We consider a Hubbard type Hamiltonian for a two-dimensional superconducting plane with a tight-binding dispersion relation. In addition, the energy gap is considered to be either an extended s-wave, a d-wave form or a combination of both. We then derive the resultant coupled field equations of motion for the spin-up and spin-down fields. The equations are of a highly nonlinear character but are still tractable. The s-wave and d-wave regimes are treated separately. It is shown that the superposition of s- and d-wave components results in the emergence of striped patterns of superconducting order parameter densities and of square and triangular order parameter distributions. (C) 1999 Published by Elsevier Science B.V. All rights reserved.
Understanding competing instabilities in systems with correlated fermions remains one of the holy grails of modern condensed matter physics. Among the fermionic lattice models used to this effect, the extended Hubbard model occupies a prime place due to the potential relevance of its repulsive and attractive versions for both electronic materials and artificial systems. Using the recently introduced multichannel fluctuating field approach, we address the interplay of fluctuations in the charge density wave,
s-wave superconducting, and phase separation channels in the attractive extended Hubbard model. Despite the fact that this model has been intensively studied for decades, our approach allows us to identify a phase that has not been analyzed before and which is characterized by the coexistence of collective
s-wave superconducting and phase separation fluctuations. Our findings resonate with previous observations of interplaying phase separation and superconducting phases in electronic systems, most importantly in high-temperature superconductors.