Noise and Full Counting Statistics of Incoherent Multiple Andreev Reflection

We present a general theory for the full counting statistics of multiple Andreev reflections in incoherent superconducting-normal-superconducting contacts. The theory, based on a stochastic path integral approach, is applied to a superconductor-double barrier system. It is found that all cumulants of the current show a pronounced subharmonic gap structure at voltages $V=2\Delta/en$. For low voltages $V\ll\Delta/e$, the counting statistics results from diffusion of multiple charges in energy space, giving the $p$th cumulant $\propto V^{2-p}$, diverging for $p\geq 3$. We show that this low-voltage result holds for a large class of incoherent superconducting-normal-superconducting contacts.Comment: 4 pages, 4 figure

Proximity Effect in Normal Metal - High Tc Superconductor Contacts

We study the proximity effect in good contacts between normal metals and high Tc (d-wave) superconductors. We present theoretical results for the spatially dependent order parameter and local density of states, including effects of impurity scattering in the two sides, s-wave pairing interaction in the normal metal side (attractive or repulsive), as well as subdominant s-wave paring in the superconductor side. For the [100] orientation, a real combination d+s of the order parameters is always found. The spectral signatures of the proximity effect in the normal metal includes a suppression of the low-energy density of states and a finite energy peak structure. These features are mainly due to the impurity self-energies, which dominate over the effects of induced pair potentials. For the [110] orientation, for moderate transparencies, induction of a d+is order parameter on the superconductor side, leads to a proximity induced is order parameter also in the normal metal. The spectral signatures of this type of proximity effect are potentially useful for probing time-reversal symmetry breaking at a [110] interface.Comment: 10 pages, 10 figure

ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs

We introduce a model for charge and heat transport based on the Landauer-Buttiker scattering approach. The system consists of a chain of $N$ quantum dots, each of them being coupled to a particle reservoir. Additionally, the left and right ends of the chain are coupled to two particle reservoirs. All these reservoirs are independent and can be described by any of the standard physical distributions: Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein. In the linear response regime, and under some assumptions, we first describe the general transport properties of the system. Then we impose the self-consistency condition, i.e. we fix the boundary values (T_L,\mu_L) and (T_R,mu_R), and adjust the parameters (T_i,mu_i), for i = 1,...,N, so that the net average electric and heat currents into all the intermediate reservoirs vanish. This condition leads to expressions for the temperature and chemical potential profiles along the system, which turn out to be independent of the distribution describing the reservoirs. We also determine the average electric and heat currents flowing through the system and present some numerical results, using random matrix theory, showing that these currents are typically governed by Ohm and Fourier laws.Comment: Minor changes (45 pages

Full Counting Statistics of Multiple Andreev Reflections in incoherent diffusive superconducting junctions

We present a theory for the full distribution of current fluctuations in incoherent diffusive superconducting junctions, subjected to a voltage bias. This theory of full counting statistics of incoherent multiple Andreev reflections is valid for arbitrary applied voltage. We present a detailed discussion of the properties of the first four cumulants as well as the low and high voltage regimes of the full counting statistics. The work is an extension of the results of Pilgram and the author, Phys. Rev. Lett. 94, 086806 (2005).Comment: Included in special issue Spin Physics of Superconducting heterostructures of Applied Physics A: Materials Science & Processin

Dephasing and Measurement Efficiency via a Quantum Dot Detector

We study charge detection and controlled dephasing of a mesoscopic system via a quantum dot detector (QDD), where the mesoscopic system and the QDD are capacitively coupled. The QDD is considered to have coherent resonant tunnelling via a single level. It is found that the dephasing rate is proportional to the square of the conductance of the QDD for the Breit-Wigner model, showing that the dephasing is completely different from the shot noise of the detector. The measurement rate, on the other hand, shows a dip near the resonance. Our findings are peculiar especially for a symmetric detector in the following aspect: The dephasing rate is maximum at resonance of the QDD where the detector conductance is insensitive to the charge state of the mesoscopic system. As a result, the efficiency of the detector shows a dip and vanishes at resonance, in contrast to the single-channel symmetric non-resonant detector that has always a maximum efficiency. We find that this difference originates from a very general property of the scattering matrix: The abrupt phase change exists in the scattering amplitudes in the presence of the symmetry, which is insensitive to the detector current but {\em stores} the information of the quantum state of the mesoscopic system.Comment: 7 pages, 3 figure

Quantum-Limited Measurement and Information in Mesoscopic Detectors

We formulate general conditions necessary for a linear-response detector to reach the quantum limit of measurement efficiency, where the measurement-induced dephasing rate takes on its minimum possible value. These conditions are applicable to both non-interacting and interacting systems. We assess the status of these requirements in an arbitrary non-interacting scattering based detector, identifying the symmetries of the scattering matrix needed to reach the quantum limit. We show that these conditions are necessary to prevent the existence of information in the detector which is not extracted in the measurement process.Comment: 13 pages, 1 figur

Non equilibrium current fluctuations in stochastic lattice gases

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation principle for a space-time fluctuation $j$ of the empirical current with a rate functional \mc I (j). We then estimate the probability of a fluctuation of the average current over a large time interval; this probability can be obtained by solving a variational problem for the functional \mc I . We discuss several possible scenarios, interpreted as dynamical phase transitions, for this variational problem. They actually occur in specific models. We finally discuss the time reversal properties of \mc I and derive a fluctuation relationship akin to the Gallavotti-Cohen theorem for the entropy production.Comment: 36 Pages, No figur

Proximity effects and characteristic lengths in ferromagnet-superconductor structures

We present an extensive theoretical investigation of the proximity effects that occur in Ferromagnet/Superconductor ($F/S$) systems. We use a numerical method to solve self consistently the Bogoliubov-de Gennes equations in the continuum. We obtain the pair amplitude and the local density of states (DOS), and use these results to extract the relevant lengths characterizing the leakage of superconductivity into the magnet and to study spin splitting into the superconductor. These phenomena are investigated as a function of parameters such as temperature, magnet polarization, interfacial scattering, sample size and Fermi wavevector mismatch, all of which turn out to have important influence on the results. These comprehensive results should help characterize and analyze future data and are shown to be in agreement with existing experiments.Comment: 24 pages, including 26 figure

Measurement of finite-frequency current statistics in a single-electron transistor

Electron transport in nano-scale structures is strongly influenced by the Coulomb interaction which gives rise to correlations in the stream of charges and leaves clear fingerprints in the fluctuations of the electrical current. A complete understanding of the underlying physical processes requires measurements of the electrical fluctuations on all time and frequency scales, but experiments have so far been restricted to fixed frequency ranges as broadband detection of current fluctuations is an inherently difficult experimental procedure. Here we demonstrate that the electrical fluctuations in a single electron transistor (SET) can be accurately measured on all relevant frequencies using a nearby quantum point contact for on-chip real-time detection of the current pulses in the SET. We have directly measured the frequency-dependent current statistics and hereby fully characterized the fundamental tunneling processes in the SET. Our experiment paves the way for future investigations of interaction and coherence induced correlation effects in quantum transport.Comment: 7 pages, 3 figures, published in Nature Communications (open access

Superconducting proximity effect in clean ferromagnetic layers

We investigate superconducting proximity effect in clean ferromagnetic layers with rough boundaries. The subgap density of states is formed by Andreev bound states at energies which depend on trajectory length and the ferromagnetic exchange field. At energies above the gap, the spectrum is governed by resonant scattering states. The resulting density of states, measurable by tunneling spectroscopy, exhibits a rich structure, which allows to connect the theoretical parameters from experiments.Comment: 11 pages, 5 figures (included