Probing superconducting phase fluctuations from the current noise spectrum of pseudogaped metal-superconductor tunnel junctions

We study the current noise spectra of a tunnel junction of a metal with strong pairing phase fluctuation and a superconductor. It is shown that there is a characteristic peak in the noise spectrum at the intrinsic Josephson frequency $\omega_J=2eV$ when $\omega_J$ is smaller than the pairing gap but larger than the pairing scattering rate. In the presence of an AC voltage, the tunnelling current noise shows a series of characteristic peaks with increasing DC voltage. Experimental observation of these peaks will give direct evidence of the pair fluctuation in the normal state of high-$T_c$ superconductors and from the half width of the peaks the pair decay rate can be estimated.Comment: 4 pages, 3 figure

Nonequilibrium electron cooling by NIS tunnel junctions

We discuss the theoretical framework to describe quasiparticle electric and heat currents in NIS tunnel junctions in the dirty limit. The approach is based on quasiclassical Keldysh-Usadel equations. We apply this theory to diffusive NIS'S tunnel junctions. Here N and S are respectively normal metal and superconductor reservoirs, I is an insulator layer and S' is a nonequilibrium superconducting lead. We calculate the quasiparticle electric and heat currents in such structures and consider the effect of inelastic relaxation in the S' lead. We find that in the absence of strong relaxation the electric current and the cooling power for voltages $eV < \Delta$ are suppressed. The value of this suppression scales with the diffusive transparency parameter. We ascribe this suppression to the effect of backtunneling of nonequilibrium quasiparticles into the normal metal.Comment: 12 pages, 6 figures, proceedings, to be published in JLT

Circuit theory of multiple Andreev reflections in diffusive SNS junctions: the incoherent case

The incoherent regime of Multiple Andreev Reflections (MAR) is studied in long diffusive SNS junctions at applied voltages larger than the Thouless energy. Incoherent MAR is treated as a transport problem in energy space by means of a circuit theory for an equivalent electrical network. The current through NS interfaces is explained in terms of diffusion flows of electrons and holes through tunnel and Andreev resistors. These resistors in diffusive junctions play roles analogous to the normal and Andreev reflection coefficients in OTBK theory for ballistic junctions. The theory is applied to the subharmonic gap structure (SGS); simple analytical results are obtained for the distribution function and current spectral density for the limiting cases of resistive and transparent NS interfaces. In the general case, the exact solution is found in terms of chain-fractions, and the current is calculated numerically. SGS shows qualitatively different behavior for even and odd subharmonic numbers, and the maximum slopes of the differential resistance correspond to the gap subharmonics. The influence of inelastic scattering on the subgap anomalies of the differential resistance is analyzed.Comment: 14 pages, 9 figures, title and text revised, to appear in PR

Two-dimensional array of diffusive SNS junctions with high-transparent interfaces

We report the first comparative study of the properties of two-dimensional arrays and single superconducting film - normal wire - superconducting film (SNS) junctions. The NS interfaces of our SNS junctions are really high transparent, for superconducting and normal metal parts are made from the same material (superconducting polycrystalline PtSi film). We have found that the two-dimensional arrays reveal some novel features: (i) the significant narrowing of the zero bias anomaly (ZBA) in comparison with single SNS junctions, (ii) the appearance of subharmonic energy gap structure (SGS), with up to n=16 (eV=\pm 2\Delta/n), with some numbers being lost, (iii) the transition from 2D logarithmic weak localization behavior to metallic one. Our experiments show that coherent phenomena governed by the Andreev reflection are not only maintained over the macroscopic scale but manifest novel pronounced effects as well. The behavior of the ZBA and SGS in 2D array of SNS junctions strongly suggests that the development of a novel theoretical approach is needed which would self-consistently take into account the distribution of the currents, the potentials, and the superconducting order parameter.Comment: RevTex, 5 pages, 5 figure

Full Current Statistics in Diffusive Normal-Superconductor Structures

We study the current statistics in normal diffusive conductors in contact with a superconductor. Using an extension of the Keldysh Green's function method we are able to find the full distribution of charge transfers for all temperatures and voltages. For the non-Gaussian regime, we show that the equilibrium current fluctuations are enhanced by the presence of the superconductor. We predict an enhancement of the nonequilibrium current noise for temperatures below and voltages of the order of the Thouless energy E_Th=D/L^2. Our calculation fully accounts for the proximity effect in the normal metal and agrees with experimental data. We demonstrate that the calculation of the full current statistics is in fact simpler than a concrete calculation of the noise.Comment: 4 pages, 2 figures (included

Charge and Spin Effects in Mesoscopic Josephson Junctions

We consider the charge and spin effects in low dimensional superconducting weak links. The first part of the review deals with the effects of electron-electron interaction in Superconductor/Luttinger liquid/Superconductor junctions. The experimental realization of this mesoscopic hybrid system can be the individual single wall carbon nanotube that bridges the gap between two bulk superconductors. The dc Josephson current through a Luttinger liquid in the limits of perfectly and poorly transmitting junctions is evaluated. The relationship between the Josephson effect in a long SNS junction and the Casimir effect is discussed. In the second part of the paper we review the recent results concerning the influence of the Zeeman and Rashba interactions on the thermodynamical properties of ballistic S/QW/S junction fabricated in two dimensional electron gas. It is shown that in magnetically controlled junction there are conditions for resonant Cooper pair transition which results in giant supercurrent through a tunnel junction and a giant magnetic response of a multichannel SNS junction. The supercurrent induced by the joint action of the Zeeman and Rashba interactions in 1D quantum wires connected to bulk superconductors is predicted.Comment: 36 pages, 8 figures; minor changes in reference

Обоснование выбора параметров эллипсоидальных рефлекторов биомедицинских фотометров

Biomedical photometersʼ information-measuring systems with ellipsoidal reflectors have acceptable results in determining of biological tissues optical properties in the visible and near-infrared spectral range. These photometers make it possible to study the optical radiation propagation in turbid media for direct and inverse problems of light-scattering optics. The purpose of this work is to study the influence of the ellipsoidal reflectors design parameters on the results of biomedical photometry when simulating the optical radiation propagation in a system of biological tissue and reflectors in transmitted and reflected light.The paper substantiates the choice of the ellipsoidal reflectors’ focal parameter for efficient registration of forward and backscattered light. The methodology of the process is illustrated by the results of a model experiment using the Monte Carlo simulation for samples of human brain white and gray matter at the visible range of 405 nm, 532 nm, and 650 nm. The total transmittance, diffuse reflectance, and absorption graphs depending on the sample thickness were obtained. Based on the introduced concepts of the ellipsoidal reflector efficiency index and its efficiency factor, the expediency of choosing the ellipsoidal reflectors focal parameter is analyzed to ensure the registration of the maximum amount of scattered light. The graphs of efficiency index in reflected and transmitted light for different thickness samples of white and gray matter and efficiency factors depending on the sample thickness were obtained.The influence of the reflectors ellipticity on the illuminance of various zones of photometric images using the example of an absorbing biological medium – pig liver tissue – at wavelength of 405 nm with a Monte Carlo simulation was analyzed.The optical properties of biological media (scattering and absorption coefficients, scattering anisotropy factor, refractive index) and the samples’ geometric dimensions, particularly the thickness, are predetermined when choosing the ellipsoidal reflectors parameters for registration of the scattered light. Coordinates of the output of photons and their statistical weight obtained in the Monte Carlo simulation of light propagation in biological tissue have a physical effect on a characteristic scattering spot formation in the receiving plane of a biomedical photometer with ellipsoidal reflectors.Информационно-измерительные системы биомедицинских фотометров с эллипсоидальными рефлекторами показали приемлемые результаты при определении оптических свойств биологических тканей в видимом и ближнем инфракрасном спектральном диапазоне. Такие фотометры позволяют исследовать распространение оптического излучения в мутных средах при прямой и инверсной задачах оптики светорассеяния. Целью данной работы являлось исследование влияния конструктивных параметров эллипсоидальных рефлекторов на результаты биомедицинской фотометрии при симуляции распространения оптического излучения в системе биологической ткани и рефлекторов.В работе обоснован выбор фокального параметра эллипсоидальных рефлекторов для эффективной регистрации рассеянного вперёд и назад света. Методика процесса проиллюстрирована результатами модельного эксперимента при использовании метода Монте-Карло для образцов белого и серого вещества мозга человека на длинах волн видимого диапазона 405 нм, 532 нм и 650 нм. Получены графики зависимости полного пропускания, диффузного отражения и поглощения в зависимости от толщины исследуемого образца. На основе введённых понятий показателя эффективности и коэффициента эффективности проанализирована целесообразность выбора фокального параметра эллипсоидальных рефлекторов для обеспечения регистрации максимального количества рассеянного света. Получены графики показателей эффективности в отражённом и прошедшем свете для разнотолщинных образцов белого и серого веществ, а также коэффициентов эффективности в зависимости от толщины образца. Проанализировано влияние эллиптичности рефлекторов на освещённость различных зон фотометрических изображений на примере поглощающей биологической среды – ткани печени свиньи – на длине волны 405 нм при симуляции Монте-Карло.Оптические свойства биологических сред (коэффициенты рассеяния и поглощения, коэффициент анизотропии рассеяния, показатель преломления) и геометрические размеры образцов, в частности толщина, предопределяют выбор параметров эллипсоидальных рефлекторов для регистрации рассеянного света. Координаты выхода фотонов и их статистический вес, полученные при моделировании распространения света в биологической ткани методом Монте-Карло, оказывают физическое влияние на формирование характерного пятна рассеяния в приёмной плоскости биомедицинского фотометра