Figure 1

Energy of (a) the best orbital current wf and of (b) the best spin-density wave wf. The reference was taken as the projected Fermi sea (full Jastrow projector). Inset of (a): The symmetry of the best current phase found (${\Theta }_2$ pattern in the notations of 4). Although the OC phase is stable on an intermediate size 16 copper lattice, the energy gain is strongly reduced when the size increases. To the accuracy of the calculation, we did not find any energy optimization on a 100 Cu lattice for the OC instability.Reuse & Permissions

Figure 2

Circulation of current around a $p_x-p_z-p_y$ plaquette (triangles) and around a $p_x-d_{3z2-r2}-p_y$ plaquette (squares) measured in our best variational ansatz for the eight-band Hubbard model. The phenomenological parameter $\eta$ renormalizes the amplitudes of the out-of-plane transfer integrals. The symmetry of the OC pattern is ${\Theta }_2$ as follows: There are (a) two out-of-plane current loops in the upper pyramid and (b) two current loops in the Cu plane. Finally, the current pattern in the lower pyramid (not shown) is obtained by a horizontal mirror reflection of the upper pyramid. The calculations were done at $x=0.125$ hole doping, and with periodic boundary conditions. Inset: Energies for both the SDW wf and the circulating current (CC) ones showing the stabilization of the CC phase for $\eta >1.2$.Reuse & Permissions