Nonmagnetic impurities in two-dimensional superconductors

Abstract

A numerical approach to disordered 2D superconductors described by BCS mean field theory is outlined. The energy gap and the superfluid density at zero temperature and the quasiparticle density of states are studied.The method involves approximate self-consistent solutions of the Bogolubovde Gennes equations on finite square lattices. Where comparison is possible, the results of standard analytic approaches to this problem are reproduced.Detailed modeling of impurity effects is practical using this approach. The range of the impurity potential is shown to be of quantitative importance in the case of strong potential scatterers. We discuss the implications for experiments, such as the rapid suppression of superconductivity by Zn doping in Copper-Oxide superconductors.

Gap Inhomogeneities and the Density of States in Disorderedd-Wave Superconductors

“…Another limitation of most SCTMA calculations is the use of a δ-function potential as an impurity model. While this simplifies the calculation substantially, numerical results hint that the detailed structure of the impurity potential may be important [8]. A related issue, which will be discussed at length in this Letter, is inhomogeneous order-parameter suppression.…”

“…Analytic expressions for Ω 0 (u 0 ) have been given for a symmetric band [2], and in this special instance the unitary limit Ω 0 → 0 coincides with u 0 → ∞. For a realistic (asymmetric) band, the relationship is more complex [3].For a finite concentration of impurities n i , the SCTMA predicts that the impurity resonances broaden, with tails which overlap at the Fermi energy, leading to a finite residual DOS ρ(0) [3][4][5][6][7][8]. The region over which ρ(E) ≈ ρ(0), the "impurity band", and has a width comparable to the scattering rate γ at E = 0.…”

“…For a finite concentration of impurities n i , the SCTMA predicts that the impurity resonances broaden, with tails which overlap at the Fermi energy, leading to a finite residual DOS ρ(0) [3][4][5][6][7][8]. The region over which ρ(E) ≈ ρ(0), the "impurity band", and has a width comparable to the scattering rate γ at E = 0.…”

Analysis of the Knight shift data on Li and Zn substituted YBa2Cu3O6+x

“…There is considerable support for using an extended impurity potential for modelling the effective impurity potential [26,27]. Here, it will be assumed that the effective interaction between an impurity located at site r 0 and a quasiparticle at r can be approximated by the static potential V eff (r 0 , r) = V 0 δ(r 0 , r) + V 1 4 α=1 δ(r, r 0 + ρ α ),…”

Density of states of ad-wave superconductor in the presence of strong impurity scatterers: A nonperturbative result

“…18 concluded that the density of states is finite above a very low energy scale (essentially the level spacing of a localization volume), below which a pseudo-gap appears. Early numerical simulations 19 seem to confirm finite density of states at zero energy.…”