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Register a new userLocal density of states in clean two-dimensional superconductor--normal metal--superconductor heterostructures
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Motivated by recent advances in the fabrication of Josephson junctions in which the weak link is made of a low-dimensional non-superconducting material, we present here a systematic theoretical study of the local density of states (LDOS) in a clean 2D normal metal (N) coupled to two s-wave superconductors (S). To be precise, we employ the quasiclassical theory of superconductivity in the clean limit, based on Eilenbergers equations, to investigate the phase-dependent LDOS as function of factors such as the length or the width of the junction, a finite reflectivity, and a weak magnetic field. We show how the the spectrum of Andeeev bound states that appear inside the gap shape the phase-dependent LDOS in short and long junctions. We discuss the circumstances when a gap appears in the LDOS and when the continuum displays a significant phase-dependence. The presence of a magnetic flux leads to a complex interference behavior, which is also reflected in the supercurrent-phase relation. Our results agree qualitatively with recent experiments on graphene SNS junctions. Finally, we show how the LDOS is connected to the supercurrent that can flow in these superconducting heterostructures and present an analytical relation between these two basic quantities.
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We analyse the possibility of the appearance of spontaneous currents in proximated superconducting/normal metal (S/N) heterostructure when Cooper pairs penetrate into the normal metal from the superconductor. In particular, we calculate the free energy of the S/N structure. We show that whereas the free energy of the N film $F_{N}$ in the presence of the proximity effect increases compared to the normal state, the total free energy, which includes the boundary term $F_{B}$, decreases. The condensate current decreases $F_{N}$, but increases the total free energy making the current-carrying state of the S/N system energetically unfavorable.
Hybrid normal metal - insulator - superconductor microstructures suitable for studying an interference of electrons were fabricated. The structures consist of a superconducting loop connected to a normal metal electrode through a tunnel barrier . An optical interferometer with a beam splitter can be considered as a classical analogue for this system. All measurements were performed at temperatures well below 1 K. The interference can be observed as periodic oscillations of the tunnel current (voltage) through the junction at fixed bias voltage (current) as a function of a perpendicular magnetic field. The magnitude of the oscillations depends on the bias point. It reaches a maximum at energy $eV$ which is close to the superconducting gap and decreases with an increase of temperature. Surprisingly, the period of the oscillations in units of magnetic flux $Delta Phi$ is equal neither to $h/e$ nor to $h/2e$, but significantly exceeds these values for larger loop circumferences. The origin of the phenomena is not clear.
We study the linear diamagnetic response of a superconducting cylinder coated by a normal-metal layer due to the proximity effect using the clean limit quasiclassical Eilenberger equations. We compare the results for the susceptibility with those for a planar geometry. Interestingly, for $Rsim d$ the cylinder exhibits a stronger overscreening of the magnetic field, i.e., at the interface to the superconductor it can be less than (-1/2) of the applied field. Even for $Rgg d$, the diamagnetism can be increased as compared to the planar case, viz. the magnetic susceptibility $4pichi$ becomes smaller than -3/4. This behaviour can be explained by an intriguing spatial oscillation of the magnetic field in the normal layer.
We discuss the quasiparticle entropy and heat capacity of a dirty superconductor-normal metal-superconductor junction. In the case of short junctions, the inverse proximity effect extending in the superconducting banks plays a crucial role in determining the thermodynamic quantities. In this case, commonly used approximations can violate thermodynamic relations between supercurrent and quasiparticle entropy. We provide analytical and numerical results as a function of different geometrical parameters. Quantitative estimates for the heat capacity can be relevant for the design of caloritronic devices or radiation sensor applications.
In s-wave superconductors the Cooper pair wave function is isotropic in momentum space. This property may also be expected for Cooper pairs entering a normal metal from a superconductor due to the proximity effect. We show, however, that such a deduction is incorrect and the pairing function in a normal metal is surprisingly anisotropic because of quasiparticle interference. We calculate angle resolved quasiparticle density of states in NS bilayers which reflects such anisotropic shape of the pairing function. We also propose a magneto-tunneling spectroscopy experiment which could confirm our predictions.
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