Magnetic-field-induced stabilization of nonequilibrium superconductivity in a normal-metal/insulator/superconductor junction

A small magnetic field is found to enhance relaxation processes in a superconductor, thus stabilizing superconductivity in nonequilibrium conditions. In a normal-metal (N)/insulator/superconductor (S) tunnel junction, applying a field of the order of $100\mu \mathrm{T}$ leads to significantly improved cooling of the N island by quasiparticle (QP) tunneling. These findings are attributed to faster QP relaxation within the S electrodes as a result of enhanced QP drain through regions with a locally suppressed energy gap due to magnetic vortices in the S leads at some distance from the junction.

Figure 1

(a) Maximum temperature drop $\delta T$ in an optimally biased SINIS cooler in a perpendicular magnetic field $B_{\perp }$, at a bath temperature $T_0=285\mathrm{mK}$. The sketches show the S electrode geometry and qualitative vortex configurations at $B_{\perp }\lesssim 2\mathrm{G}$ and at a value of $B_{\perp }$ beyond the optimum point. The area inside the green (dashed) rectangle corresponds to that in the micrograph below. (b) Scanning electron micrograph of a typical structure, together with the measurement scheme (see the text for details). A Cu island (red, marked with N) in the middle is contacted to four superconducting Al electrodes (blue/dark) via Al oxide tunnel barriers for thermometry and temperature control. Replicas of each structure are visible due to the fabrication involving two-angle shadow evaporation of the metals.

Figure 2

(a) Temperature $T_{\mathrm{N}}$ of the N island and (b) cooler SINIS $I$-$V$ characteristic at several bath temperatures $T_0$ as functions of the cooler bias voltage $V$, in zero field (red/light) and at $B_{\perp }\simeq 3\mathrm{G}$ (blue/dark). (c) Relative minimum temperature in zero field (red/light symbols) and at $B_{\perp }\simeq 3\mathrm{G}$ (blue/dark symbols). The solid and dashed-dotted lines show the calculated temperature reduction for various degrees of thermalization of the QPs and of the island phonons (see text). (d) Optimum bias voltage $V_{\mathrm{opt}}$ vs $B_{\perp }$ at $T_0=285\mathrm{mK}$, with the corresponding temperature drop in Fig. 1a. (e) Phonon temperatures in zero (red/light,$▿$) and optimum (blue/dark, $▵$) field, required to reproduce the observed $T_{\mathrm{N},\min }$. The dashed line shows $T_{\mathit{ph}}=T_0$.

Figure 3

Cooling curves in selected magnetic fields for parallel SINIS coolers with different S electrode geometries, at fixed $T_0\simeq 130\mathrm{mK}$. (a) When initially wide S leads are followed by a narrower section, applying a finite $B_{\perp }$ weakens the cooling monotonously. (b) In a structure with initially narrow leads, the behavior is nonmonotonic, with enhanced cooling in small fields. The insets sketch one half of the cooler structure with ten NIS junctions in parallel.