Far-infrared sphere resonance in isolated superconducting particles

A strong electric-dipole resonance has been observed in the far-infrared response of small isolated superconducting particles of ${\mathrm{La}}_{2\mathrm{-}\mathrm{x}}$ ${\mathrm{Sr}}_{\mathrm{x}}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathrm{y}}$, ${\mathrm{Nd}}_{1.85}$ ${\mathrm{Ce}}_{0.15}$ ${\mathrm{CuO}}_4$, and ${\mathrm{Bi}}_4$ ${\mathrm{Ca}}_3$ ${\mathrm{Sr}}_3$ ${\mathrm{Cu}}_4$ ${\mathrm{O}}_{\mathit{z}}$, but not in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{y}}$. Because of the small-particle boundary conditions, the bulk conductivity δ function of the superconducting condensate translates from zero to finite frequency, so that sphere resonance studies of the oxide superconductors provide important information about a dc property, the London penetration depth. The far-infrared data show that the frequency and strength of this resonance decrease as the temperature approaches $T_c$ from below, and no resonance is observed above $T_c$. The effect of a magnetic field on this feature is similar to that produced by raising the temperature. The ${\mathrm{La}}_{2\mathrm{-}\mathrm{x}}$ ${\mathrm{Sr}}_{\mathrm{x}}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathrm{y}}$ system has been studied in some detail.