No Arabic abstract
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.
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.
We study low temperature electron transport in p-wave superconductor-insulator-normal metal junctions. In diffusive metals the p-wave component of the order parameter decays exponentially at distances larger than the mean free path $l$. At the superconductor-normal metal boundary, due to spin-orbit interaction, there is a triplet to singlet conversion of the superconducting order parameter. The singlet component survives at distances much larger than $l$ from the boundary. It is this component that controls the low temperature resistance of the junctions. As a result, the resistance of the system strongly depends on the angle between the insulating boundary and the ${bf d}$-vector characterizing the spin structure of the triplet superconducting order parameter. We also analyze the spatial dependence of the electric potential in the presence of the current, and show that the electric field is suppressed in the insulating boundary as well as in the normal metal at distances of order of the coherence length away from the boundary. This is very different from the case of the normal metal-insulator-normal metal junctions, where the voltage drop takes place predominantly at the insulator.
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.
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.
A topological superconductor nanowire bears a Majorana bound state at each of its ends, leading to unique transport properties. As a way to probe these, we study the finite frequency noise of a biased junction between a normal metal and a topological superconductor nanowire. We use the non-equilibrium Keldysh formalism to compute the finite frequency emission and absorption noise to all order in the tunneling amplitude, for bias voltages below and above the superconducting gap. We observe noticeable structures in the absorption and emission noise, which we can relate to simple transport processes. The presence of the Majorana bound state is directly related to a characteristic behavior of the noise spectrum at low frequency. We further compute the noise measurable with a realistic setup, based on the inductive coupling to a resonant LC circuit, and discuss the impact of the detector temperature. We have also computed the emission noise for a non-topological system with a resonant level, exhibiting a zero-energy Andreev bound state, in order to show the specificities of the topological case. Our results offer an original tool for the further characterization of the presence of Majorana bound states in condensed matter systems.