Phase-dependent Conductance Research Articles

Size and phase dependent thermal conductivity of TiO2-water nanofluid with theoretical insight

Nanomaterial based heat transfer fluid has become one of the optimistic technologies that ushered a new horizon in the heat transfer process. In this work, TiO2 powder (Degussa P25) was subjected to mechanical milling for 0–16 h and the average particle size was varied from 21.8–13.3 nm. A size induced phase transition of the TiO2 nanoparticles from anatase to rutile was observed and confirmed from both the XRD and RAMAN analysis. It was found that the rutile content increased gradually compared to anatase phase with decreasing particle size. Aqueous TiO2 based nanofluid systems of different milled samples were prepared and heat transfer properties were investigated experimentally. Particle size and phase of the TiO2 nanoparticles both affected the observed thermal conductivity. From the density functional theory based ab initio calculations it was found that the variation in lattice thermal conductivity became negligible when the dimension of the sample is greater than ~23 Å and ~26 Å for rutile and anatase TiO2 respectively, suggesting the phase to be the dominant factor for the observed variation above that size. The DFT study supports our experimental observation indicating that the thermal conductivity of rutile phase is less than that of anatase phase. This work presents for the very first time, a new investigation about the dependency of thermal conductivity on the phase content of TiO2 nanoparticles which may help in explaining various conflicting results in the literature about the thermal conductivity variation of TiO2 based nanofluids.

Phase-dependent noise in Josephson junctions

In addition to the usual superconducting current, Josephson junctions (JJs) support a phase-dependent conductance related to the retardation effect of tunneling quasi-particles. This introduces a dissipative current with a memory-resistive (memristive) character that should also affect the current noise. By means of the microscopic theory of tunnel junctions we compute the complete current autocorrelation function of a Josephson tunnel junction and show that this memristive component gives rise to both a previously noted phase-dependent thermal noise, and an undescribed non-stationary, phase-dependent dynamic noise. As experiments are approaching ranges in which these effects may be observed, we examine the form and magnitude of these processes. Their phase dependence can be realized experimentally as a hysteresis effect and may be used to probe defects present in JJ based qubits and in other superconducting electronics applications.

Influence of grain boundaries and interfaces on the electronic structure of polycrystalline CuO thin films

AbstractCuO thin films were grown by reactive magnetron sputtering and analyzed with respect to their structural, chemical, optical, and electrical properties. The films are strongly p‐type with carrier concentrations of cm−3. Carrier accumulation at grain boundaries is evident from temperature and gas phase dependent conductivity measurements. The films show high absorption coefficients with a band gap of approximately 1.5 eV. Interface formation with TiO2 and Au was studied by photoelectron spectroscopy. Regarding the TiO2/CuO interface, a strong band bending in the TiO2 substrate and a valence band offset of eV were observed. The TiO2 conduction band is therefore approximately midgap of CuO at the interface. CuO is chemically reduced upon Au deposition but an ideal ohmic contact is formed with a Fermi level at the valence band maximum of CuO. Solar cell device structures were prepared of fluorine‐doped SnO2/TiO2 substrates and Au back contacts, revealing open circuit voltages of <0.15 V and photocurrent densities of <0.1 mA/cm2. The photoactivity of the structures is ascribed mostly to the TiO2 substrate.

Superconducting Memristors

In his original work Josephson predicted that a phase-dependent conductance should be present in superconducting tunnel junctions, an effect difficult to detect, mainly because it is hard to single it out from the usual non-dissipative Josephson current. We propose a solution for this problem that consists in using different superconducting materials to realize the two junctions of a superconducting interferometer. According to the Ambegaokar-Baratoff relation the two junctions have different conductances if the critical currents are equal, thus the Josephson current can be suppressed by fixing the magnetic flux in the loop at half of a flux quantum without cancelling the phase-dependent conductance. Our proposal can be used to study the phase-dependent conductance, an effect present in principle in all superconducting weak links. From the standpoint of nonlinear circuit theory such a device is in fact an ideal memristor with possible applications to memories and neuromorphic computing in the framework of ultrafast and low energy consumption superconducting digital circuits.

Homogenization of a Doubly Nonlinear Stefan-Type Problem

Temperature and phase evolution in phase transitions are represented here by coupling the energy balance equation with a multivalued constitutive relation between the density of internal energy and the temperature, and with a nonlinear conduction law. This doubly nonlinear problem generalizes the classical Stefan model. Existence of a weak solution is proved via time discretization, a priori estimates, and passage to the limit. A medium exhibiting periodic oscillations in space is then considered; as the oscillation period vanishes, two-scale convergence (in the sense of Nguetseng) to a corresponding two-scale homogenized problem is proved. The latter is shown to be equivalent to a coarse-scale model. The cases of Fourier's law with either temperature- or phase-dependent conductivity are also treated.

Nonequilibrium Josephson effect in short-arm diffusive SNS interferometers

We study non-equilibrium Josephson effect and phase-dependent conductance in three-terminal diffusive interferometers with short arms. We consider strong proximity effect and investigate an interplay of dissipative and Josephson currents co-existing within the same proximity region. In junctions with transparent interfaces, the suppression of the Josephson current appears at rather large voltage, $eV\sim \Delta$, and the current vanishes at $eV\geq\Delta$. Josephson current inversion becomes possible in junctions with resistive interfaces, where the inversion occurs within a finite interval of the applied voltage. Due to the presence of considerably large and phase-dependent injection current, the critical current measured in a current biased junction does not coincide with the maximum Josephson current, and remains finite when the true Josephson current is suppressed. The voltage dependence of the conductance shows two pronounced peaks, at the bulk gap energy, and at the proximity gap energy; the phase oscillation of the conductance exhibits qualitatively different form at small voltage $eV<\Delta$, and at large voltage $eV>\Delta$.

Magnetoresistance oscillations of quasi-ballistic two-dimensional electron gas coupled with a superconducting ring

We have investigated normal transport in a quasi-ballistic two-dimensional electron gas (2DEG) coupled with a superconducting Nb loop. The oscillations in the resistance are observed as a function of the applied magnetic field which tunes the macroscopic phase difference of the loop. Around zero bias voltage, the resistance maxima occur at even multiples of π. For energies higher than 0.17 meV the sign of the oscillations becomes opposite, and for the middle energies both types of oscillations are observed. We interpret this crossover to be a manifestation of the two types of contributions from Andreev interfered quasi-particles. The temperature dependence of the oscillation amplitude exhibits reentrant behavior which is similar to that shown in phase-dependent conductance of a diffusive S/N system.

Non-neutral dynamics of splay states in Josephson-junction arrays.

We study the effect of the phase dependent conductance on the splay state dynamics of series Josephson arrays. In most cases, the splay states are destabilized, and the array evolves into a more coherent state, e.g., the in-phase state. A smaller parameter range exists where the splay state becomes attracting.

Microwave impedance measurements of point-contact Josephson weak links

We describe measurements of the 10 GHz dynamic impedance of niobium point-contact weak links at 2 K, biased below their critical currents. The measured quantity is Γ(ω), the complex reflection coefficient Of the weak link in parallel with a superconducting cavity resonator terminating a waveguide. Measurements were made at several frequencies close to resonance. In order to interpret the results it is only necessary to assume that the weak link is a two-terminal device consisting of a phase-dependent susceptance in parallel with a phase-dependent conductivity, which is connected to the waveguide through a lossless, phase-independent two-port. The data are consistent with the resistively shunted junction model including a phase-dependent conductance with a negative sign. An important feature of this study was the ability to measure the d.c. IV characteristic simultaneously. The point-contacts investigated had nearly ideal I c R products, and exhibited reproducibile structure in the differential conductance at the superconducting energy gap voltage.

Shunted-Josephson-junction model. I. The autonomous case

The shunted-Josephson-junction model: the parallel combination of a capacitance, a phase-dependent conductance, and an ideal junction element biased by a constant current, is discussed for arbitrary values of the junction parameters. The main objective is to provide a qualitative understanding of the junction behavior in different regions of the parameter space. Approximate formulas are given for the parameter-space decomposition into regions of qualitatively different junction behavior corroborated by the associated-phase plane portraits and also approximate expressions for the corresponding dc current-voltage curves are presented. The case with a time-dependent monochromatic bias current is treated in a similar fashion in the companion paper.

Shunted-Josephson-junction model. II. The nonautonomous case

The shunted-Josephson-junction model with a monochromatic ac current drive is discussed employing the qualitative methods of the theory of nonlinear oscillations. As in the preceding paper dealing with the autonomous junction, the model includes a phase-dependent conductance and a shunt capacitance. The mathematical discussion makes use of the phase-space representation of the solutions to the differential equation. The behavior of the trajectories in phase space is described for different characteristic regions in parameter space and the associated features of the junction $\mathrm{IV}$ curve to be expected are pointed out. The main objective is to provide a qualitative understanding of the junction behavior, to clarify which kinds of properties may be derived from the shunted-junction model, and to specify the relative arrangement of the important domains in the parameter-space decomposition.

Probing the phase-dependent conductance and nonequilibrium properties of Josephson junctions by means of flux entry into weakly closed loops

Numerical simulations have shown that the relative number of flux quanta which penetrate a weakly closed superconducting loop depends upon the magnitude and sign of the phase-dependent conductance. We examine the possible use of this dependence as an experimental probe of the $cos\ensuremath{\phi}$ term and nonequilibrium properties of Josephson junctions.

A Josephson junction analogue incorporating the effects of thermal noise and phase-dependent conductivity

An analogue model based on the equivalence between a phase-locked loop and a Josephson junction has been built to study the effect of thermal noise on junction I-V characteristics. The model differs from previous designs by employing an FET to simulate the phase-dependent junction resistance or cos phi term. The behaviour of the analogue is in good agreement with the theoretical predictions of Ambegaokar and Halperin (1969) and of Falco et al. (1973).

Phase dependent conductance of superconducting point contacts at microwave frequencies

Measurements of the microwave impedence of superconducting point contacts as a function of the phase difference ø yields a conductance of the form G( ø) = G 0(1 + α cos ø) which can be interpreted in terms of a relaxation time of the order parameter.

A simple phenomenological model of the Josephson effects in superconducting weak links

The dependence of pair density on pair velocity is used to formulate a simple model of the total current in a superconducting weak link. The model implies a phase-dependent conductivity and predicts its temperature variation, gives a kinematic description of the Josephson oscillations, and relates the critical current to a quasiparticle-pair relaxation time.

Current-phase relation and phase-dependent conductance of superconducting point contacts from rf impedance measurements

The rf impedance of superconducting point contacts has been measured as a function of the quantum-mechanical phase difference $\ensuremath{\varphi}$ across the point contact. By representing the point contact as a parallel combination of an inductor $\mathfrak{L}(\ensuremath{\varphi})=(\frac{\ensuremath{\hbar}}{2e}){(\frac{\ensuremath{\partial}{I}_{p}}{\ensuremath{\partial}\ensuremath{\varphi}})}^{\ensuremath{-}1}$ and a resistor $R\ensuremath{\equiv}\frac{1}{G(\ensuremath{\varphi})}$ the current-phase relation ${I}_{p}(\ensuremath{\varphi})$ and the phase-dependent conductance $G(\ensuremath{\varphi})$ have been determined from measurements at 30 MHz on phase-biased niobium point contacts. For point contacts with sufficiently small critical current ${I}_{c}$, the inductance was $\mathfrak{L}(\ensuremath{\varphi})=\frac{\ensuremath{\hbar}}{2e{I}_{c}cos\ensuremath{\varphi}}$ yielding the expected negative inductance branch for $\frac{\ensuremath{\pi}}{2}\ensuremath{\le}\ensuremath{\varphi}\ensuremath{\le}\ensuremath{\pi}$ and a sinusoidal current-phase relation. For larger critical currents there were departures from the sinusoidal form for the measured ${I}_{p}(\ensuremath{\varphi})$. There was a phase-dependent conductance that is an increasing function of $\ensuremath{\varphi}$ corresponding to a negative coefficient for the $cos\ensuremath{\varphi}$ term in the Josephson current.

Observation of a Phase-Dependent Conductivity in Superconducting Point Contacts

Observation of a Phase-Dependent Conductivity in Superconducting Point Contacts

A simple phenomenological approach to the phase-dependent conductivity of a superconducting weak link

Dependence of the pair density on pair velocity and consequently on the phase difference for a metallic weak link implies a phase-dependent conductivity which is calculated using a simple phenomenological approach.