Size effects in the density of states in normal-metal–superconductor and superconductor–normal-metal–superconductor junctions

Blaauboer, M.; Koperdraad, R. T. W.; Lodder, A.; Lenstra, D.

doi:10.1103/physrevb.54.4283

Cited by 10 publications

(8 citation statements)

References 24 publications

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“…Different behaviors of the LDOS are expected in cases of junction systems with non-superconducting samples and other shapes such as a triangle, a circle, and so on. In particular, in junction systems such as superconductor-normal metal-superconductor (SNS) junction systems [33][34][35] and superconductor-ferromagnet-superconductor (SFS) junction systems [36][37][38], the LDOS is more complicated because of the Andreev reflection and the proximity effect. The nano-structured Josephson junction system is expected as applications such as the nano-SQUID, the quantum computer, and the single flux quantum (SFQ) logic.…”

Section: Discussionmentioning

confidence: 99%

Dependences of local density of state on temperature, size, and shape in two-dimensional nano-structured superconductors

Fukui

Wang

Kato

2019

Preprint

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In this paper, we investigate a local density of state (LDOS) in two-dimensional nano-structured superconductors. We solve the Bogoliubov-de Gennes equations self-consistently with the twodimensional finite element method. In nano-structured superconductors, the LDOS as a function of the energy has many discrete peaks. A discretization of the LDOS comes from a discretization of energy levels due to the quantum confinement effect in nano-structured systems. When the temperature increases, a width of a peak in the LDOS is spread to a large energy range and neighbor peaks are superposed due to the thermal effect. On the other hand, for the fixed temperature, the behavior of the LDOS is different between nano-scaled rectangular and square systems. In the nano-scaled rectangular system, when only a lateral length increases, a contribution of the quantum confinement effect from the lateral side is suppressed, while the contribution from a longitudinal side remains large. Then, some peaks are left in the LDOS even when the lateral length is very large. These peaks form a periodic structure and can be regarded as gaps in a multi gap structure due to the quantum confinement effect. On the other hand, energy levels in the square system tend to arrange equally. Then, in the square system, peaks in the LDOS which exist in the rectangular system are small. Also, the period between peaks in the LDOS in the square system is smaller than the period in the rectangular system. I.

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Section: Discussionmentioning

confidence: 99%

Dependences of local density of state on temperature, size, and shape in two-dimensional nano-structured superconductors

Fukui

Wang

Kato

2019

Preprint

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“…Finally, in addition to an SNS junction, a system with four instead of two interfaces will be treated; it is shown schematically in figure 1. Some preliminary results for an NS junction, not containing a self-consistent gap function yet, have been published by Blaauboer et al [10].…”

Section: Introductionmentioning

confidence: 99%

Multiple-scattering theory for clean superconducting layered structures

Koperdraad¹,

Otadoy²,

Blaauboer³

et al. 2001

J. Phys.: Condens. Matter

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An exact expression is derived for the matrix Green's function of a clean superconducting layered structure with an arbitrary number of interfaces. A multiple-scattering approach is employed, in which the interfaces act as the scattering centres. Some initial applications of the theory to systems with transverse dimensions which vary from narrow to wide are given. The local density of states is calculated for an SNS and for an SNSNS junction (‘S’ standing for a superconducting layer and ‘N’ for a normal layer). For certain critical transverse widths the exact theory shows remarkable features not seen in the Andreev approximation. If the gap function for the systems is calculated self-consistently it turns out that for transverse dimensions smaller than twenty per cent of the superconducting coherence length, superconductivity is suppressed.

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“…The peaks represent discrete energy states. 12 We make the width of the curves, determined by the parameter ␦ in Eϩi␦, wide enough so that the fundamental features can be seen. The numbers in parentheses denote the mode to which the energy belongs.…”

Section: ͑25͒mentioning

confidence: 99%

“…In an initial application of the theory the local density of states of normal metal-superconductor ͑NS͒ and SNS junctions were calculated, but the breakdown of the Andreev approximation was not noticed. 12 The paper is organized as follows. First we give a concise account of the main features of the theory.…”

Section: Introductionmentioning

confidence: 99%

“…Interestingly, in many cases the AA works remarkably well, implying negligible effects of less than 0.1%. 12 In the present paper we address transverse size effects in a situation where neither the quasiclassical approach nor the Andreev approximation can help, and we have to proceed with an exact calculation. In many studies the systems are treated as being infinite in the transverse directions, by which breakdown of the AA hardly can show up.…”

Section: Introductionmentioning

confidence: 99%

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Andreev bound states and self-consistent gap functions in clean layered superconductor/normal metal systems with finite transverse width

Otadoy

Lodder

2001

Phys. Rev. B

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Andreev bound states in clean, ballistic SNS and SNSNS junctions are calculated exactly and by using the Andreev approximation ͑AA͒. The AA appears to break down for junctions with transverse dimensions chosen such that the motion in the longitudinal direction is very slow. The doubly degenerate states typical for the traveling waves found in the AA are replaced by two standing waves in the exact treatment and the degeneracy is lifted. A multiple-scattering Green's function formalism is used, from which the states are found through the local density of states. The scattering by the interfaces in any layered system of ballistic normal metals and clean superconducting materials is taken into account exactly. The formalism allows, in addition, for a selfconsistent determination of the gap function. In the numerical calculations the pairing coupling constant for aluminum is used. Various features of the proximity effect are shown.

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Size effects in the density of states in normal-metal–superconductor and superconductor–normal-metal–superconductor junctions

Cited by 10 publications

References 24 publications

Dependences of local density of state on temperature, size, and shape in two-dimensional nano-structured superconductors

Dependences of local density of state on temperature, size, and shape in two-dimensional nano-structured superconductors

Multiple-scattering theory for clean superconducting layered structures

Andreev bound states and self-consistent gap functions in clean layered superconductor/normal metal systems with finite transverse width

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