The theory of the reentrant effect in susceptibility of cylindrical mesoscopic samples

A theory has been developed to explain the anomalous behavior of the magnetic susceptibility of a normal metal-superconductor (NS) structure in weak magnetic fields at millikelvin temperatures. The effect was discovered experimentally (A.C. Mota et al., Phys. Rev. Lett. 65, 1514 (1990)). In cylindrical superconducting samples covered with a thin normal pure metal layer, the susceptibility exhibited a reentrant effect: it started to increase unexpectedly when the temperature lowered below 100 mK. The effect was observed in mesoscopic NS structures when the N and S metals were in good electric contact. The theory proposed is essentially based on the properties of the Andreev levels in the normal metal. When the magnetic field (or temperature) changes, each of the Andreev levels coincides from time to time with the chemical potential of the metal. As a result, the state of the NS structure experiences strong degeneracy, and the quasiparticle density of states exhibits resonance spikes. This generates a large paramagnetic contribution to the susceptibility, which adds up to the diamagnetic contribution thus leading to the reentrant effect. The explanation proposed was obtained within the model of free electrons. The theory provides a good description for experimental results

On the nature of the reentrant effect in susceptibility of mesoscopic cylindrical samples

Theory of the reentrant effect in susceptibility of mesoscopic cylindrical NS samples is proposed, which is essentially based on the properties of the Andreev levels. The specific feature of the quantum levels of the structure is that in a varying magnetic field (or temperature) each level periodically comes into coincidence with the chemical potential of the metal. As a result, the state of the system becomes strongly degenerate and the amplitude of the paramagnetic contribution to the susceptibility increases sharply

Coherent quantum phenomena in mesoscopicmetallic conductors (Review Article)

The quantum coherent phenomena in mesoscopic cylindrical metallic conductors have been considered. Pure double-and single-connected normal samples were placed in a longitudinal magnetic field, which generated interference phenomena depending on the magnetic flux through the cross-section of the conductor. The period of the induced oscillations is equal to the flux quantum hc/e of the normal metal. The quantum states are formed in the structures by collisions of the electrons with the dielectric boundary of the sample. The magnetic flux is included in the expression for the spectrum of quasiparticles. The proximity effect and its influence on the modification of the spectrum of quantum coherent phenomena have been investigated. The behavior of cylindrical samples consisting of a superconducting (S) metal with a deposited thin pure normal (N) metal layer has been analyzed. In this structure the electrons are localized in a well bounded by a dielectric on one side and by a superconductor on the other. The specific feature of the generated quantized Andreev levels is that in the varying field H (or temperature T) each of the levels in the well can coincide periodically with the chemical potential of the metal. As a result, the state of the system experiences strong degeneracy and the density of states exhibits resonance spikes of the energy of the NS sample. This makes a significant contribution to the magnetic moment. A theory of the reentrant effect for NS structures has been developed, which interprets the anomalous behavior of the magnetic susceptibility of such structures as a function of the magnetic field and temperatures

The role of the self-consistent equation in identifying the Andreev spectrum in a mesoscopic NS structure

Adifferential self-consistent equation has been obtained for a dimensionless magnetic flux in a NS structure, which is responsible for the magnetic moment jumps in the system.A differential self-consistent equation has been obtained for a dimensionless magnetic flux in a NS structure, which is responsible for the magnetic moment jumps in the system

Coherent quantum phenomena in a normal cylindrical conductor with a superconducting coating

The thermodynamic properties of a mesoscopic-size, simply connected cylindrical normal metal in good metallic contact with superconducting banks are studied theoretically. It is commonly accepted that if the superconductor thickness is quite small (of the order of the coherence length), as is assumed to be the case here, a vector potential field, whose value can be varied, exists inside the normal layer. It is further assumed that the quasiparticles with energy E<Δ (2Δ is the superconducting gap) move ballistically through the normal metal and undergo Andreev scattering caused by the off-diagonal potential of the superconductor. An equation is obtained within the multidimensional quasiclassical method which permits us to determine the spectrum of the Andreev levels and to calculate the density of states of the system in question. It is shown that the Andreev levels shift as the trapped flux Φ changes inside the normal conductor. At a certain flux value they coincide with the Fermi level. A resonance spike in the density of states ν(E) appears in this case, since near E=0 there is strong degeneracy of the quasiparticle states in respect to the quantum number q characterizing their motion along the cylinder axis. As a result, a macroscopic number of q states contribute to the amplitude of the effect. As the flux is increased, the density of states v(E) behaves as a stepwise function of Φ. The distance between the steps is equal to the superconducting flux quantum hc/2e

Supercurrents through gated superconductor-normal-metal-superconductor contacts: the Josephson-transistor

We analyze the transport through a narrow ballistic superconductor-normal- metal-superconductor Josephson contact with non-ideal transmission at the superconductor-normal-metal interfaces, e.g., due to insulating layers, effective mass steps, or band misfits (SIN interfaces). The electronic spectrum in the normal wire is determined through the combination of Andreev- and normal reflection at the SIN interfaces. Strong normal scattering at the SIN interfaces introduces electron- and hole-like resonances in the normal region which show up in the quasi-particle spectrum. These resonances have strong implications for the critical supercurrent $I_c$ which we find to be determined by the lowest quasi-particle level: tuning the potential $\mu_{x0}$ to the points where electron- and hole-like resonances cross, we find sharp peaks in $I_{\rm c}$, resulting in a transitor effect. We compare the performance of this Resonant Josephson-Transistor (RJT) with that of a Superconducting Single Electron Transistor (SSET).Comment: to appear in PRB, 11 pages, 9 figure