Spectral Features of the Proximity Effect

We calculate the local density of states (LDOS) of a superconductor-normal metal sandwich at arbitrary impurity concentration. The presence of the superconductor induces a gap in the normal metal spectrum that is proportional to the inverse of the elastic mean free path $l$ for rather clean systems. For a mean free path much shorter than the thickness of the normal metal, we find a gap size proportional to $l$ that approaches the behavior predicted by the Usadel equation (diffusive limit).Comment: LT22 proceeding

Statistics of Heat Transfer in Mesoscopic Circuits

A method to calculate the statistics of energy exchange between quantum systems is presented. The generating function of this statistics is expressed through a Keldysh path integral. The method is first applied to the problem of heat dissipation from a biased mesoscopic conductor into the adjacent reservoirs. We then consider energy dissipation in an electrical circuit around a mesoscopic conductor. We derive the conditions under which measurements of the fluctuations of heat dissipation can be used to investigate higher order cumulants of the charge counting statistics of a mesoscopic conductor.Comment: 9 pages, 6 figure

The excitation spectrum of mesoscopic proximity structures

We investigate one aspect of the proximity effect, viz., the local density of states of a superconductor-normal metal sandwich. In contrast to earlier work, we allow for the presence of an arbitrary concentration of impurities in the structure. The superconductor induces a gap in the normal metal spectrum that is proportional to the inverse of the elastic mean free path l_N for rather clean systems. For a mean free path much shorter than the thickness of the normal metal, we find a gap size proportional to l_N that approaches the behavior predicted by the Usadel equation (diffusive limit). We also discuss the influence of interface and surface roughness, the consequences of a non-ideal transmittivity of the interface, and the dependence of our results on the choice of the model of impurity scattering.Comment: 7 pages, 8 figures (included), submitted to PR

Stub model for dephasing in a quantum dot

As an alternative to Buttiker's dephasing lead model, we examine a dephasing stub. Both models are phenomenological ways to introduce decoherence in chaotic scattering by a quantum dot. The difference is that the dephasing lead opens up the quantum dot by connecting it to an electron reservoir, while the dephasing stub is closed at one end. Voltage fluctuations in the stub take over the dephasing role from the reservoir. Because the quantum dot with dephasing lead is an open system, only expectation values of the current can be forced to vanish at low frequencies, while the outcome of an individual measurement is not so constrained. The quantum dot with dephasing stub, in contrast, remains a closed system with a vanishing low-frequency current at each and every measurement. This difference is a crucial one in the context of quantum algorithms, which are based on the outcome of individual measurements rather than on expectation values. We demonstrate that the dephasing stub model has a parameter range in which the voltage fluctuations are sufficiently strong to suppress quantum interference effects, while still being sufficiently weak that classical current fluctuations can be neglected relative to the nonequilibrium shot noise.Comment: 8 pages with 1 figure; contribution for the special issue of J.Phys.A on "Trends in Quantum Chaotic Scattering

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

Full counting statistics of a chaotic cavity with asymmetric leads

We study the statistics of charge transport in a chaotic cavity attached to external reservoirs by two openings of different size which transmit non-equal number of quantum channels. An exact formula for the cumulant generating function has been derived by means of the Keldysh-Green function technique within the circuit theory of mesoscopic transport. The derived formula determines the full counting statistics of charge transport, i.e., the probability distribution and all-order cumulants of current noise. It is found that, for asymmetric cavities, in contrast to other mesoscopic systems, the third-order cumulant changes the sign at high biases. This effect is attributed to the skewness of the distribution of transmission eigenvalues with respect to forward/backward scattering. For a symmetric cavity we find that the third cumulant approaches a voltage-independent constant proportional to the temperature and the number of quantum channels in the leads.Comment: new section on probability distribution and new references adde

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

Anomalous density of states in a metallic film in proximity with a superconductor

We investigated the local electronic density of states in superconductor-normal metal (Nb-Au) bilayers using a very low temperature (60 mK) STM. High resolution tunneling spectra measured on the normal metal (Au) surface show a clear proximity effect with an energy gap of reduced amplitude compared to the bulk superconductor (Nb) gap. Within this mini-gap, the density of states does not reach zero and shows clear sub-gap features. We show that the experimental spectra cannot be described with the well-established Usadel equations from the quasi-classical theory.Comment: 4 pages, 5 figure

Aspects of metallic low-temperature transport in Mott-insulator/ band-insulator superlattices: optical conductivity and thermoelectricity

We investigate the low-temperature electrical and thermal transport properties in atomically precise metallic heterostructures involving strongly-correlated electron systems. The model of the Mott-insulator/ band-insulator superlattice was discussed in the framework of the slave-boson mean-field approximation and transport quantities were derived by use of the Boltzmann transport equation in the relaxation-time approximation. The results for the optical conductivity are in good agreement with recently published experimental data on (LaTiO$_3)_N$/(SrTiO$_3)_M$ superlattices and allow us to estimate the values of key parameters of the model. Furthermore, predictions for the thermoelectric response were made and the dependence of the Seebeck coefficient on model parameters was studied in detail. The width of the Mott-insulating material was identified as the most relevant parameter, in particular, this parameter provides a way to optimize the thermoelectric power factor at low temperatures

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