Excess Noise in Biased Superconducting Weak Links

Non-equilibrium excess noise of a short quasi one-dimensional constriction between two superconductors is considered. A general expression for the current-current correlation function valid for arbitrary temperatures and bias voltages is derived. This formalism is applied to a current-carrying quantum channel with perfect transparency. Contrary to a transparent channel separating two normal conductors, a weak link between two superconductors exhibits a finite level of noise. The source of noise is fractional Andreev scattering of quasiparticles with energies $|E|$ greater than the half-width $\Delta$ of the superconducting gap. For high bias voltages, $V \gg \Delta /e$, the relation between the zero-frequency limit of the noise spectrum, $S(0)$, and the excess current $I_{\text{exc}}$ reads $S(0)=(1/5)|e|I_{\text{exc}}$. As $\Delta \rightarrow 0$ both the excess noise and the excess current vanish linearly in $\Delta$, %$\propto \Delta$, their ratio being constant.Comment: 8 pages (Latex), 1 figur

Noise in a Quantum Point Contact due to a Fluctuating Impurity Configuration

We propose a theoretical model for the low-frequency noise observed in a quantum point contact (QPC) electrostatically defined in the 2D electron gas at a GaAs-AlGaAs interface. In such contacts electron scattering by soft impurity- or boundary potentials coherently splits an incoming wave function between different transverse modes. Interference between these modes have been suggested to explain observed non-linearities in the QPC-conductance. In this study we invoke the same mechanism and the time-dependent current due to soft dynamical impurity scattering in order to analyze the low-frequency (telegraph-like) noise which has been observed along with a nonlinear conductance. For the simplified case of a channel with two extended (current carrying) modes, a simple analytical formula for the noise intensity is derived. Generally we have found qualitative similarities between the noise and the square of the transconductance. Nevertheless, incidentally there may be situations when noise is suppressed but transconductance enhanced.Comment: 9 revte

Quantum Scalar Field on the Massless (2+1)-Dimensional Black Hole Background

The behavior of a quantum scalar field is studied in the metric ground state of the (2+1)-dimensional black hole of Ba\~nados, Teitelboim and Zanelli which contains a naked singularity. The one-loop BTZ partition function and the associate black hole effective entropy, the expectation value of the quantum fluctuation as well as the renormalized expectation value of the stress tensor are explicitly computed in the framework of the $\zeta$-function procedure. This is done for all values of the coupling with the curvature, the mass of the field and the temperature of the quantum state. In the massless conformally coupled case, the found stress tensor is used for determining the quantum back reaction on the metric due to the scalar field in the quantum vacuum state, by solving the semiclassical Einstein equations. It is finally argued that, within the framework of the 1/N expansion, the Cosmic Censorship Hypothesis is implemented since the naked singularity of the ground state metric is shielded by an event horizon created by the back reaction.Comment: 18 pages, RevTeX, no figures, minor changes, final version accepted for publication in Phys. Rev.

Radiation from the extremal black holes

The radiation from extreme Reissner-Nordstr\"{o}m black holes is computed by explicitly considering the collapse of a spherical charged shell. No neutral scalar radiation is found but there is emission of charged particles, provided the charge to mass ratio be different from one. The absence of thermal effects is in accord with the predictions of the euclidean theory but since the body emits charged particles the entropy issue is not the same as for eternal extreme black holes.Comment: 4 pages, LaTex, no figure

Finite voltage shot noise in normal-metal - superconductor junctions

We express the low-frequency shot noise in a disordered normal-metal - superconductor (NS) junction at finite (subgap) voltage in terms of the normal scattering amplitudes and the Andreev reflection amplitude. In the multichannel limit, the conductance exhibits resonances which are accompanied by an enhancement of the (differential) shot noise. In the study of multichannel single and double barrier junctions we discuss the noise properties of coherent transport at low versus high voltage with respect to the Andreev level spacing.Comment: 6 pages, Latex, 2 eps-figures, to be published in PRB, Appendix on Bogoliubov equation

Flicker Noise Induced by Dynamic Impurities in a Quantum Point Contact

We calculate low-frequency noise (LFN) in a quantum point contact (QPC) which is electrostatically defined in a 2D electron gas of a GaAs-AlGaAs heterostructure. The conventional source of LFN in such systems are scattering potentials fluctuating in time acting upon injected electrons. One can discriminate between potentials of different origin -- noise may be caused by the externally applied gate- and source-drain voltages, the motion of defects with internal degrees of freedom close to the channel, electrons hopping between localized states in the doped region, etc. In the present study we propose a model of LFN based upon the assumption that there are many dynamic defects in the surrounding of a QPC. A general expression for the time-dependent current-current correlation function is derived and applied to a QPC with quantized conductance. It is shown that the level of LFN is significantly different at and between the steps in a plot of the conductance vs. gate voltage. On the plateaus, the level of noise is found to be low and strongly model-dependent. At the steps, LFN is much larger and only weakly model-dependent. As long as the system is biased to be at a fixed position relative the conductance step,Comment: 26 revtex APR 94-4

Shot noise in normal metal-d-wave superconducting junctions

We present theoretical calculations and predictions for the shot noise in voltage biased junctions of $d_{x^2-y^2}$ superconductors and normal metal counter-electrodes. In the clean limit for the d-wave superconductor the shot noise vanishes at zero voltage because of resonant Andreev reflection by zero-energy surface bound states. We examine the sensitivity of this resonance to impurity scattering. We report theoretical results for the magnetic field dependence of the shot noise, as well the fingerprints of subdominant $s$- and $d_{xy}$ pairing channels.Comment: 15 pages, 8 figures and 3 tables embedde

Shot noise in mesoscopic systems

This is a review of shot noise, the time-dependent fluctuations in the electrical current due to the discreteness of the electron charge, in small conductors. The shot-noise power can be smaller than that of a Poisson process as a result of correlations in the electron transmission imposed by the Pauli principle. This suppression takes on simple universal values in a symmetric double-barrier junction (suppression factor 1/2), a disordered metal (factor 1/3), and a chaotic cavity (factor 1/4). Loss of phase coherence has no effect on this shot-noise suppression, while thermalization of the electrons due to electron-electron scattering increases the shot noise slightly. Sub-Poissonian shot noise has been observed experimentally. So far unobserved phenomena involve the interplay of shot noise with the Aharonov-Bohm effect, Andreev reflection, and the fractional quantum Hall effect.Comment: 37 pages, Latex, 10 figures (eps). To be published in "Mesoscopic Electron Transport," edited by L. P. Kouwenhoven, G. Schoen, and L. L. Sohn, NATO ASI Series E (Kluwer Academic Publishing, Dordrecht