s-wave superconductivity phase diagram in the inhomogeneous two-dimensional attractive Hubbard model

Abstract

We study s-wave superconductivity in the two-dimensional square lattice attractive Hubbard Hamiltonian for various inhomogeneous patterns of interacting sites. Using the Bogoliubov-de Gennes (BdG) mean field approximation, we obtain the phase diagram for inhomogeneous patterns in which the on-site attractive interaction Ui between the electrons takes on two values, Ui = 0 and −U/(1 − f ) (with f the concentration of non-interacting sites) as a function of average electron occupation per site n, and study the evolution of the phase diagram as f varies. In certain regions of the phase diagram, inhomogeneity results in a larger zero temperature average pairing amplitude (order parameter) and also a higher superconducting (SC) critical temperature Tc, relative to a uniform system with the same mean interaction strength (Ui = −U on all sites). These effects are observed for stripes, checkerboard, and even random patterns of the attractive centers, suggesting that the pattern of inhomogeneity is unimportant. The phase diagrams also include regions where superconductivity is obliterated due to the formation of various charge ordered phases. The enhancement of Tc due to inhomogeneity is robust as long as the electron doping per site n is less than twice the fraction of interacting sites [2(1 − f )] regardless of the pattern. We also show that for certain inhomogeneous patterns, when n = 2(1 − f ), increasing temperature can work against the stability of existing charge ordered phases for large f and as a result, enhance Tc. PACS numbers:I. MOTIVATION Fascination with inhomogeneous superconducting (SC) phases extends back several decades, with many conferences and monographs having been devoted to the subject.1,2,3 For conventional superconductors, the inhomogeneities were extrinsic, arising from a granular nature of samples or due to the deliberate synthesis of disordered built materials or films. The high temperature superconductors (HTS) introduced new aspects into this area of study. First, inhomogeneous states (normal and SC) seem to be intrinsic to HTS, at least in the underdoped regime, similar to quenched disorder in the metalinsulator transition in two dimensions.4,5 Secondly, the inhomogeneity occurs on a smaller length scale of just a few lattice constants as evidenced by scanning tunneling spectroscopy (STS) at the nanoscale. 6,7,8,9 In addition, the strong electronic correlation in HTS cuprates plays a major role in the elucidation of the inhomogeneous SC state; indeed the inhomogeneity is widely believed to arise from the strong intra-atomic interactions that tend to frustrate bandlike conduction, to induce local magnetic moments, and to drive charge and spin order on a few lattice constant scale. The study of the doped Mott insulating phase has been one of the most active areas of theoretical study of HTS, one that has proven to be unexpectedly complex and rich and which is still under intense exploration and debate. Surprisingly, holes doped into the high temperature superconductors tend to arrange themse...

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