Optical study of an untwinned (Bi_1.57Pb_0.43)Sr₂CaCu₂O _8+δ single crystal: ab-plane anisotropy

We report on the ab-plane polarized reflectance of an untwinned (Bi_1.57Pb_0.43)Sr₂CaCu₂O _8+δ single crystal over the frequency range from 80 to 32 000 cm^-1 (10 meV-4 eV) at temperatures between 10 and 300 K. We find a clear anisotropy in the ab-plane optical conductivity above and below T_c, which is very similar to that formerly published data of Bi₂Sr₂CaCu₂O₈ (M.A. Quijada et al., Z. Phys. B 94, 255 (1994)). We employ both the one-component and two-component analyses to the optical data, which suggest that the normal-state infrared anisotropy of (Bi_1.57Pb_0.43)Sr₂CaCu₂O _8+δ originates not only from the mass anisotropy, but also from the scattering rate anisotropy. Our results provide evidence that the electronic structures within the CuO₂ plane are anisotropic. In the superconducting state, there is a definite ab-plane anisotropy to the far-infrared absorption. This anisotropy could be due either to anisotropy of the superconducting gap or to anisotropy of the mid-infrared component to the conductivity. We also observe the superconducting condensate is anisotropic: The value of the superconducting penetration depth in the a-direction is slightly smaller than that along the b-axis.