Strengthened correlations near [110] edges of $d$-wave superconductors in the t-J model with the Gutzwiller approximation

Abstract

We report results of a study of strongly correlated $d$-wave superconducting slabs within a t-J model solved using the statistically consistent Gutzwiller approach. For different dopings, we model slabs cut at 45$^\circ$ relative to the main crystallographic $ab$-axes, i.e., [110] orientation, and conclude that quasiparticle charge is drawn to the edges. Thus, the correlations are locally strengthened, and a region near the edge is closer to the Mott insulating state with reduced hopping amplitudes on the links. Superconductivity is locally weakened near the edges in the correlated state, and the spectral weight of zero-energy Andreev bound states is substantially reduced compared to weak coupling theory. The renormalization of the edge states leaves no room for an extended $s$-wave component to form for hole dopings ranging from strongly underdoped to slightly overdoped.