Field theory of mesoscopic fluctuations in superconductor/normal-metal systems

Altland, Alexander; Simons, Benjamin D.; Taras-Semchuk, D.

doi:10.1134/1.567622

Cited by 31 publications

(61 citation statements)

References 66 publications

(160 reference statements)

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“…(3.19), with respect toQ, reproduces the matrix Usadel equations forQ (1) andQ (2) together with the corresponding boundary conditions [39,32] (cf. similar derivation in [40]):…”

Section: A Tunneling Term In the Actionmentioning

confidence: 95%

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Keldysh action for disordered superconductors

2000

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Keldysh representation of the functional integral for the interacting electron system with disorder is used to derive microscopically an effective action for dirty superconductors. In the most general case this action is a functional of the 8×8 matrix Q(t, t ′ ) which depends on two time variables, and on the fluctuating order parameter field and electric potential. We show that this approach reproduces, without the use of the replica trick, the well-known result for the Coulomb-induced renormalization of the electron-electron coupling constant in the Cooper channel. Turning to the new results, we calculate the effects of the Coulomb interaction upon: i) the subgap Andreev conductance between superconductor and 2D dirty normal metal, and ii) the Josephson proximity coupling between superconductive islands via such a metal. These quantities are shown to be strongly suppressed by the Coulomb interaction at sufficiently low temperatures due to both zero-bias anomaly in the density of states and disorder-enhanced repulsion in the Cooper channel.

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“…(3.19), with respect toQ, reproduces the matrix Usadel equations forQ (1) andQ (2) together with the corresponding boundary conditions [39,32] (cf. similar derivation in [40]):…”

Section: A Tunneling Term In the Actionmentioning

confidence: 95%

“…However, in the presence of superconductivity, some excitations on the metallic SPM, having been massless, acquire a gap proportional to ∆. A detailed discussion of the hierarchy of gaps in the σ-model for N-S systems can be found in the review [32].…”

Section: σ-Modelmentioning

confidence: 99%

Keldysh action for disordered superconductors

2000

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“…In this note we revisit this problem, refining some of the existing results and replacing numerical answers with analytical ones. We design this note as a quick reference on the structure of the minigap in a long disordered SNS junction which may be useful in view of renewed interest in such systems in connection with problems related to π-junctions [5,6] and to mesoscopic fluctuations [7,8]. As a byproduct, we derive two useful identities for solutions to Usadel equations which simplify our analytical calculations.…”

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confidence: 99%

“…Inside the junction, both θ and χ turn into complex functions. For simplicity, we choose ideally transparent interfaces and assume the normal metal to be much more disordered than the superconductor; in this case the boundary conditions become "rigid" [7,9],…”

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confidence: 99%

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Minigap in a long disordered SNS junction: Analytical results

2002

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We review and refine analytical results on the density of states in a long disordered superconductor-normal-metal-superconductor junction with transparent interfaces. Our analysis includes the behavior of the minigap near phase differences zero and π across the junction, as well as the density of states at energies much larger than the minigap but much smaller than the superconducting gap.A superconductor in contact with a normal metal induces pairing correlations in the metal, a phenomenon known as the proximity effect. One of the most remarkable consequences of such induced correlations is the appearance of a gap, usually referred to as the "minigap", in the electronic excitation spectrum of the normal metal [1]. A very common setup exhibiting a minigap is the superconductor-normal-metal-superconductor (SNS) junction made of two superconducting leads connected via a disordered normal layer. The gap in this junction is determined by the diffusion time across the normal layer and is sensitive to the phase difference across the junction, reaching a maximum at zero phase difference and vanishing at the phase difference π [2].The appearance of a minigap and its phase dependence is well understood in the quasiclassical description. Provided the scattering length is much larger than the Fermi wave length but much smaller than the junction dimensions, the motion of the electrons in the normal layer is diffusive and the proximity effect may be described by the Usadel equations [3]. These equations are nonlinear, which complicates their analytical treatment except for several simple limits. One of the cases most accessible to an analytical treatment is the limit of a long disordered SNS junction (with the minigap energy scale much smaller than the superconducting gap) with transparent normal-metal-superconductor interfaces. The spectral properties of such a junction have been previously studied in Refs. [2,4] and we find it possible to further improve on those results. In this note we revisit this problem, refining some of the existing results and replacing numerical answers with analytical ones. We design this note as a quick reference on the structure of the minigap in a long disordered SNS junction which may be useful in view of renewed interest in such systems in connection with problems related to π-junctions [5,6] and to mesoscopic fluctuations [7,8]. As a byproduct, we derive two useful identities for solutions to Usadel equations which simplify our analytical calculations.Assuming a quasi-one-dimensional geometry of the contact, the proximity effect in the normal layer may be described via the Usadel equations (in our paper we conform to the definitions of Ref.where θ(x, ε) and χ(x, ε) are the variables parameterizing the zero angular momentum component of the Green's functions, g = cos θ and f = sin θ exp(iχ); here, χ is the phase of the superconducting correlations, and the local density of states ρ(x, ε) (in units of the normal electron density in the bulk) is given byNote that we measure lengths in units of ...

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Phase Coherence Phenomena in Disordered Superconductors

Lamacraft

Simons

2002

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Field theory of mesoscopic fluctuations in superconductor/normal-metal systems

Cited by 31 publications

References 66 publications

Keldysh action for disordered superconductors

Keldysh action for disordered superconductors

Minigap in a long disordered SNS junction: Analytical results

Phase Coherence Phenomena in Disordered Superconductors

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