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arXiv:cond-mat/0702457 · Physical Review B

Impurity resonant state in d -wave superconductors: In favor of a Kondo-like response

Marijana Kirćan

Published Jun 13, 2008• 7 citations
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Abstract

We investigate the impurity resonant state induced by nonmagnetic impurities in $d$-wave cuprate superconductors in two different impurity models: (i) in a pure potential scattering model within the $T$-matrix approach and (ii) in a Bose--Fermi Kondo model within the large-$\mathcal{N}$ formalism. We modify the superconducting host to resemble the nanoscale electronic inhomogeneities seen in the scanning tunneling microscopy (STM) spectra (i.e., the small-and large-gap domains) and study how this influences the impurity resonance. In the pure potential scattering model, the resonant state is found to be a rather robust feature appearing in all host domains. On the other hand, in the Kondo-like model the impurity resonance can appear in the small-gap regions of the host and be completely suppressed in the large-gap regions; this is in agreement with the STM experimental data for Zn-doped ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+\ensuremath{\delta}}$. Our results imply that the Kondo spin dynamics of the impurity moment is the origin of the impurity resonant state in $d$-wave superconductors, rather than the pure potential scattering.

DOI
10.1103/physrevb.77.214508

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We investigate the impurity resonant state induced by nonmagnetic impurities in ddd-wave cuprate superconductors in two different impurity models: (i) in a pure potential scattering model within the TTT-matrix approach and (ii) in a Bose--Fermi Kondo model within the large-N\mathcal{N}N formalism. We modify the superconducting host to resemble the nanoscale electronic inhomogeneities seen in the scanning tunneling microscopy (STM) spectra (i.e., the small-and large-gap domains) and study how this influences the impurity resonance. In the pure potential scattering model, the resonant state is found to be a rather robust feature appearing in all host domains. On the other hand, in the Kondo-like model the impurity resonance can appear in the small-gap regions of the host and be completely suppressed in the large-gap regions; this is in agreement with the STM experimental data for Zn-doped Bi2Sr2CaCu2O8+\ensuremathδ{\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+\ensuremath{\delta}}Bi2​Sr2​CaCu2​O8+\ensuremathδ​. Our results imply that the Kondo spin dynamics of the impurity moment is the origin of the impurity resonant state in ddd-wave superconductors, rather than the pure potential scattering.
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We consider the screening of an impurity moment in a d-wave superconductor under the influence of a Zeeman magnetic field. Using the numerical renormalization group technique, we investigate the resulting pseudogap Kondo problem, in particular the field-induced crossover behavior in the vicinity of the zero-field boundary quantum phase transition. The impurity spectral function and the resulting changes in the local host density of states are calculated, giving specific predictions for high-field scanning tunneling microscopy measurements on impurity-doped cuprates.
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The local density of states near dopants or impurities has recently been probed by scanning tunneling microscopy in both the parent and very lightly doped compounds of the high-Tc{T}_{c}Tc​ cuprate superconductors. We use a slave-rotor representation of the Hubbard model to compute the local density of states on impurities in a Mott insulator. Our calculation accounts for the following key features of the experimental observation: (i) positions and amplitudes of the in-gap spectral weights of a single impurity; (ii) the spectral weight transfer from the upper Hubbard band to the lower Hubbard band; (iii) the difference between the cases of single and multiple impurities. For multiple impurities, our study explains the complete suppression of spectral weight observed at precisely the Fermi energy and links this property to zeros of the underlying bulk Green's function of the Mott insulating phase.
A microscopic theory of resonant states for the Zn-doped CuO_2 plane in superconducting phase is formulated within the effective t-J model. In the model derived from the original p-d model Zn impurities are considered as vacancies for the d states on Cu sites. In the superconducting phase in addition to the local static perturbation induced by the vacancy a dynamical perturbation appears which results in frequency-dependent perturbation matrix. By employing the T-matrix formalism for the Green functions in terms of the Hubbard operators the local density of electronic states with d-, p- and s-symmetry is calculated.
Effects of nonmagnetic impurities with unitarity scattering in two-dimensional d -wave superconductors are investigated by the numerical diagonalization of finite-size systems of up to 35×35 sites. It is shown that a localized state with almost zero excitation energy is formed around an impurity site if it is isolated. However, its localized state is extended in real space along the direction of the node of the d -wave gap, so that the localized states of adjacent impurities easily interfere with each other forming a kind of impurity band, i.e., resonance states around the zero energy. It is also pointed out that there exists a strong association between the resonance density of states due to impurity scattering in the unitarity limit and the so-called zero-bias anomaly of tunneling conductance.