Superconductivity versus phase separation, stripes, and checkerboard ordering: A two-dimensional Monte Carlo study

Abstract

Using Monte Carlo techniques, we study a simple model which exhibits a competition between superconductivity and other types of order in two dimensions. The model is a site-diluted $XY$ model, in which the $XY$ spins are mobile, and also experience a repulsive interaction extending to one, two, or many shells of neighbors. Depending on the strength and range of the repulsion and spin concentration, the spins arrange themselves into a remarkable variety of patterns at low temperatures $T$, including phase separation, checkerboard order, and straight or labyrinthine patterns of stripes, which sometimes show hints of nematic or smectic order. This pattern formation profoundly affects the superfluid density $\ensuremath{\gamma}$. Phase separation tends to enhance $\ensuremath{\gamma}$, checkerboard order suppresses it, and stripe formation increases the component of $\ensuremath{\gamma}$ parallel to the stripes and reduces the perpendicular one. We verify that $\ensuremath{\gamma}(T=0)$ is proportional to the effective conductance of a random conductance network whose conductances equal the couplings of the $XY$ system. Possible connections between the model and real materials, such as single high-${T}_{c}$ cuprate layers, are briefly discussed.