Model of the commensurate charge-density wave in bilayer cuprate superconductors

We propose a two-layer Ising model of the commensurate charge-density wave (CCDW) that can form in bilayer cuprate superconductors such as YBa₂Cu3O_7-δ (YBCO) and Bi₂Sr₂CaCu₂O_8+δ (Bi2212). The excess oxygen concentrations on neighboring oxygen sites within the superconducting CuO₂ layers is opposite in sign, and is represented in this model by the repulsive interaction J. There is also a repulsive interaction J' between excess oxygen concentrations on near-neighbor interlayer sites, where J' > J. We calculated the partition function for continuous blocks of NM11 sites within the same layer and NM12 sites containing both layers. We found that for all of the blocks studies, in the limit that J'→ ∞, the effective coupling between the intralayer oxygen sites becomes 2J. This implies that the bilayer cuprates are likely to have a stronger CCDW that are single layer cuprates such as Bi₂Sr_2-xLa_xCuO_6+y (Bi2201). This implies also that the enhanced emission power observed in underdoped Bi2212 may be stabilized by the CCDW. In addition, the spatial form of the CCDW has d_x²-y² symmetry that is rotated by 45°from the Cu-Cu near-neighbor directions, suppressing the superconducting order parameter in those directions. In addition, the symmetry of the CCDW is difficult to distinguish from the orbital symmetry of the superconducting order parameter, and has likely confused many workers.