We calculate the Casimir interaction between parallel planar crystals of Au and the anisotropic cuprate superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ (BSCCO), with BSCCO’s optical axis either parallel or perpendicular to the crystal surface, using suitable generalizations of the Lifshitz theory. We find that the strong anisotropy of the BSCCO permittivity gives rise to a difference in the Casimir force between the two orientations of the optical axis, which depends on distance and is of order 10–20 % at the experimentally accessible separations $10\text{to}5000\mathrm{nm}$.

• Received 17 March 2008

DOI:https://doi.org/10.1103/PhysRevA.78.042110