Order parameter quantum fluctuations in a two-dimensional system of mesoscopic Josephson junctions

The boson lattice Hubbard model is used to study the role of quantum fluctuations of the phase and local density of the superfluid component in establishing a global superconducting state for a system of mesoscopic Josephson junctions or grains. The quantum Monte Carlo method is used to calculate the density of the superfluid component and fluctuations in the number of particles at sites of the two-dimensional lattice for various average site occupation numbers n ₀ (i.e., number of Cooper pairs per grain). For a system of strongly interacting bosons, the phase boundary of the ordered superconducting state lies above the corresponding boundary for its quasiclassical limit—the quantum XY-model—and approaches the latter as n ₀ increases. When the boson interaction is weak in the boson Hubbard model (i.e., the quantum fluctuations of the phase are small), the relative fluctuations of the order parameter modulus are significant when n ₀<10, while quantum fluctuations in the phase are significant when n ₀<8; this determines the region of mesoscopic behavior of the system. Comparison of the results of numerical modeling with theoretical calculations show that mean-field theory yields a qualitatively correct estimate of the difference between the phase diagrams of the quantum XY-model and the Hubbard model. For a quantitative estimate of this difference the free energy and thermodynamic averages of the Hubbard model are expanded in powers of 1/n ₀ using the method of functional integration. Zh. éksp. Teor. Fiz. 113, 261–277 (January 1998)     

The Relation Between Barrier Structure and Current Uniformity in YBCO Josephson Junctions

Electromagnetic transport measurements were combined with high-resolution electron microscopy observations to study the relation between structure and local critical currents in YBa₂Cu₃O_7–x (YBCO) Josephson junctions. The spatial variation of the critical current J(x) along the length of the boundary for interface engineered Josephson junctions and bicrystal grain boundary Josephson junctions was determined using a phase retrieval algorithm. The current distribution solutions were found to be highly uniform along the length of interface engineered junctions in contrast to solutions for grain boundary junctions. The latter showed significant spatial oscillations in the critical current as well as areas along the boundary that carried no current. Microstructural evaluation of interface engineered junctions fabricated using identical processing parameters to the junctions used for transport measurements suggest that the uniform current distribution is controlled by a highly uniform barrier layer formed between the superconducting electrodes. Microstructural evaluation of grain boundary junctions similar to the junctions used for transport measurements show considerable variations of the grain boundary structure within a single junction.     

Nanosize patterns as reference structures for macroscopic transport properties and vortex phases in YBCO films

This paper reports on the striking correlation between nanosize mosaic domain walls in YBCO films and 1D rows of parallel Josephson junctions, determining the J _c vs.B curves. From X-ray data analysis, it results that the average “hidden" domain wall, faceted at a nanometric scale, is almost mimicking the Josephson Junction (JJ) 1D array. The assumption that the JJs and the domain-wall arrays are coincident, enables to find out the particular scaling field, making the J _c vs.B curves independent of temperature. This scaling field can be interpreted in terms of the Josephson nature of the transport current across these particular patterns in the intermediate temperature range. By means of our model it is also possible to calculate two asymptotic behaviors of the pinning force as a function of field, for low and high fields, respectively. These behaviors are punctually repeated by the experimental results in the same asymptotic limit, so that two corresponding vortex regimes are clearly pointed out. All results can be interpreted by concluding that in the intermediate temperature range, the strong pinning observed in high quality YBCO films is due to the Josephson Junctions average patterns. These patterns are the counterpart related to the transport mechanisms of “hidden" structural nano-domains. Received 16 October 2000 and Received in final form 28 November 2000     

External electric field control in the charge qubits including three Josephson junctions

Based on the standard canonical quantization principle, this paper gives the quantization scheme for the charge qubits mesoscopic circuit including three Josephson junctions coupled capacitively. By virtue of the Heisenberg equation, the time evolution of the phase difference operators across the polar plates and the number operators of the Cooper-pairs on the island are investigated and the modification of the Josephson equation is discussed. The time evolution of the phase difference operators is analysed when the Josephson junctions are irradiated by the external electrical field, which is referred to as also the obtainable controlling parameter.     

Analysis of irreducible representations of the group U (4) Up(2) × Un(2)

The general method of projection operators is used to construct the noncanonical nonorthogonal basis of arbitrary irreducible representation of the group U (4) in the reduction U (4) U_p(2) × U_n(2), where U_p(2)(U_n(2)) is the transformation group in the proton (neutron) spin space. The completeness of this basis is proved and the matrices of the U (4) group generators and of the Bargmann-Moshinsky operator Ω in this basis are obtained. The matrix Ω exhibits a nondegenerate spectrum of the eigenvalues which may be used as the missing quantum number.     

Fluctuation power spectrum of a Josephson junction

The fluctuation power spectrum of the Josephson junction has been evaluated in the limit of large energy barriers [(U _n ^max−U _n ^min)γ]≫1 and small currents [x≪x _e]. The result is valid for finite capacitance of the junction. The effect of the fluctuating Josephson current on the voltageV(t) across the junction has also been taken into account.     

Renormalization and quantum effects in a two-dimensional planar model

We examine the influence of the charging energy on the vortex unbinding transition in two-dimensional arrays of Josephson junctions. The fluctuations of the phase about the time-dependent vortex solutions are treated within the self-consistent harmonic approximation. A new relation between the renormalized vortex unbinding temperature T_c and the charging energy U is derived. We predict a continuous drop of T_c at a critical value of U well below the spurious first order transition of the rigidity constant. The results are interpreted as a quantum assisted dissociation of vortex pairs.     

Ursell operators in statistical physics of dense systems: the role of high order operators and of exchange cycles

The purpose of this article is to discuss cluster expansions in dense quantum systems, as well as their interconnection with exchange cycles. We show in general how the Ursell operators of order l≥ 3 contribute to an exponential which corresponds to a mean-field energy involving the second operator U₂, instead of the potential itself as usual - in other words, the mean-field correction is expressed in terms of a modification of a local Boltzmann equilibrium. In a first part, we consider classical statistical mechanics and recall the relation between the reducible part of the classical cluster integrals and the mean-field; we introduce an alternative method to obtain the linear density contribution to the mean-field, which is based on the notion of tree-diagrams and provides a preview of the subsequent quantum calculations. We then proceed to study quantum particles with Boltzmann statistics (distinguishable particles) and show that each Ursell operator U_n with n≥ 3 contains a “tree-reducible part”, which groups naturally with U₂ through a linear chain of binary interactions; this part contributes to the associated mean-field experienced by particles in the fluid. The irreducible part, on the other hand, corresponds to the effects associated with three (or more) particles interacting all together at the same time. We then show that the same algebra holds in the case of Fermi or Bose particles, and discuss physically the role of the exchange cycles, combined with interactions. Bose condensed systems are not considered at this stage. The similarities and differences between Boltzmann and quantum statistics are illustrated by this approach, in contrast with field theoretical or Green's functions methods, which do not allow a separate study of the role of quantum statistics and dynamics. Received 18 October 2001     

Quantum phase fluctuations in an array of mesoscopic Josephson junctions

The effects of macroscopic ordering in a system of mesoscopic Josephson junctions are investigated by the quantum Monte Carlo simulation technique (using path integrals). The phase diagram of the system in the T-q plane (q is the dimensionless quantum parameter , where J is the Josephson coupling constant and C ₀ is the self-capacitance of the granules) is investigated in detail. An analysis of the behavior of the relative root-mean-square phase shifts, as well as the helicity and vorticity moduli, demonstrates the need to employ these two quantities as the parameters which most completely reflect the character of the topological phase transition in the quantum system under consideration. Two methods are proposed for calculating the vorticity modulus: 1) a modification of the Gibbs-Bogolyubov variational principle for calculating the free energy change in response to alteration of the type of boundary conditions; 2) calculation of the response to the introduction of an infinitesimal magnetic flux at some point in the system. The calculations confirm the absence of reentrant melting and phase transitions of a non-Kosterlitz-Thouless type in the region of strong quantum phase fluctuations q>1. Fiz. Tverd. Tela (St. Petersburg) 39, 1513–1519 (September 1997)     

Nonstandard q-deformation of the Euclidean Lie algebra and its representations

A nonstandard q-deformed Euclidean algebra U _q(iso _n ), based on the definition of the twisted q-deformed algebra U _qso_n) (different from the Drinfeld–Jimbo algebra U _q(so _n )), is defined. Infinite dimensional representations R of U _q(iso _n ) are described. Explicit formulas for operators of these representations in the orthonormal basis are given. The spectra of the operators R(T _n) corresponding to a q-analogue of the infinitesimal operator of shifts along the n-th axis are described. Contrary to the case of the classical Euclidean Lie algebra iso _n , these spectra are discrete and spectral points have one point of accumulation.     

Synchronization of high-frequency vibrations of slipping phase centers in a tin whisker under microwave radiation

Current-voltage characteristics of a system with a variable number of slipping phase centers resulting from phase separation in a tin whisker under external microwave field with a frequency Ω/2π≅35–45 GHz have been studied experimentally. Emergence and disappearance of steps with zero slope in a whisker’s current-voltage characteristic at U _m/n =(m/n)U _Ω, where m and n are integers and U _Ω is determined by Josephson’s formula _ℏΩ=2eU _Ω, have been investigated. Microwave field generated by slipping phase centers is nonharmonic, and the system of slipping phase centers permits synchronization of internal oscillations at a microwave frequency by an external field with a frequency which is the n-th harmonic of internal oscillations. The estimated microwave power generated by a whisker is 10⁻⁸ W. Stimulation of superconductivity in a current-carrying whisker has been detected. Zh. éksp. Teor. Fiz. 113, 1364–1375 (April 1998)     

New approach in theory of Clebsch-Gordan coefficients foru(n) andU q(u(n))

A new method for calculation of Clebsch-Gordan coefficients (CGCs) of the Lie algebrau(n) and its quantum analogU _q(u(n)) is developed. The method is based on the projection operator method in combination with the Wigner-Racah calculus for the subalgebrau(n−1) (U _q(u(n−1))). The key formulas of the method are couplings of the tensor and projection operators and also a tensor form of the projection operator ofu(n) andU _q(u(n)). It is shown that theU _q(u(n)) CGCs can be presented in terms of theU _q(u)(n−1)) q−9j-symbols. Presented at the 9th International Colloquium: “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. Supported by Russian Foundation for Fundamental Research, grant 99-01-01163. Supported in part by the U.S. National Science Foundation under Grant PHY-9970769 and Cooperative Agreement EPS-9720652 that includes matching from the Louisiana Board of Regents Support Fund.     

Superconducting-insulator transition in disordered Josephson junctions networks

The superconducting-insulator transition is simulated in disordered networks of Josephson junctions with thermally activated Arrhenius-like resistive shunt. By solving the conductance matrix of the network, the transition is reproduced in different experimental conditions by tuning thickness, charge density and disorder degree. In particular, on increasing fluctuations of the parameters entering the Josephson coupling and the Coulomb energy of the junctions, the transition occurs for decreasing values of the critical temperature T _c and increasing values of the activation temperature T _o . The results of the simulation compare well with recent experiments where the mesoscopic fluctuations of the phase have been suggested as the mechanism underlying the phenomenon of emergent granularityin otherwise homogeneous films. The proposed approach is compared with the results obtained on TiN films and nanopatterned arrays of weak-links, where the superconductor-insulator transition is directly stimulated.     

Non-Standard Schwinger Fermionic Representation of Unitary Group

The non-standard Schwinger fermionic representation of the unitary group is studied by using n-fermion operators. One finds that the Schwinger fermionic representation of the U(n) group is not unique when n≥3. In general, based on n-fermion operators, the non-standard Schwinger fermionic representation of the U(n) group can be established in a uniform approach, where all the generators commute with the total number operators. The Schwinger fermionic representation of U(C _n ^m ) group is also discussed.     

Superconductivity with s and p symmetries in an extended Hubbard model with correlated hopping

We consider a generalized Hubbard model with on-site and nearest-neighbour repulsions U and V respectively, and nearest-neighbour hopping for spin up (down) which depends on the total occupation n_b of spin down (up) electrons on both sites involved. The hopping parameters are t _AA , t_AB and t_BB for n _b =0,1,2 respectively. We briefly summarize results which support that the model exhibits s-wave superconductivity for certain parameters and extend them by studying the Berry phases. Using a generalized Hartree-Fock(HF) BCS decoupling of the two and three-body terms, we obtain that at half filling, for t _AB <t _AA =t _BB and sufficiently small U and V the model leads to triplet p-wave superconductivity for a simple cubic lattice in any dimension. In one dimension, the resulting phase diagram is compared with that obtained numerically using two quantized Berry phases (topological numbers) as order parameters. While this novel method supports the previous results, there are quantitative differences. Received: 2 February 1998 / Accepted: 17 March 1998     

Josephson array of mesoscopic objects. Modulation of system properties through the chemical potential

The phase diagram of a two-dimensional Josephson array of mesoscopic objects (superconducting granules, superfluid helium in a porous medium, traps with Bose-condensed atoms, etc.) is examined. Quantum fluctuations in both the modulus and phase of the superconducting order parameter are taken into account within a lattice boson Hubbard model. Modulating the average occupation number n ₀ of the sites in the system (the “number of Cooper pairs” per granule, the number of atoms in a trap, etc.) leads to changes in the state of the array, and the character of these changes depends significantly on the region of the phase diagram being examined. In the region where there are large quantum fluctuations in the phase of the superconducting order parameter, variation of the chemical potential causes oscillations with alternating superconducting (superfluid) and normal states of the array. On the other hand, in the region where the bosons interact weakly, the properties of the system depend monotonically on n ₀. Lowering the temperature and increasing the particle interaction force lead to a reduction in the width of the region of variation in n ₀ within which the system properties depend weakly on the average occupation number. The phase diagram of the array is obtained by mapping this quantum system onto a classical two-dimensional XY model with a renormalized Josephson coupling constant and is consistent with our quantum path-integral Monte Carlo calculations. Zh. éksp. Teor. Fiz. 114, 591–604 (August 1998)     

Characteristics of the Surface-Intrinsic Josephson Junction

During the fabrication of intrinsic Josephson junctions (IJJs) with Bi₂Sr₂CaCu₂O_8+δ (BSCCO) single crystals, the superconductivity of the surface Cu-O layer is degraded because of a deposited metal film on top of the stack. Thus, the characteristics of the surface junction consisting of the surface Cu-O double layers remarkably differ from those of the junctions deep in the stack, which will be referred to as ordinary IJJs. The electrical transport characteristics of the surface junction, such as I-V, I _c′-T, and R-T, show that the critical temperature T _c′ of the surface junction is always lower than that of ordinary IJJs, and that the change of its critical current I _c′ with temperature is different from that of ordinary IIJs. Furthermore, by shunting the surface junction resistively, we are able to observe the AC Josephson effect at 3-mm waveband. Translated from Chinese Journal of Low Temperature Physics, 2005, 27(2) (in Chinese)     

Multiple Andreev reflections in diffusive SNS structures

We report new measurements on subgap energy structures originating from multiple Andreev reflections in mesoscopic SNS junctions. The junctions were fabricated in a planar geometry with high-transparency superconducting contacts of Al deposited on highly diffusive and surface δ -dopedn ^{+ +} -GaAs. For samples with a normal GaAs region of active length 0.3μ m, the Josephson effect with a maximal supercurrent I_c = 3μ A at T = 237 mK was observed. The subgap structure was observed as a series of local minima in the differential resistance at dc bias voltages V = ± 2Δ / (ne) with n = 1, 2, 4, i.e. only the even subgap positions. While at V = ± 2Δ / e(n = 1) only one dip is observed, then = 2 and the n = 4 subgap structures each consists of two separate dips in the differential resistance. The mutual spacing of these two dips is independent of temperature, and the mutual spacing of the n = 4 dips is half the spacing of the n = 2 dips. The voltage bias positions of the subgap differential resistance minima coincide with the maxima in the oscillation amplitude when a magnetic field is applied in an interferometer configuration, where one of the superconducting electrodes has been replaced by a flux-sensitive open loop.     

Influence of transport current and thermal fluctuations on the resistive properties of HTSC+CuO composites

Measurements of the temperature dependence of the electrical resistance R(T) below the superconducting transition temperature have been performed at different values of the transport current in HTSC+CuO composites modeling a network of weak S-I-S Josephson junctions (S—superconductor, I—insulator). It has been shown experimentally that the temperature dependence R(T) at different values of the transport current is adequately described by means of the mechanism of thermally activated phase slippage developed by Ambegaokar and Halperin for tunnel structures. Within the framework of this model we have numerically calculated the temperature dependence of the critical current J _c(T) as defined by various criteria. Qualitative agreement obtains between the measured and calculated temperature dependences J _c(T). Fiz. Tverd. Tela (St. Petersburg) 41, 969–974 (June 1999)