Narrow Results

The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction has been studied. Analytic expressions for the fermion Green function, its spectral density and the density of states are derived. The resultant single-particle Green function clearly demonstrates non-Fermi liquid behavior. The results show that as the temperature increases through the 2D critical temperature the width of the quasiparticle peaks broadens significantly. At the same time one retains the gap in quasiparticle spectrum. The spectral density for the dynamical fluctuations can also be obtained. Clearly the dynamical fluctuations fill the gap giving the observed pseudogap behaviour.

We study the effects of low-energy nodal quasiparticles on the classical phase fluctuations in a two-dimensional d-wave superconductor. The singularities of the phase-only action at T→0 are removed in the presence of disorder, which justifies using an extended classical XY-model to describe phase fluctuations at low temperatures.

The temperature variations of electrical resistivity have been measured on pure and 5 wt% Ag doped (La_1.6Y_0.4)Ba₂Ca_0.8Cu_4.8O_z superconductors. These data were analyzed in terms of fluctuation-induced excess conductivity in the mean field regime by using the Aslamazov–Larkin (AL), Lawrence–Doniach (LD) and Maki–Thompson (MT) models. The fluctuations in the amplitude of order parameter are found to be two dimensional in nature in the mean field region. The estimated values of the average phase breaking time τ_ϕ (100 K) are found to be 3.9×10^-16s and 4.6×10^-16s for pure and Ag doped samples respectively. The resistivity data were also analyzed in terms of excess conductivity due to phase fluctuations of the order parameter in the paracoherence region. The critical exponent is found to be mostly comparable to that of the 3D XY ferromagnet in the vicinity of zero resistivity temperature and the diluted Heisenberg model at a higher temperature.

We investigate the Ginzburg–Landau (GL) functional to infinite orders. The GL functional can be substituted for a renormalized infinite series method (RISM). The Curie–Weiss law happens only if the GL functioal has a divergence using an adjustable infinite series. It is shown that the superconducting gap is not contributed by phase fluctuations in cuprate superconductors using the RISM. The results by the RISM applied to ferroelectric materials are similar to those by the GL theory. For ferromagnetic materials, the RISM is equivalent to the GL theory, and is applied to functionals to show a Curie–Weiss type susceptibility, χ.

In fullerides, the deviation of the superconducting energy gap from BCS prediction, especially close to T_C, in experiments is an old, but not well-understood problem. If phase fluctuations are considered, the calculated temperature temperature of the energy gap is accurately consistent with the experimental one, and the deviation of the gap is a certain result.

We analyze a simple model of a scalar optical wave with partial coherence. The model is devised to describe the influence on the coherence of the wave, of the statistical properties of its random phase, including both the second-order statistics (phase correlation) — which is classic, but also the first-order statistics (phase distribution) — which is nonclassic. Expectedly, upon increasing the disorder of the fluctuating phase through a reduction of its correlation duration, the model shows that the coherence of the wave is always reduced. By contrast, upon increasing the disorder of the fluctuating phase through an increase of its dispersion, the model reveals that the coherence of the wave can sometimes be enhanced. This beneficial consequence of an increase in disorder is related to the phenomenon of stochastic resonance or improvement by noise in signal processing.

It is well known that the metal-insulator transition in two dimensions for non-interacting fermions takes place at infinitesimal disorder. In contrast, the superconductor-to-insulator transition takes place at a finite critical disorder (on the order of V_c ~ 2t), where V is the typical width of the distribution of random site energies and t is the hopping scale. In this article we compare the localization/delocalization properties of one and two particles. Whereas the metal-insulator transition is a consequence of single-particle Anderson localization, the superconductor-insulator transition (SIT) is due to pair localization – or, alternatively, fluctuations of the phase conjugate to pair density. The central question we address is how superconductivity emerges from localized single-particle states. We address this question using inhomogeneous mean field theory and quantum Monte Carlo techniques and make several testable predictions for local spectroscopic probes across the SIT. We show that with increasing disorder, the system forms superconducting blobs on the scale of the coherence length embedded in an insulating matrix. In the superconducting state, the phases on the different blobs are coherent across the system whereas in the insulator long-range phase coherence is disrupted by quantum fluctuations. As a consequence of this emergent granularity, we show that the single-particle energy gap in the density of states survives across the transition, but coherence peaks exist only in the superconductor. A characteristic pseudogap persists above the critical disorder and critical temperature, in contrast to conventional theories. Surprisingly, the insulator has a two-particle gap scale that vanishes at the SIT despite a robust single-particle gap.

It is well known that the metal-insulator transition in two dimensions for non-interacting fermions takes place at infinitesimal disorder. In contrast, the superconductor-to-insulator transition takes place at a finite critical disorder (on the order of V_c ∼ 2t), where V is the typical width of the distribution of random site energies and t is the hopping scale. In this article we compare the localization/delocalization properties of one and two particles. Whereas the metal-insulator transition is a consequence of singleparticle Anderson localization, the superconductor-insulator transition (SIT) is due to pair localization – or, alternatively, fluctuations of the phase conjugate to pair density. The central question we address is how superconductivity emerges from localized single-particle states. We address this question using inhomogeneous mean field theory and quantum Monte Carlo techniques and make several testable predictions for local spectroscopic probes across the SIT. We show that with increasing disorder, the system forms superconducting blobs on the scale of the coherence length embedded in an insulating matrix. In the superconducting state, the phases on the different blobs are coherent across the system whereas in the insulator long-range phase coherence is disrupted by quantum fluctuations. As a consequence of this emergent granularity, we show that the single-particle energy gap in the density of states survives across the transition, but coherence peaks exist only in the superconductor. A characteristic pseudogap persists above the critical disorder and critical temperature, in contrast to conventional theories. Surprisingly, the insulator has a two-particle gap scale that vanishes at the SIT despite a robust single-particle gap.