First-order superconducting transition near a ferromagnetic quantum critical point

We address the issue of how triplet superconductivity emerges in an electronic system near a ferromagnetic quantum critical point (FQCP). Previous studies found that the superconducting transition is of second order, and T(c) is strongly reduced near the FQCP due to pair-breaking effects from thermal spin fluctuations. In contrast, we demonstrate that near the FQCP, the system avoids pair-breaking effects by undergoing a first order transition at a much larger T(c). A second order superconducting transition emerges only at some distance from the FQCP.     

A scaling analysis of the critical conditions for a deflagration-to-detonations transition

In this paper an intuitive criterion for the deflagration-to-detonations transition (DDT) by turbulent mixing was deduced. An analysis was first carried out to determine the critical conditions for detonation initiation within a reactive mixture, which is non-uniformly heated. It was demonstrated that the critical conditions depend on both the size and the characteristic heating time of the energy source. If the characteristic heating time is larger than a critical value, no detonation initiation can be expected, no matter how large the total energy of the heat source is. The critical parameters obtained were then applied to determine the critical conditions for detonation initiation via turbulent mixing. It was found that the DDT depends on both the mixing time and length scales. According to the Damkohler number, there are two regimes. (a) When the Damkohler number is smaller than unity, the critical integral length scale for DDT decreases as the inverse of the turbulent velocity. (b) When the Damkohler number is larger than unity, the critical integral length scale increases according to the cube of the turbulent velocity. These critical conditions were explained in a turbulent phase diagram of Borghi.(Some figures in this article appear in colour in the electronic version; see www.iop.org)     

The Anderson transition in three-dimensional quasiperiodic lattices: finite-size scaling and critical exponent

The influence of quasiperiodicity on the metalinsulator transition (MIT) in the Anderson model of localization is investigated. The eigenstates of a 3D Amman-Kramer lattice are studied in the vertex model. The participation numbers are calculated and evaluated by means of a finitesize scaling procedure to characterize the MIT. The critical disorder W _c = 21.2 ± 0.6 and the exponent υ = 1.4 ± 0.3 are computed.     

Critical scaling of shear viscosity at the jamming transition

We carry out numerical simulations to study transport behavior about the jamming transition of a model granular material in two dimensions at zero temperature. Shear viscosity eta is computed as a function of particle volume density rho and applied shear stress sigma, for diffusively moving particles with a soft core interaction. We find an excellent scaling collapse of our data as a function of the scaling variable sigma/|rho(c)-rho|(Delta), where rho(c) is the critical density at sigma=0 ("point J"), and Delta is the crossover scaling critical exponent. We define a correlation length xi from velocity correlations in the driven steady state and show that it diverges at point J. Our results support the assertion that jamming is a true second-order critical phenomenon.     

Finite-size scaling of the level compressibility at the Anderson transition

We compute the number level variance Σ ₂ and the level compressibility χ from high precision data for the Anderson model of localization and show that they can be used in order to estimate the critical properties at the metal-insulator transition by means of finite-size scaling. With N, W, and L denoting, respectively, linear system size, disorder strength, and the average number of levels in units of the mean level spacing, we find that both χ(N, W) and the integrated Σ ₂ obey finite-size scaling. The high precision data was obtained for an anisotropic three-dimensional Anderson model with disorder given by a box distribution of width W/2. We compute the critical exponent as ν≈ 1.45±0.12 and the critical disorder as W _c≈ 8.59±0.05 in agreement with previous transfer-matrix studies in the anisotropic model. Furthermore, we find χ≈ 0.28±0.06 at the metal-insulator transition in very close agreement with previous results. Received 1st November 2001 and Received in final form 8 March 2002 Published online 6 June 2002     

The effect of boundary conditions on the superconducting transition critical temperature in superlattices

For a superconducting superlattice consisting of alternating layers of two materials with thicknesses a and b, an analogue of the Cooper formula is obtained for boundary conditions in the general form. The effect of the boundary conditions on the critical temperature is studied, and the possibility of order parameter localization in the layers with a higher critical temperature is demonstrated.     

Electron density variation at copper sites at the superconducting transition in cuprates

The temperature dependence of the center of gravity S of the Mössbauer spectrum produced by ⁶⁷Zn²⁺ impurity ions occupying copper and yttrium sites in YBa₂Cu₃O_6.6, YBa₂Cu₃O_6.9, YBa₂Cu₄O₈, Bi₂Sr₂CaCu₂O₈, HgBa₂CuO₄, and HgBa₂CaCu₂O₆ at temperatures above the superconducting transition point T_c was shown to be dominated by the second-order Doppler shift. For T<T_c, the quantity S is affected by the band mechanism associated with the formation of Cooper pairs and their Bose condensation. The variation of electron density at a metal site of the crystal was found to be related to the superconducting transition temperature. The variation of electron density created by the Cooper pair Bose condensate in compounds with two structurally inequivalent copper positions was shown to be different for these copper sites. The experimental dependence of the fraction of superconducting electrons on temperature agrees with the analogous dependence following from BCS theory for all the sites studied.     

Anomalous scaling at the quantum critical point in itinerant antiferromagnets

We show that the Hertz phi(4) theory of quantum criticality is incomplete as it misses anomalous nonlocal contributions to the interaction vertices. For antiferromagnetic quantum transitions, we found that the theory is renormalizable only if the dynamical exponent z=2. The upper critical dimension is still d=4 - z=2; however, the number of marginal vertices at d=2 is infinite. As a result, the theory has a finite anomalous exponent already at the upper critical dimension. We show that for d<2 the Gaussian fixed point splits into two non-Gaussian fixed points. For both fixed points, the dynamical exponent remains z=2.     

Current vortices in superconducting films at the surface parallel critical field

An idealized superconducting film in a homogeneous magnetic field parallel to the surface is considered in the range of validity of the linearized Ginzburg-Landau equation. The invoking of a simple symmetry principle leads directly to the existence of current vortices (flux tubes) for certain thicknesses and field strengths. Streamlines of the supercurrent for numerical solutions of the equations are shown.     

Quantized conductance at the Majorana phase transition in a disordered superconducting wire

Superconducting wires without time-reversal and spin-rotation symmetries can be driven into a topological phase that supports Majorana bound states. Direct detection of these zero-energy states is complicated by the proliferation of low-lying excitations in a disordered multimode wire. We show that the phase transition itself is signaled by a quantized thermal conductance and electrical shot noise power, irrespective of the degree of disorder. In a ring geometry, the phase transition is signaled by a period doubling of the magnetoconductance oscillations. These signatures directly follow from the identification of the sign of the determinant of the reflection matrix as a topological quantum number.     

Critical scaling properties at the superfluid transition of 4He in aerogel

We study the superfluid transition of 4He in aerogel by Monte Carlo simulations and finite size scaling analysis. Aerogel is a highly porous silica glass, which we model by a diffusion limited cluster aggregation model. The superfluid is modeled by a three dimensional XY model, with excluded bonds to sites on the aerogel cluster. We obtain the correlation length exponent nu=0.73+/-0.02, in reasonable agreement with experiments and with previous simulations. For the heat capacity exponent alpha, both experiments and previous simulations suggest deviations from the Josephson hyperscaling relation alpha=2-dnu. In contrast, our Monte Carlo results support hyperscaling with alpha=-0.2+/-0.05. We suggest a reinterpretation of the experiments, which avoids scaling violations and is consistent with our simulation results.     

Change in the chemical potential of niobium at transition to the superconducting state

A temperature-modulation technique was applied to investigate change in the chemical potential of niobium film at transition to the superconducting state. The first derivative of the chemical potential is continuous at T _c whereas the second derivative shows a jump. Received 10 April 2000     

Universal scaling behavior at the upper critical dimension of nonequilibrium continuous phase transitions

In this work we analyze the universal scaling functions and the critical exponents at the upper critical dimension of a continuous phase transition. The consideration of the universal scaling behavior yields a decisive check of the value of the upper critical dimension. We apply our method to a nonequilibrium continuous phase transition. By focusing on the equation of state of the phase transition it is easy to extend our analysis to all equilibrium and nonequilibrium phase transitions observed numerically or experimentally.     

Anisotropy in the length change of gallium single crystals at their superconducting transition

The magnetostriction of gallium single crystals has been measured for the three principal axes between 0.3K and 1.1 K. It is found that the length change at the transition from the superconducting to the normal state is given approximately by (Δl/l)_a = − 3.10⁻⁹, (Δl/l)_b = + 4.4 · 10⁻⁹ and (Δl/l)_c = + 1.8 · 10⁻⁹, for the a, b and c axes at T = 0 K. A short discussion of the results with respect to microscopic theory is presented.     

Novel voltage signal at proximity-induced superconducting transition temperature in gold nanowires

We observed a novel voltage peak in the proximity-induced superconducting gold (Au) nanowire while cooling the sample through the superconducting transition temperature. The voltage peak turned dip during warming. The voltage peak or dip was found to originate respectively from the emergence or vanishing of the proximity-induced superconductivity in the Au nanowire. The amplitude of the voltage signal depends on the temperature scanning rate, and it cannot be detected when the temperature is changed slower than 0.03 K/min. This transient feature suggests the non-equilibrium property of the effect. Ginzburg-Landau model clarified the voltage peak by considering the emergence of Cooper pairs of relatively lower free energy in superconducting W contact and the non-equilibrium diffusion of Cooper pairs and quasiparticles.     

Upper critical fields of superconducting superconducting rare-earth molybdenum selenides

Upper critical fields, H_c2(T), for superconducting LaMo₆Se₈, La_0.8Eu_0.2Mo₆Se₈, La_0.8Ce_0.2Mo₆Se₈ and PrMo₆Se₈ were measured. For the best material, LaMo₆Se₈, T_c = 11.3 K, (dH_c²/dT)_T=Tc=70 kG/K and and H_c² (4.2 K) = 370 kG. These selenide compounds show promise as very high field superconductors.     

Optimisation of multifractal analysis at the 3D Anderson transition using box-size scaling

We study various box-size scaling techniques to obtain the multifractal properties, in terms of the singularity spectrum f(α), of the critical eigenstates at the metal-insulator transition within the 3-D Anderson model of localisation. The typical and ensemble averaged scaling laws of the generalised inverse participation ratios are considered. In pursuit of a numerical optimisation of the box-scaling technique we discuss different box-partitioning schemes including cubic and non-cubic boxes, use of periodic boundary conditions to enlarge the system and single and multiple origins for the partitioning grid are also implemented. We show that the numerically most reliable method is to divide a system of linear size L equally into cubic boxes of size l for which L/l is an integer. This method is the least numerically expensive while having a good reliability.