Destruction of superconductivity by impurities in the attractive Hubbard model

Abstract

We study the effect of U = 0 impurities on the superconducting and thermodynamic properties of the attractive Hubbard model on a square lattice. Removal of the interaction on a critical fraction of fcrit ≈ 0.30 of the sites results in the destruction of off-diagonal long range order in the ground state. This critical fraction is roughly independent of filling in the range 0.75 < ρ < 1.00, although our data suggest that fcrit might be somewhat larger below half-filling than at ρ = 1. We also find that the two peak structure in the specific heat is present at f both below and above the value which destroys long range pairing order. It is expected that the high T peak associated with local pair formation should be robust, but apparently local pairing fluctuations are sufficient to generate a low temperature peak. PACS numbers:The study of the interplay of disorder and interactions is one of the central problems in condensed matter physics, and has been analyzed through a wide range of techniques. [1,2,3,4,5,6,7] Quantum Monte Carlo (QMC) is one approach which has been applied only relatively recently, but now a number of investigations of the disordered, repulsive Hubbard model exist, both on finite lattices [8,9,10] and within dynamical mean field theory where the momentum dependence of the selfenergy is neglected.[11] Several interesting effects, including the possibility of the enhancement of T Neel by site disorder [11], the occurrence of a Mott transition away from half-filling, [12] and a change in the temperature dependence of the resistivity from insulating to metallic behavior when interactions are turned on, [13] have been observed. These studies have also explored different types of disorder, including randomness in the chemical potential, hopping, Zeeman fields, and on-site interaction. [14] At half-filling, some of these disorder types preserve particle-hole symmetry which has an important effect both on the behavior of the static (magnetic and charge) correlations, [8] and on the conductivity.[15]The work described above concerns the interplay of randomness and repulsive interactions. Superconductorinsulator transitions provide a motivation to explore models with an effective attractive electron-electron interaction, since these novel transitions are widely studied experimentally, especially in two dimensions. [16,17,18,19] However, QMC studies of models like the attractive Hubbard Hamiltonian with disorder are less numerous than for the repulsive case. [13,20] Previous work focused on locating the critical site disorder strength for the insulating transition and determining the value of the conductivity and its possible universality, [21] and on the interplay between the loss of phase coherence and the closing of the gap in the density of states. [22,23] Another particularly interesting application of the attractive Hubbard model with disorder is the question of how inhomogeneities and pairing affect each other in high-temperature superconductors. The attractive Hubbard model is the simplest Hamilton...

Pair correlations and the survival of superconductivity in and around a superconducting impurity

“…On the other hand, If U lies within the band the hole excitations are periodic, and generate long-range pair correlations. While this effect may be due to the finite size of the normal system, these long-ranged correlations may have a crucial effect 16 on the global behaviour of a system with many negative-U impurities (so-called dilute negative-U model 14,17,18 ), as they determine the effective Josephson coupling between the different impurities. …”

Stability of the superfluid state in a disordered one-dimensional ultracold fermionic gas

“…Phase rigidity: Pairing structure factor A popular choice [25] is the averaged equal-time pairing structure factor,…”

“…Finally we mention that the effect of disorder in Fermi gases of higher dimensions has been investigated in [23] using mean field techniques and neglecting Anderson localization effects [24]. For numerical studies on the attractive Hubbard model in a disordered potential we refer to [25].…”

Disordered two-dimensional superconductors: Roles of temperature and interaction strength

“…As discussed previously, 18 a useful quantity to locate the transition is the configurationally averaged equal-time pairing structure factor,…”