Influence of quantum resonance-percolation trajectories in a disordered <Emphasis Type="Italic">I</Emphasis> layer on the critical current of a Josephson <Emphasis Type="Italic">S-I-S</Emphasis> junction

Formulae for critical current and the magnitude of its mesoscopic structural fluctuations in the tunneling resonance energy range of an S-I-S (S = superconductor, I = insulator) tunnel junction with a weak structural disorder (low impurity density) in an I layer at temperature T = 0 are obtained in the form of sums describing the quantum resonant-percolation trajectories [1] that randomly form in a disordered I layer and the connecting opposite S banks of a contact.     

Emission and absorption asymmetry in the quantum noise of a Josephson junction

We measure current fluctuations of mesoscopic devices in the quantum regime, when the frequency is of the order of or higher than the applied voltage or temperature. Detection is designed to probe separately the absorption and emission contributions of current fluctuations, i.e. the positive and negative frequencies of the Fourier transformed nonsymmetrized noise correlator. It relies on measuring the quasiparticles photon assisted tunneling current across a superconductor-insulator-superconductor junction (the detector junction) caused by the excess current fluctuations generated by quasiparticles tunneling across a Josephson junction (the source junction). We demonstrate unambiguously that the negative and positive frequency parts of the nonsymmetrized noise correlator are separately detected and that the excess current fluctuations of a voltage biased Josephson junction present a strong asymmetry between emission and absorption.     

Self-averaging criterion of the resonant tunnel conductance of an <Emphasis Type="Italic">N-I-N</Emphasis> contact with weak structural disorder in the <Emphasis Type="Italic">I</Emphasis> layer

In the range of tunnel resonance energies of a disordered N-I-N (N is a normal metal, I is an insulator) contact, its tunnel conductance is represented as the sum over the quantum resonance-percolation trajectories that are randomly formed in the disordered I layer and connect the opposite junction edges [1]. Such a representation made it possible to obtain a formula for the mesoscopic conductance fluctuations, on the basis of which the self-averaging criterion was derived.     

Mesoscopic Josephson effect

In the classical Josephson effect the phase difference across the junction is well defined, and the supercurrent is reduced only weakly by phase diffusion. For mesoscopic junctions with small capacitance the phase undergoes large quantum fluctuations, and the current is also decreased by Coulomb blockade effects. We discuss the behavior of the current–voltage characteristics in a large range of parameters comprising the phase diffusion regime with coherent Josephson current as well as the supercurrent peak due to incoherent Cooper pair tunneling in the Coulomb blockade regime.     

Even-odd effect in spontaneously coherent bilayer quantum Hall droplets

Using exact diagonalization in the disk geometry we predict a novel even-odd effect in the Coulomb-blockade spectra of vertically coupled double quantum dots under an external magnetic field. The even-odd effect in the tunneling conductance is a direct manifestation of spontaneous interlayer phase coherence, and is similar to the even-odd resonance in the Cooper pair box problem in mesoscopic superconducting grains. Coherent fluctuations in the number of Cooper pairs in superconductors are analogous to the fluctuations in the relative number difference between the two layers in quantum Hall droplets.     

Spin-polarized transport through a coupled double-dot

We investigate the quantum transport through a mesoscopic device consisting of an open, lateral double-quantum-dot coupled by time oscillating and spin-polarization dependent tunneling which results from a static magnetic field applied in the tunneling junction. In the presence of a non-vanishing bias voltage applied to two attached macroscopic leads both spin and charge currents are driven through the device. We demonstrate that the spin and charge currents are controllable by adjusting the gate voltage, the frequency of driving field and the magnitude of the magnetic field as well. An interesting resonance phenomenon is observed.     

Lower critical field of a long Josephson <Emphasis Type="Italic">S-I-S</Emphasis> tunnel junction with quantum jumpers in <Emphasis Type="Italic">I</Emphasis> layer

The formulas in which the lower critical field and its mesoscopic structural fluctuations in the energy range of tunnel resonances of a long S-I-S (superconductor-insulator-superconductor) tunnel junction with weak (low impurity concentrations) structural disorder in the I layer at T = 0 are represented as sums over quantum resonant percolation trajectories (quantum jumpers), randomly formed in the disordered I layer [1], are derived.     

Tunable Fermi-edge resonance in an open quantum dot

Resonant tunneling in an open mesoscopic quantum dot is proposed as a vehicle to realize a tunable Fermi-edge resonance with variable coupling strength. We solve the x-ray edge problem for a generic nonseparable scatterer and apply it to describe tunneling in a quantum dot. The tunneling current power law exponent is linked to the S matrix of the dot. The control of scattering by varying the dot shape and coupling to the leads allows us to explore a wide range of exponents. The sensitivity of mesoscopic coherence to the Wigner-Dyson ensemble symmetry is replicated in the Fermi-edge singularity.     

Mesoscopic fluctuations of tunneling and cotunneling in quantum dots

Recent measurements of mesoscopic tunneling and cotunneling fluctuations in Coulomb blockaded ballistic quantum dots are presented. The statistics and parametric fluctuations (as a function of magnetic field) of Coulomb blockade peak heights are found to be consistent with random-matrix-theory predictions. Mesoscopic fluctuations of elastic cotunneling, measured in the valleys between blockade peaks, are also presented along with a semiclassical explanation of the observed enhancement of the magnetic field scale of cotunneling fluctuations compared to resonant tunneling fluctuations.     

The effect of superconducting fluctuations on the resistance of tunneling junction: The existence of ultrathin surface layer in NbN films

The effect of superconducting fluctuations on quasi-particle current of tunneling junction is discussed. The anomalous contribution in tunneling current from interacting across the barrier fluctuations is found. It gives rise to pseudogap minimum in R_d(V). Similar dependence is observed experimentally in NbN-I-Pb junctions. Reasons are given to suggest that there is some ultrathin layer on the surface of NbN films whose properties drastically differ from the bulk one.     

Strong electron tunneling through a small metallic grain

Electron tunneling through mesoscopic metallic grains can be treated perturbatively only under the conduction that the tunnel junction conductances are sufficiently small. If that is not the case, fluctuations of the grain charge become strong. As a result (i) the contributions of all—including high energy—charge states become important, and (ii) the excited charge states become broadened and essentially overlap. At the same time, the grain charge remains discrete and the system conductance e-periodically depends on the gate charge. We develop a non-perturbative approach which accounts for all these features and calculate the temperature-dependent conductance of the system in the strong tunneling regime at different values of the gate charge. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 953–958 (25 June 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Reduced quantum fluctuation in mesoscopic Josephson junction with nonclassical radiation field at finite temperature

We have investigated the reduced fluctuation properties in a mesoscopic Josephson junction with the squeezed state at a finite temperature. It is shown that the fluctuations increase with increasing temperature and the mesoscopic Josephson junction subsystem can exhibit squeezing behaviour at an appropriately low temperature.     

Influence of structural disorder on the current-voltage characteristic of a quasi-one-dimensional tunnel junction

The influence of the subbarrier impurity scattering of tunneling electrons on the current-voltage characteristic of a quasi-one-dimensional insulator layer with weak structural disorder (a small impurity concentration) is considered in the one-electron approximation at T=0. An expansion in powers of the impurity concentration gives the form of the current-voltage characteristic and the conditions for small mesoscopic fluctuations of the static tunneling conductance of such a layer in the cases of resonant and nonresonant tunneling. Zh. éksp. Teor. Fiz. 113, 1522–1530 (April 1998)     

Current-distance-voltage characteristics of electron tunneling through an electrochemical STM junction

We have studied the electron tunneling process through an electrochemical scanning tunneling microscopic (STM) junction formed by a gold tip and a gold electrode immersed in an inert NaClO₄ solution. Current-distance-voltage characteristics of the tunneling process are examined by simultaneous measurement of tunneling current, voltage, and distance. The results indicate that the tunneling voltage across the junction changes with tunneling distance; however, tunneling conductance is an inverse exponential function of distance over the entire investigated range of tunneling current, voltage, and distance. The results provide clear evidence for the validity of a one-dimensional tunneling model for the aqueous tunneling process. Implications of the observation are mentioned with regard to the distance-dependent STM imaging and the origin of a low tunneling barrier height.     

Subharmonic gap structure in superconducting scanning tunneling microscope junctions

We observe a subharmonic gap structure (SGS) and the Josephson effect in superconducting scanning tunneling microscope junctions with resistances below 100 kΩ. The magnitude of the n=2 SGS is shown to scale with the square of the junction normal state conductance, in agreement with theory. We show by analyzing the Josephson effect in these junctions that the superconducting phase dynamics are strongly affected by thermal fluctuations. We estimate the linewidth of the Josephson oscillations due to phase fluctuations, a quantity that may be important in modern theories of the subgap structure. While phase fluctuations may smear the SGS current onsets, we conclude that the sharpness of these onsets in our data is not limited by fluctuations.     

Mesoscopic fluctuations of the resonant tunneling conductance in a disordered <Emphasis Type="Italic">S-I-S</Emphasis> junction in magnetic field

The conditions for the smallness of mesoscopic fluctuations of resonant tunneling conductance are obtained for a small S-I-S-junction with weak structural disorder in the I layer in a magnetic field parallel to its plane at temperature T= 0.     

Stochastic simulation of variations in the autoignition delay time of premixed methane and air

A mesoscopic stochastic particle model for homogeneous combustion is introduced. The model can be used to investigate the physical fluctuations in a system of coupled chemical reactions with energy (heat) release/consumption. In the mesoscopic model, the size of the homogeneous gas volume is an additional variable, which is eliminated in macroscopic continuum models by the thermodynamic limit N→∞. Thus, continuous homogeneous models are macroscopic models wherein fluctuations are excluded by definition. Fluctuations are known to be of particular importance for systems close to the autoignition limits. The new model is used to investigate the stochastic properties of the autoignition delay time in a homogeneous system with stoichiometric premixed methane and air. Temperature and species concentrations during autoignition of sub-macroscopic volumes, including physically meaningful fluctuations, are presented. It is found that different realizations mainly differ in the time when ignition occurs; besides this the development is similar. The mesoscopic range and the macroscopic limit are identified. Which range a specific system is assigned to is not only a question of the length scale or particle number, but also depends on the complete thermodynamic state. The stochastic algorithm yields the correct results for the macroscopic limit compared to the continuous balance equations. The sensitivity of the results to two different detailed reaction mechanisms (for the same system) is studied and found to be low. We show that when approaching the autoignition limit by decreasing the temperature, the fluctuations in the autoignition delay time increase and an increasing number of realizations will have exceedingly long ignition delay times, meaning they are in practice not autoignitable. With this result the mesoscopic simulations offer an explanation of the transition between autoignitable and non-autoignitable conditions. The calculated distributions were compared with ten repetitions of the same experiment. A mesoscopic distribution that matches the experimental results was found.     

Multi-Scale Jacobi Method for Anderson Localization

We prove that the fluctuations of mesoscopic linear statistics for orthogonal polynomial ensembles are universal in the sense that two measures with asymptotic recurrence coefficients have the same asymptotic mesoscopic fluctuations (under an additional assumption on the local regularity of one of the measures). The convergence rate of the recurrence coefficients determines the range of scales on which the limiting fluctuations are identical. Our main tool is an analysis of the Green’s function for the associated Jacobi matrices.As a particular consequencewe obtain a central limit theorem for the modified Jacobi Unitary Ensembles on all mesoscopic scales.     

Structures of energy spectrum and persistent currents in mesoscopic rings with radial potential barrier in magnetic field

The energy spectrum and the persistent currents are calculated for finite-width mesoscopic annular structures with radial potential barrier in the presence of a magnetic field. The introduction of the tunneling barrier leads to the creation of extra edge states around the barrier and the occurrence of oscillatory structures superimposed on the bulk Landau level plateaus in the energy spectrum. We found that the Fermi energy E _F increases with the number of electrons N emerging many kinks. The single eigenstate persistent current exhibits complicated structures with vortex-like texture, “bifurcation”, and multiple “furcation” patterns as N is increased. The total currents versus N display wild fluctuations.