Local quasiparticle states around an Anderson impurity in ad-wave superconductor: Kondo effects

Abstract

The mutual influence between a Kondo impurity and a d-wave superconductor is numerically studied within the slave-boson mean-field approach. The Bogoliubov-de Gennes type equations are derived and solved using 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. In the Kondo regime the double 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 at the impurity site.PACS numbers: 74.25Jb, 72.15.Qm, 74.50.+r, 73.20.Hb The identification of d-wave pairing state in high-T c superconductors [1] has renewed much interest in lowenergy quasiparticle states in unconventional superconductors. Different from conventional s-wave superconductors having a constant energy gap, the d-wave superconductors have an anisotropic energy gap which changes sign along the nodal directions on the essentially cylindrical Fermi surface. The anisotropy of the energy gap makes the d-wave superconductors very sensitive to impurity or other potential scattering, in contrast to the s-wave superconductors which, as dictated by the Anderson theorem [2], are almost unaffected by the presence of nonmagnetic impurities. As an important signature of the sign change of d-wave order parameter (OP), Balatsky, Salkola and co-workers [3,4], based on the T-matrix approximation, theoretically predicted that a strong atomic-like nonmagnetic impurity can induce a virtual bound state. Later studies [5,6] showed that the resonant state would show up in the local density of states (LDOS), which could be measured by the local differential tunneling conductance. Recent scanning tunneling spectroscopy measured on high-T c superconductor Bi 2 Sr 2 CaCu 2 O 8+δ (BSCCO) with individual atomicscale defects [7] or strong impurities [8,9], has provided strong evidence for the existence of low-energy quasibound states. Especially, the experiment by Pan et al. [9] on the observation of quasiparticle resonant states has a high spatial and energy resolution and the identity of impurity atoms is known in a controlled way. Very interestingly, the imaging of the effect of a single zinc (Zn) impurity atom showed the strongest intensity of the LDOS at resonance directly on the Zn atom, which is opposite to the earlier theories [3][4][5][6]. In our previous work [10], we explained the novel pattern of the tunneling conductance in terms of the blocking effect of the BiO and SrO layers which exist between the tunneling tip and the CuO 2 layer being probed. This explanation may not exclude other possibilities and needs further experimental justification [11]. Although almost all existing theories are treating the Zn atom as a static potential scatterer, there exists a few experiments [12] indicating that Zn impurity may possess a magnetic moment. It is now an appropriate ti...

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