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arXiv:cond-mat/0110013 · Journal of Experimental and Theoretical Physics

Superconductivity in the exactly solvable model of pseudogap state: The absence of self-averaging

É. Z. Kuchinskii, M. V. Sadovskii

Published Mar 1, 2002• 3 citations
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Abstract

The features of the superconducting state are studied in the simple exactly solvable model of the pseudogap state induced by fluctuations of the short-range “dielectric” order in the model of the Fermi surface with “hot” spots. The analysis is carried out for arbitrary short-range correlation lengths ξ corr . It is shown that the superconducting gap averaged over such fluctuations differs from zero in a wide temperature range above the temperature T c of the uniform superconducting transition in the entire sample, which is a consequence of non-self-averaging of the superconducting order parameter over the random fluctuation field. In the temperature range T > T c , superconductivity apparently exists in individual regions (drops). These effects become weaker with decreasing correlation length ξ corr ; in particular, the range of existence for drops becomes narrower and vanishes as ξ corr → 0, but for finite values of ξ corr , complete self-averaging does not take place.

DOI
10.1134/1.1469163

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The features of the superconducting state are studied in the simple exactly solvable model of the pseudogap state induced by fluctuations of the short-range “dielectric” order in the model of the Fermi surface with “hot” spots. The analysis is carried out for arbitrary short-range correlation lengths ξ corr . It is shown that the superconducting gap averaged over such fluctuations differs from zero in a wide temperature range above the temperature T c of the uniform superconducting transition in the entire sample, which is a consequence of non-self-averaging of the superconducting order parameter over the random fluctuation field. In the temperature range T > T c , superconductivity apparently exists in individual regions (drops). These effects become weaker with decreasing correlation length ξ corr ; in particular, the range of existence for drops becomes narrower and vanishes as ξ corr → 0, but for finite values of ξ corr , complete self-averaging does not take place.
We analyze the non-Fermi-liquid (NFL) behavior of the fluctuating gap model (FGM) of pseudogap behavior in both one and two dimensions. A detailed discussion of quasiparticle renormalization (Z-factor) is given, demonstrating a kind of marginal Fermi-liquid or Luttinger-liquid behavior and topological stability of the bare Fermi surface (the Luttinger theorem). In the two-dimensional case, we discuss the effective picture of the Fermi surface destruction both in the hot spot model of dielectric (AFM, CDW) pseudogap fluctuations and for the qualitatively different case of superconducting d -wave fluctuations, reflecting the NFL spectral density behavior and similar to that observed in ARPES experiments on copper oxides.
We analyze several almost exactly solvable models of the electronic spectrum of two-dimensional systems with well-developed short-range-order dielectric (e.g., antiferromagnetic) or superconducting fluctuations that give rise to an anisotropic pseudogap state in certain segments of the Fermi surface. We develop a recurrence procedure for calculating the one-electron Green’s function that is equivalent to summing all Feynman diagrams. The procedure is based on an approximate ansatz for higher order terms in the perturbation series. We do detailed calculations of the spectral densities and the one-electron density of states. Finally, we analyze the limits of the adopted approximations and some important points concerning the substantiation of these approximations.
The effect of random on-site disorder on s-wave (BCS) superconductors described by a two dimensional negative-U Hubbard model is studied using Bogoliubov-de Gennes (BdG) method. The mean field pairing amplitudes become spatially inhomogeneous at large values of disorder where the system breaks up into superconducting islands with large pairing amplitudes, separated by insulating strips. The amplitude fluctuations are correctly accounted for via BdG calculations, however it misses phase fluctuations which are inherent to low dimensions. The phase fluctuations affect superconducting properties strongly, and the effect is more pronounced in the limit of large disorder. We provide a close estimate of the actual transition temperature, Tcby incorporating phase fluctuations about the inhomogeneous BdG state. This is obtained by relating the jump in renormalized Ds(obtained from a self consistent Harmonic approximation on a phase-only Hamiltonian) at the Kosterlitz-Thouless (KT) transition and the KT transition temperature, TKTobtained from Ds(T) = (2/π)TKTas temperature tends to TKTfrom below. This yields opening of a large region sandwiched between [Formula: see text] (obtained by the vanishing of [Formula: see text]) and TKTwhere there is no phase coherence between the pairs, however amplitude correlations continue to exist, reminiscent of a pseudogap phase in high-Tcsuperconductors which is marked by short ranged preformed pairs without any definite phase relation between them. Further, the appearance of the superconducting islands from a homogeneous phase indicates the evolution of a system consisting of large and overlapping pairs to one that contains short and tightly bound pairs - a scenario termed as BCS-BEC crossover. We have investigated in details the crossover phenomenon as a function of disorder and confirmed it's existence at small values of electron concentration, however, absent at larger densities.
I study the effect of Coulomb interaction on superconducting order in a ddd-wave lattice superconductor at T=0T=0T=0 by considering the superconducting saddle point in the two-dimensional $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ model with a repulsion UUU. The theory of low-energy superconducting phase fluctuations around this saddle point is derived in terms of the effective hard-core bosons (representing the density of spin-up electrons and the phase of the order parameter), interacting with the fluctuating density of spin-down electrons. Whereas the saddle-point value of the superconducting gap is found to continuously increase towards half filling, the phase stiffness at T=0T=0T=0 has a maximum, and then decreases with further underdoping. Right at half filling the phase stiffness vanishes for large UUU. This argues that the pseudogap phenomenon of the type observed in cuprates is in principle possible without a development of any competing order, purely as a result of growing correlations in the superconducting state. Implications for the finite temperature superconducting transition and the effects of static disorder are discussed qualitatively.
We study the phase fluctuations in the normal state of generic two-dimensional superconducting systems with sss-wave pairing. The effect of phase fluctuations of the pairing fields can be dealt with perturbatively using disorder averaging, after we treat the local superconducting order parameter as a static disordered background. It is then confirmed that the phase fluctuations above the two-dimensional Berezinskii-Kosterlitz-Thouless transition lead to a significant broadening of the single-particle spectrum, giving birth to the pseudogap phenomenon. Quantitatively, the broadening of spectral weights near the BCS gap is characterized by the ratio of the superconducting coherence length and the spatial correlation length of the superconducting pairing order parameter. Our results are tested on the fermionic attractive-UUU Hubbard model on the square lattice, using the unbiased determinant quantum Monte Carlo method and stochastic analytic continuation.