Andreev current for low temperature thermometry

“…In addition, their responsivity tends to saturate at low temperature due to particular tunneling processes such as environment assisted tunneling 7 or Andreev reflections. 8 We are proposing to use the disorder enhanced Andreev current as a temperature probe. When a single electron attempts to leave the normal metal (N) trough a tunnel barrier (I), it is usually reflected if no states are available in the superconductor (S), i.e., if eV < D. Due to elastic scattering, this reflected electron may bounce around and finally make one or several attempts to tunnel.…”

Environment-Assisted Tunneling as an Origin of the Dynes Density of States

“…1(b). This leakage is typically attributed to Andreev current [17][18][19][20], smeared DOS of the superconductor [21], nonvanishing DOS in the insulator within the gap [9], nonequilibrium quasiparticles [22], or physical imperfections in the junction. Our junctions, like the one in Fig.…”