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arXiv:cond-mat/0011292 · Physical Review Letters

Marginal Fermi Liquid Resonance Induced by a Quantum Magnetic Impurity in d -Wave Superconductors

Guang-Ming Zhang, Hui Hu, Lu Yu

Published Jan 22, 2001• 41 citations
arXivHTMLPDF

Abstract

We consider a model of an Anderson impurity embedded in a d(x(2)-y(2))--wave superconducting state to describe the low-energy excitations of cuprate superconductors doped with a small amount of magnetic impurities. Because of the Dirac-like energy dispersion, a sharp localized resonance above the Fermi energy, showing a marginal Fermi liquid behavior ( omega ln omega as omega-->0), is predicted for the impurity states. The same logarithmic dependence of self-energy and a linear frequency dependence of the relaxation rate are also derived for the conduction electrons, characterizing a new universality class for the strong coupling fixed point. At the resonant energies, the spatial distribution of the electron density of states around the magnetic impurity is also calculated.

DOI
10.1103/physrevlett.86.704

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We consider a model of an Anderson impurity embedded in a d(x(2)-y(2))--wave superconducting state to describe the low-energy excitations of cuprate superconductors doped with a small amount of magnetic impurities. Because of the Dirac-like energy dispersion, a sharp localized resonance above the Fermi energy, showing a marginal Fermi liquid behavior ( omega ln omega as omega-->0), is predicted for the impurity states. The same logarithmic dependence of self-energy and a linear frequency dependence of the relaxation rate are also derived for the conduction electrons, characterizing a new universality class for the strong coupling fixed point. At the resonant energies, the spatial distribution of the electron density of states around the magnetic impurity is also calculated.
We discuss the dynamics of magnetic moments in d-wave superconductors. In particular, we focus on moments induced by doping nonmagnetic impurities into cuprates. The interaction of such moments with the Bogoliubov quasiparticles of the superconductors can be described by variants of the pseudogap Kondo model, characterized by a power-law density of states at the Fermi level. The numerical renormalization-group technique is employed to investigate this Kondo problem for realistic band structures and particle-hole asymmetries, both at zero and finite temperatures. In particular, we study the boundary quantum phase transition between the local-moment and asymmetric strong-coupling phases, and argue that this transition has been observed in recent nuclear magnetic resonance experiments. We determine the spectral properties of both phases and the location of the critical point as a function of Kondo coupling and doping, and discuss quantum-critical crossovers near this phase transition. In addition, changes in the local density of states around the impurity are calculated as functions of temperature, being relevant to scanning tunneling microscopy experiments.
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We solve for the properties of an impurity model abstracted from a model of copper oxide superconductors. At mixed valence, provided that Friedel's screening condition is satisfied, the marginal-Fermi-liquid spectrum is obtained for the spin and charge susceptibilities. The frequency dependence of the self-energies is \ensuremath{\Sigma}(\ensuremath{\omega})\ensuremath{\sim}\ensuremath{\omega} ln\ensuremath{\omega}+i\ensuremath{\omega}. This critical point is surrounded by two different Fermi-liquid phases. A simplified two-impurity version of this model is also addressed, and presents similar features, including a logarithmic divergence for coherent pair susceptibility.
The variational approach of Gunnarsson and Sch\"onhammer to the Anderson impurity model is generalized to study d-wave superconductors in the presence of dilute spin-12\frac{1}{2}21​ impurities. We show that the local moment is screened when the hybridization exceeds a nonzero critical value at which the ground state changes from a spin doublet to a spin singlet. The electron spectral functions are calculated in both phases. We find that while a Kondo resonance develops above the Fermi level in the singlet phase, the spectral function exhibits a low-energy spectral peak below the Fermi level in the spin-doublet phase. The origin of such a ``virtual Kondo resonance'' is the existence of low-lying collective excitations in the spin-singlet sector. We discuss our results in connection with recent spectroscopic experiments in Zn-doped high-Tc{T}_{c}Tc​ superconductors.
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 ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+\ensuremath{\delta}}$. Our results imply that the Kondo spin dynamics of the impurity moment is the origin of the impurity resonant state in ddd-wave superconductors, rather than the pure potential scattering.