Gap inhomogeneities and the density of states in disordered d-wave superconductors

We report on a numerical study of disorder effects in 2D d-wave BCS superconductors. We compare exact numerical solutions of the Bogoliubov-de Gennes (BdG) equations for the density of states rho(E) with the standard T-matrix approximation. Local suppression of the order parameter near impurity sites, which occurs in self-consistent solutions of the BdG equations, leads to apparent power-law behavior rho(E) approximately |E|(alpha) with nonuniversal alpha over an energy scale comparable to the single-impurity resonance energy Omega(0). We show that the novel effects arise from static spatial correlations between the order parameter and the impurity distribution.     

Pair breaking parameter of two-dimensional dirty superconductors

Intrinsic mechanism of pair breaking is given for dirty superconducting films. Dynamical interaction between electrons such as Coulomb interaction plays an essential role. The diffusion processes of both density- and pair-fluctuations are also important. The problem of the Thompson's parameter for the Maki term of fluctuation conductivity is solved and the correct dependence of the parameter of the sheet resistance R_sq is given.     

Spin and density fluctuations in disordered narrow-band superconductors

A tight-binding theory of strong-coupling superconductivity is formulated on the basis of a random lattice model with local electron-electron and contact-type electronphonon interactions. Functional-derivative technique yields a systematic deduction of the electron self-energy in terms of Coulomb repulsion, density and spin fluctuations. A novel procedure is proposed to average disordered Berk-Schrieffer-type equations. The phonon ( ^ph)-, Coulomb ^C-, and paramagnon ( ^m)-mediated coupling parameters entering the superconductingT _c are calculated for diffusive behaviour in dirty systems or alloys. The critical reduction ofT _c due to ^m differs from the logarithmic singularity for a clean sample.     

On edge states in superconductors with time inversion symmetry breaking

The efficiency of conversion of the heat flux into hard x radiation (HXR) is analyzed, via time-dependent two-temperature one-dimensional non-LTE-radiation-hydrodynamic numerical modeling, for a heat-to-radiation flux converter linked to the edge of a low-atomic-number hot Z-pinch. The domain of parameters in this scheme is found where about the same HXR yield can be achieved at values of input energy which are an order of magnitude lower than in the conventional scheme of a radially imploding plasma. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 7, 502–506 (10 April 1997) Published in English in the original Russian Journal. Edited by Steve Torstveit.     

Influence of pair breaking and phase fluctuations on disordered high Tc cuprate superconductors

Electron irradiation has been used to introduce point defects in a controlled way in underdoped and optimally doped YBa(2)Cu(3)O(7-delta) crystals. This technique allows us to perform very accurate measurements of T(c) and of the ab plane resistivity in a wide range of defect contents x(d) down to T(c)=0. The variation of T(c) and of the transition width with x(d) do not follow current predictions of pair-breaking theories. The data are rather compatible, at least for the highly damaged regime, with the expected influence of phase fluctuations. These results open new questions about the evolution of the defect induced T(c) depression over the phase diagram of the cuprates.     

Pair density wave in the pseudogap state of high temperature superconductors

Recent scanning tunneling microscopy experiments of Bi(2)Sr(2)CaCu(2)O(8+delta) have shown evidence of real-space organization of electronic states at low energies in the pseudogap state [Science 303, 1995 (2004)]]. We argue based on symmetry considerations as well as model calculations that the experimentally observed modulations are due to a density wave of d-wave Cooper pairs without global phase coherence. We show that scanning tunneling microscopy measurements can distinguish a pair density wave from more typical electronic modulations such as those due to charge density wave ordering or scattering from an on site periodic potential.     

Pair effects in the impurity band density of states

Results of a simple two center approximation for impurity bands are presented. For low concentrations the density of states deviates strongly from the single site CPA and agrees well with numerical “exact” results.     

On spectral density of electronic states in disordered systems

In the present paper, the averaged spectral density of electronic states, 〈?(k, E)〉, has been computed for three-dimensional disordered systems with spherical well type atomic potentials. The formula for 〈?(k, E)〉 is derived by using a realistic perturbational approach that takes propagator modification into account, together with a handy approximation due toBallentine. 〈?(k, E)〉 has been computed for various sets of potential strength and concentration, and the dependence of 〈?(k, E)〉 upon these parameters has been discussed. The motivation behind the computations reported here, is to examine the circumstances under which the electron motion in disordered systems is expected to be almost free electronic. Our principal finding is that a simultaneous existence of weak electron-scatterer interaction-potential and high density of scatterers would tend to make the motion of an electron in a disordered system almost like that of a free one.     

Bounds on the density of states in disordered systems

For a class of tight-binding models governed by short-range one-particle Hamiltonians with site-diagonal and/or off-diagonal disorder and continuous distribution of the matrix elements it is proven that the averaged density of states does neither vanish nor diverge inside the band. This refutes for these models conjectures that the density of states vanishes or diverges at the mobility edge.Work supported in part by the Sonderforschungsbereich 123 Stochastic Mathematical Models of the Deutsche Forschungsgemeinschaft     

Low energy density of states in several disordered systems

Disordered systems of arbitrary dimension consisting of randomly distributed scatterers are studied in the low energy limit (Roger Waxler, Ph.D. thesis, Columbia University). We evaluate the density of electronic energy levels for long range, attractive, and electric dipole scatterers.     

Bounds on the density of states in disordered systems

In magnetic systems the radio frequency fieldH ₁ seen by the nuclei is often enhanced by a factor . If the atomic spins are distributed in multi directions, as in Bloch walls or spin glasses, one has to consider a spatial distribution (r) of enhancement factors. The usual way to define a mean enhancement factor is shown to lead to inconsistent results giving rise to errors up to more than 100%. One has to distinguish between two mean factors, and , depending on measuring conditions. Their deviations from the true value are discussed.     

Local density of states of vortex state in mesoscopic superconductors

We study local density of states (LDOS) of vortex state in mesoscopic square superconductors with Bogoliubov-de Gennes (BdG) equation. We develop one effective numerical method based on the finite element method to self-consistently solve the BdG equation. The LDOS for various vortex states is obtained. Our results about the single vortex show that the LDOS has the particle-hole asymmetry and the results for one- and two-vortex state agree very well with the experimental observation. Besides, we predict the LDOS of multi-vortex states, which is crucial for the further STM/STS experimental study of vortex state in mesoscopic superconducting system.     

Singularity of the vortex density of states in d-wave superconductors

In d-wave superconductors, the electronic density of states (DOS) induced by a vortex exhibits a divergence at low energies: N _vortex(E) ∼1/|E|. This divergence is the result of gap nodes in the spectrum of excitation outside the vortex core. The heat capacity in two regimes, T ²/T _c ² ≫ B/B _c 2 and T ²/T _c ² ≪ B/B _c 2, is discussed. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 9, 641–645 (10 November 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Singularity in the density of states of quasi-one-dimensional disordered systems

We have calculated the correction to the density-of-states in two-dimensional weakly disordered systems. It is shown that the electron-electron interaction gives rise to a singularity in the density-of-states at the Fermi level, the form of which is very sensitive to the width of the sample. The transition from a two-dimensional behaviour to the quasi-one-dimensional regime is discussed. The effects should be observable by electron tunnelling measurements.