Proximity effect in planar Superconductor/Semiconductor junction

We have measured the very low temperature (down to 30 mK) subgap resistance of Titanium Nitride (Superconductor, Tc = 4.6 K)/highly doped Silicon (Semiconductor) SIN junction (the insulating layer stands for the Schottky barrier). As the temperature is lowered, the resistance increases as expected in SIN junction. Around 300 mK, the resistance shows a maximum and decreases at lower temperature. This observed behavior is due to coherent backscattering towards the interface by disorder in Silicon ("Reflectionless tunneling"). This effect is also observed in the voltage dependence of the resistance (Zero Bias Anomaly) at low temperature (T<300 mK). The overall resistance behavior (in both its temperature and voltage dependence) is compared to existing theories and values for the depairing rate, the barrier resistance and the effective carrier temperature are extracted.Comment: Submitted to LT22, Helsinki - August 1999, phbauth.cls include

Definition and stability of Lorentzian manifolds with distributional curvature

Following Geroch, Traschen, Mars and Senovilla, we consider Lorentzian manifolds with distributional curvature tensor. Such manifolds represent spacetimes of general relativity that possibly contain gravitational waves, shock waves, and other singular patterns. We aim here at providing a comprehensive and geometric (i.e., coordinate-free) framework. First, we determine the minimal assumptions required on the metric tensor in order to give a rigorous meaning to the spacetime curvature within the framework of distribution theory. This leads us to a direct derivation of the jump relations associated with singular parts of connection and curvature operators. Second, we investigate the induced geometry on a hypersurface with general signature, and we determine the minimal assumptions required to define, in the sense of distributions, the curvature tensors and the second fundamental form of the hypersurface and to establish the Gauss-Codazzi equations.Comment: 28 page