Consistent picture of electronic Raman scattering and infrared conductivity in the cuprates

Impurity effects in the cuprates have played a major role in clarifying the nature of unconventional superconductivity. Via the change in the density of states ~DOS! near the Fermi level, crossover behavior of low-temperature transport and thermodynamics quantities could be explored as a testing ground for unconventional pairing. Examples include the T to T crossover in the low-temperature magnetic penetration depth l(T), T to T crossover in the NMR rate, and the v to v crossover in the low-frequency B1g Raman response. Simple theories based on nearly resonant scattering in the impurity T-matrix approximation ~‘‘dirty’’ d wave! have accounted for these behaviors seen in materials of various quality and impurity dopings. However, several inconsistencies arise when attempting to put together a complete picture. First, the magnitude of the impurity scattering needed to fit l(T) and the extrapolated T50 resistivity are generally much smaller than those needed to fit the measured frequency dependence of the infrared conductivity ~IR! and the Raman response. In particular, the impurity scattering rate 1/t imp52G needed to fit the IR on high-quality Y-123 was 100 times larger than that needed to fit microwave measurements, while values of G/D0 ranging up to 0.5 were needed to interpret the Raman data taken on Bi-2201, and some samples of Tl-2201 ~Ref. 4! and Hg-1223. Second, the ‘‘universal’’ dc conductivity s(v→0,T50)5(e2/2p\)j/a ~Ref. 6! has not been convincingly observed and the low-temperature variation of the conductivity ds(T) changes slower than T2. Third, the transition temperature Tc is only moderately reduced by planar impurities compared to Abrikosov-Gorkov theory ~by about a factor of 2–3!. Lastly, the residual resistivity obtained for Zn-doped Y-123 suggests that a strong contribution is present in d-wave scattering channels. These inconsistencies reveal that the usual treatment of pointlike s-wave impurities in a T-matrix approach may be too naive and neglects electronic correlations. Experimental evidence from transport measurements in Zn-doped Y-BaCu-O have revealed that the a single impurity embedded in the CuO2 plane disturbs the local environment and yields an effective scattering cross-section diameter of Zn of 4.2 Å, and is thus extended. Theoretical studies have shown that static vacancies in a Heisenberg antiferromagnet en-