Inelastic relaxation and noise temperature in S/N/S junctions

We studied electronic relaxation in long diffusive superconductor / normal metal / superconductor (S/N/S) junctions by means of current noise and transport measurements down to very low temperature (100mK). Samples with normal metal lengths of 4, 10 and 60 micrometer have been investigated. In all samples the shot noise increases very rapidly with the voltage. This is interpreted in terms of enhanced heating of the electron gas confined between the two S/N interfaces. Experimental results are analyzed quantitatively taking into account electron-phonon interaction and heat transfer through the S/N interfaces. Transport measurements reveal that in all samples the two S/N interfaces are connected incoherently, as shown by the reentrance of the resistance at low temperature. The complementarity of noise and transport measurements allows us to show that the energy dependence of the reentrance at low voltage is essentially due to the increasing effective temperature of the quasiparticles in the normal metal.Comment: 5 pages, 4 figures, to be published in EPJ

Proximity effect in planar TiN-Silicon junctions

We measured the low temperature subgap resistance of titanium nitride (superconductor, Tc=4.6K)/highly doped silicon (degenerated semiconductor) SIN junctions, where I stands for the Schottky barrier. At low energies, the subgap conductance is enhanced due to coherent backscattering of the electrons towards the interface by disorder in the silicon (''reflectionless tunneling''). This Zero Bias Anomaly (ZBA) is destroyed by the temperature or the magnetic field above 250mK or 0.04T respectively. The overall differential resistance behavior (vs temperature and voltage) is compared to existing theories and values for the depairing rate and the barrier transmittance are extracted. Such an analysis leads us to introduce an effective temperature for the electrons and to discuss heat dissipation through the SIN interface.Comment: 23 pages, 6 figures, added references and minor corrections. Accepted to Journal of Low Temperature Physic

Noise Correlations in Three-Terminal Diffusive Superconductor-Normal Metal-Superconductor Nanostructures

We present measurements of current noise and cross-correlations in three-terminal Superconductor-Normal metal-Superconductor (S-N-S) nanostructures that are potential solid-state entanglers thanks to Andreev reflections at the N-S interfaces. The noise correlation measurements spanned from the regime where electron-electron interactions are relevant to the regime of Incoherent Multiple Andreev Reflection (IMAR). In the latter regime, negative cross-correlations are observed in samples with closely-spaced junctions.Comment: Include Supplemental Materia

Mesoscopic transition in the shot noise of diffusive S/N/S junctions

We experimentally investigated the current noise in diffusive Superconductor/Normal metal/Superconductor junctions with lengths between the superconducting coherence length xi_Delta and the phase coherence length L_Phi of the normal metal (xi_Delta < L < L_Phi). We measured the shot noise over a large range of energy covering both the regimes of coherent and incoherent multiple Andreev reflections. The transition between these two regimes occurs at the Thouless energy where a pronounced minimum in the current noise density is observed. Above the Thouless energy, in the regime of incoherent multiple Andreev reflections, the noise is strongly enhanced compared to a normal junction and grows linearly with the bias voltage. Semi-classical theory describes the experimental results accurately, when taking into account the voltage dependence of the resistance which reflects the proximity effect. Below the Thouless energy, the shot noise diverges with decreasing voltage which may indicate the coherent transfer of multiple charges.Comment: 5 pages, 5 figures, accepted for publication in Phys. Rev. B, Rapid Communicatio

A level-set method for the evolution of cells and tissue during curvature-controlled growth

Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic, or cell behavioural in nature. The control of geometry on tissue growth has been evidenced in many in-vivo and in-vitro experiments, including bone remodelling, wound healing, and tissue engineering scaffolds. In this paper, we propose a generalisation of a mathematical model that captures the mechanistic influence of curvature on the joint evolution of cell density and tissue shape during tissue growth. This generalisation allows us to simulate abrupt topological changes such as tissue fragmentation and tissue fusion, as well as three dimensional cases, through a level-set-based method. The level-set method developed introduces another Eulerian field than the level-set function. This additional field represents the surface density of tissue synthesising cells, anticipated at future locations of the interface. Numerical tests performed with this level-set-based method show that numerical conservation of cells is a good indicator of simulation accuracy, particularly when cusps develop in the tissue's interface. We apply this new model to several situations of curvature-controlled tissue evolutions that include fragmentation and fusion.Comment: 15 pages, 10 figures, 3 supplementary figure

Doubled Full Shot Noise in Quantum Coherent Superconductor - Semiconductor Junctions

We performed low temperature shot noise measurements in Superconductor (TiN) - strongly disordered normal metal (heavily doped Si) weakly transparent junctions. We show that the conductance has a maximum due to coherent multiple reflections at low energy and that shot noise is then twice the Poisson noise (S=4eI). The shot noise changes to the normal value (S=2eI) due to a large quasiparticle contribution.Comment: published in Physical Review Letter

Ballistic effects in a proximity induced superconducting diffusive metal

Using a Scanning Tunneling Microscope (STM), we investigate the Local Density of States (LDOS) of artificially fabricated normal metal nano-structures in contact with a superconductor. Very low temperature local spectroscopic measurements (100 mK) reveal the presence of well defined subgap peaks at energy |E|<Delta in the LDOS at various positions of the STM tip. Although no clear correlations between the LDOS and the shape of the samples have emerged, some of the peak features suggest they originate from quasi-particle bound states within the normal metal structures (De Gennes St James states). Refocusing of electronic trajectories induced by the granular srtucture of the samples can explain the observation of spatially uncorrelated interference effects in a non-ballistic medium.Comment: 4 pages, 4 figure

Nonlinear hyperbolic systems: Non-degenerate flux, inner speed variation, and graph solutions

We study the Cauchy problem for general, nonlinear, strictly hyperbolic systems of partial differential equations in one space variable. First, we re-visit the construction of the solution to the Riemann problem and introduce the notion of a nondegenerate (ND) system. This is the optimal condition guaranteeing, as we show it, that the Riemann problem can be solved with finitely many waves, only; we establish that the ND condition is generic in the sense of Baire (for the Whitney topology), so that any system can be approached by a ND system. Second, we introduce the concept of inner speed variation and we derive new interaction estimates on wave speeds. Third, we design a wave front tracking scheme and establish its strong convergence to the entropy solution of the Cauchy problem; this provides a new existence proof as well as an approximation algorithm. As an application, we investigate the time-regularity of the graph solutions $(X,U)$ introduced by the second author, and propose a geometric version of our scheme; in turn, the spatial component $X$ of a graph solution can be chosen to be continuous in both time and space, while its component $U$ is continuous in space and has bounded variation in time.Comment: 74 page