Generalized proximity effect model in superconducting bi- and trilayer films

Abstract

This paper presents a general model for calculating the density of states and the Cooper pair potential in proximised superconducting bi-and trilayer films. It is valid for any kind of bilayer S 1 -S 2 , whatever the quality of the materials S 1 and S 2 , the quality of the S 1 -S 2 interface and the layer thicknesses. The trilayer model is valid for a thin S 3 layer, whereas the other two layers have arbitrary thicknesses. Although the equations of the dirty limit are used, it is argued that the model stays valid in clean bi-and trilayer films. The typical example of superconducting tunnel junctions is used to show that existing models, applying to very thin or very thick layers, or to perfectly transparent S 1 -S 2 interfaces, are too restrictive to apply to any bilayer. The new model is applied to existing junctions, with layer thicknesses intermediate between the 'thick' and the 'thin' approximation. 1 I INTRODUCTIONUnderstanding the proximity effect in superconducting films is important for the development of practical devices such as superconducting tunnel junctions (STJ's). Depositing a superconductor S 1 onto another S 2 modifies the properties of both S 1 and S 2 materials. If both superconductors are thick enough (typically thicker than 10 ξ S 1 (S 2 ) , with ξ S 1 (S 2 ) the coherence length of S 1 (S 2 )), the extremities of the bilayer behave as bulk materials obeying the BCS theory, though not necessarily like bulk S 1 and bulk S 2 . The intermediate region around the S 1 -S 2 interface is characterised by a relatively sharp transition between the two bulk-like regions, and can be pretty far from a BCS-like description. If the layers are relatively thin, any BCS-like behaviour can be absent from the structure. Finally, in the case where the layers are extremely thin, as described by McMillan [1], each layer behaves again like a BCS superconductor.The physical quantities affected in a proximised bulk superconductor, are the Cooper pair potential ∆, the density of states for the Cooper pairs, P , and the density of states for the quasiparticles, N. As the density of states in both superconductors is modified due to the proximity effect, the resultant bandgap ∆ g lies at an intermediate value between the bulk values for S 1 and S 2 , ∆ g,S 1 and ∆ g,S 2 respectively. This feature has been fully described in the specific case, of a thin, low bandgap material S 2 next to a thick, high bandgap material S 1 , with both superconductors in the dirty limit [2,3].The goal of the present paper is to present the need for, and develop a model of, the proximity effect, which is not restricted to this very specific case.In particular section V shows that there are many situations where this special case does not apply, and for which the simple BCS approach does not provide a satisfactory description.Specifically, in the case of STJ's used as photon detectors, a more general description of the proximity effect is required to adequately address such issues as device performance.The general conditions for an ...

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Cooling electrons from 1 to 0.4 K with V-based nanorefrigerators

“…This behavior markedly differs from the Ambegaokar-Baratoff prediction 11 and is expected for tunnel junctions embedding an interlayer like the present. 12,13 In order to validate our temperature calibration and rule out spurious overheating in the small island we also measured the I c ͑T bath ͒ dependence on similar junctions fabricated on a large-volume Al electrode, i.e., device C shown in Fig. 1͑d͒ ͑open squares͒.…”

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“…1,2 Over the last few years both the quality of the devices fabricated and the understanding of the relevant physical processes have improved greatly. Notable among the latter are the proximity effect, which determines the properties of the bilayer electrodes commonly used, [3][4][5] the various diffusion and loss mechanisms which limit the energy resolution of a STJ, 6,7 and the details of the quasiparticle interactions through which the overall performance of the detector is modeled. [8][9][10] In this article, we describe a major advance in the treatment of quasiparticle dynamics, which is essential for modeling the latest generation of low-gap, multitunneling STJs designed to operate at mK temperatures.…”