In the case of superconductors whose electrons attract each other only if they are near certain centers, the question arises of how many such centers are needed to make the ground state superconducting? We shall examine it in the context of a random U Hubbard model. In short, we study the case where
Ui is $\ensuremath{-}|U|$ and 0 with probability c and $1\ensuremath{-}c,$ respectively, on a lattice whose sites are labeled i using the Gorkov decoupling and the coherent potential approximation. We argue that for this model there is a critical concentration
c0 below which the system is not a superconductor.
We study the effect of random dilution of attraction centers on electron pairing in a generalization of the negative
U Hubbard model where the interaction
Ui, defined on the two dimensional lattice, can be
−∣U∣ and 0 with probability
c and
1−c depending on the lattice site
i. Using the determinant quantum Monte Carlo approach, we find the critical concentration
c0 of negative centers which leads to superconductivity, and show how the evolution of the local density on the two types of sites lends insight into the formation of global phase coherence.
We have considered the half-filled disordered attractive Hubbard model on a square lattice, in which the on-site attraction is switched off on a fraction
f of sites, while keeping a finite
U on the remaining ones. Through quantum Monte Carlo simulations for several values of
f and
U and for system sizes ranging from $8\ifmmode\times\else\texttimes\fi{}8$ to $16\ifmmode\times\else\texttimes\fi{}16$, we have calculated the configurational averages of the equal-time pair structure factor
Ps and, for a more restricted set of variables, the helicity modulus ${\ensuremath{\rho}}_{s}$, as functions of temperature. Two finite-size scaling Ans\"atze for
Ps have been used: one for zero temperature and the other for finite temperatures. We have found that the system sustains superconductivity in the ground state up to a critical impurity concentration
fc, which increases with
U, at least up to
U=4 (in units of the hopping energy). Also, the normalized zero-temperature gap as a function of
f shows a maximum near $f\ensuremath{\sim}0.07$ for $2\ensuremath{\lesssim}U\ensuremath{\lesssim}6$. Analyses of the helicity modulus and of the pair structure factor led to the determination of the critical temperature as a function of
f for
U=3, 4, and 6: they also show maxima near $f\ensuremath{\sim}0.07$, with the highest
Tc increasing with
U in this range. We argue that, overall, the observed behavior results from both the breakdown of charge-density-wave-superconductivity degeneracy and the fact that free sites tend to ``push'' electrons toward attractive sites; the latter effect being more drastic at weak couplings.
The ground-state instabilities for a one-dimensional lattice system of electrons with onsite (Hubbard) and bond-site (hopping) interactions are analyzed in a perturbative approach. The zero temperature phase diagram at different band fillings is drawn; an attractive (repulsive) bond-site interaction favors the appearance of a superconductor state at low concentrations of electrons (holes). A comparison with the exact results for the Hubbard model and previous works for particular cases is also discussed.
Tweaking the Hubbard model Modeling high-temperature superconductivity (HTS) remains extremely challenging. Many researchers believe that the simplest model that captures HTS is the Hubbard model, which accounts for interactions and allows for electrons to hop from one site of a lattice to another. However, even just determining whether the ground state of this model supports superconductivity is tricky. Jiang and Devereaux undertook an extensive computational study based on a method known as density matrix renormalization group. They found that for a particular concentration of empty lattice sites, superconductivity indeed appears as a long-range state, but only if electrons are allowed to hop to sites that are next to their immediate neighbors on the lattice. Science , this issue p. 1424
We use the correlated-random-field approximation and a conditional coherent-potential approximation to study the ground-state phase diagram of the one-band Hubbard model. Our approach incorporates both spin and electron correlations. It has been found that for certain values of the parameters of the model, in addition to paramagnetic, ferromagnetic, antiferromagnetic, and spin-glass or spin-liquid phases found in our earlier studies, a phase-separated phase is found to be favored for 0.7\ensuremath{\le}n\ensuremath{\le}1.0 and U/B\ensuremath{\ge}2 in good agreement with results obtained in the t-J model using the technique of the 1/N expansion. The present approach also allows one to watch the dependence of the electron density of states on the number of electrons per site and gives a single physical picture for the occurrence of a metal-insulator transition. Implications of these results for the existence of superconducting ground state as well as comparison to other studies will be briefly discussed.