Superconducting pairing amplitude and local density of states in presence of repulsive centers

Abstract

We study the properties of superconductor in presence of a finite concentration of repulsive centers. The superconductor is described by the negative U Hubbard model while repulsive centers are treated as randomly distributed impurities with repulsive interaction. Analyzing the paring potential and local density of states at impurity sites we find a wide range of the system parameters where the π -like state could possibly be realized. Comparison of our results to the single repulsive center case is also given.Key words: superconductivity, non-magnetic impurities, tunneling PACS: 74.20.-z; 74.25.-q; 74.40.+k; 74.50.+r A superconducting system is regarded as in the π-phase if there is a sign change of the order parameter between two subsystems. The simplest example is the junction made from two superconductors with the phase of the order parameter equal to π [1,2]. In this case Josephson current becomes negative in contrast to the usual 0-phase junction. Another example are granular high-Tc materials which can likely form network of microscopic π-junctions [3] between small regions with different phases of the order parameter. In such systems the zero-energy Andreev bound states, zerobias conductance peaks, paramagnetic Meisner effect and spontaneously generated currents take place [1,2]. In our recent report [4] we have considered a single impurity with repulsive interaction embedded in a swave superconductor on two dimensional lattice showing conditions which should be fulfilled to obtain the 'π' state. For a uniform embedding system such a state has been found in the limit of very strong repulsion at the impurity site. In the present paper we discuss an- * Corresponding author. Tel: +48-81-5381573; Fax: +48-81-5241004Email address: g.litak@pollub.pl (Grzegorz Litak ).other possibility. Our superconductor possesses a finite concentration of repulsive centers with random distribution. With such assumptions 'π' sates could appear for moderate values of repulsive interactions at impurities due to additional disorder in paring potential ∆i. The system is described by random U Hubbard model [5] with the Hamiltonianwhere i, j label sites on a square lattice, tij = −t is the hopping integral between nearest neighbor sites and µ is the chemical potential. Disorder is introduced through the random site interaction Ui. Depending on site i (i = A or B with binary alloy distribution A1−cBc) Ui describes attraction (UA < 0) or repulsion (UB > 0) between electrons with opposite spins occupying the same site. In the Hartree-Fock approximation [6] (we dropped the Hartree terms Ui niσ , and considered only the half field system n = 1, for simplicity) the corresponding Gorkov equation at zero temperature (T = 0) has the following form

Properties of the π state induced by impurities in a d-wave superconductor

“…In such systems the zero-energy Andreev bound states, zero-bias conductance peaks, paramagnetic Meisner effect and spontaneously generated currents take place [4,5]. The situation is also possible for paramagnetic impurities with strong on-site Coulomb repulsion are placed in classical s-wave superconductor [7,8,9]. Due to the proximity effect the SC order parameter is created on the impurity site but change its phase by π.…”