Local Quasiparticle States around an Anderson Impurity in a d-Wave Superconductor: Kondo Effects

The Kondo effects of an Anderson impurity embedded into a d-wave superconductor is studied. Within the slave-boson mean-field approach, the derived Bogoliubov-de Gennes equations are solved via exact diagonalization. We show that a critical coupling strength, above which the Kondo effect takes place, exists regardless of whether the band particle-hole symmetry is present or not. The resonant quasiparticle peaks are found in the local density of states (LDOS) both directly at the impurity and around its neighbors, which is in sharp contrast to the case of nonmagnetic unitary impurities, where the LDOS vanishes on the impurity site.Comment: To appear in Physical Review B as a Rapid Communication (January 1, 2001

Local Quasiparticle States near a Unitary Impurity with Induced Magnetic Moment in a d-Wave Superconductor

The local quasiparticle density of states around a unitary impurity with a Kondo-like magnetic moment induced at its nearest neighbors in a d-wave superconductor is studied within the slave-boson mean-field approach. The Hamiltonian is exactly diagonalized and the results are obtained self-consistently. We show that the interference between the strong impurity potential scattering and the Kondo effect leads to novel quasiparticle spectra around the impurity, which are strikingly different from the case of a single unitary or magnetic impurity. The recent STM image of the local differential tunneling conductance around a Zn impurity in a high-T_c cuprate can be essentially explained if the blocking effect of BiO surface layer between the tip and probed CuO_2 plane [Zhu et al., Phys. Rev. B 62, 6207 (2000)] is taken into account.Comment: 4 pages, 3 ps figures, reference updated, typos remove

Some recent developments in quantization of fractal measures

We give an overview on the quantization problem for fractal measures, including some related results and methods which have been developed in the last decades. Based on the work of Graf and Luschgy, we propose a three-step procedure to estimate the quantization errors. We survey some recent progress, which makes use of this procedure, including the quantization for self-affine measures, Markov-type measures on graph-directed fractals, and product measures on multiscale Moran sets. Several open problems are mentioned.Comment: 13 page

Effect of unitary impurities in non-STM-types of tunneling in high-T_c superconductors

Based on an extended Hubbard model, we present calculations of both the local (i.e., single-site) and spatially-averaged differential tunneling conductance in d-wave superconductors containing nonmagnetic impurities in the unitary limit. Our results show that a random distribution of unitary impurities of any concentration can at most give rise to a finite zero-bias conductance (with no peak there) in spatially-averaged non-STM type of tunneling, in spite of the fact that local tunneling in the immediate vicinity of an isolated impurity does show a conductance peak at zero bias, whereas to give rise to even a small zero-bias conductance peak in the former type of tunneling the impurities must form dimers, trimers, etc. along the [110] directions. In addition, we find that the most-recently-observed novel pattern of the tunneling conductance around a single impurity by Pan et al. [Nature (London) 403,746 (2000)] can be explained in terms of a realistic model of the tunneling configuration which gives rise to the experimental results reported there. The key feature in this model is the blocking effect of the BiO and SrO layers which exist between the tunneling tip and the CuO_2 layer being probed.Comment: 9 pages, 7 ps-figures, to appear in Phys. Rev. B (Sep. 1, 2000); typos corrected, references added, figure 6 changed to expand the explanation on recent experimental measurements by S.H. Pan et al. [Nature (London) 403, 746 (2000)

Matrix Elements of Four-quark Operators Relevant to Lifetime Difference \Delta \Gamma_{B_s} from QCD Sum Rules

We extract the matrix elements of four quark operators O_{L,S} relevant to the B_s and \bar B_s life time difference from QCD sum rules. We find the vacuum saturation approximation works reasonably well, i.e., within 10%. We discuss the implications of our results and compare them with the recent lattice QCD determination.Comment: 11 pages, 4 eps figures, Latex. Some reference renewe

Quantum interference in dirty d-wave superconductors

The local differential tunneling conductance on a Zn impurity in a disordered d-wave superconductors is studied. Quantum interference between many impurities leads to definitive quasiparticle spectra. We suggest that an elaborate analysis on impurity-induced spectra with quantum interference effect included may be able to pin down the sign and strength of the scattering potential of a Zn impurity in low density limit. Numerical simulations calculated with appropriately determined impurity parameters are in satisfactory agreement with the observations from scanning tunneling microscopy (STM) experiments even in subtle details