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arXiv:cond-mat/9709121 · Physical review. B, Condensed matter

Impurity-induced moments in underdoped cuprates

Giniyat Khaliullin, R. Kilian, S. Krivenko, Peter Fulde

Published Nov 1, 1997• 52 citations
arXivHTMLPDF

Abstract

We examine the effect of a nonmagnetic impurity in a two-dimensional spin liquid in the spin-gap phase, employing a drone-fermion representation of spin-$1/2$ operators. The properties of the local moment induced in the vicinity of the impurity are investigated and an expression for the nuclear-magnetic-resonance Knight shift is derived, which we compare with experimental results. Introducing a second impurity into the spin liquid an antiferromagnetic interaction between the moments is found when the two impurities are located on different sublattices. The presence of many impurities leads to a screening of this interaction as is shown by means of a coherent-potential approximation. Further, the Kondo screening of an impurity-induced local spin by charge carriers is discussed.

DOI
10.1103/physrevb.56.11882

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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.
Abstract We study the Kondo effect of spin-1/2 magnetic impurities in gapped Z2 spin liquids on two-dimensional lattices. We find that if the impurity is placed at a high-symmetry location, a nontrivial spinon fractionalization class of the impurity site symmetry group will necessarily lead to a non-Kramers doublet in the Kondo screening regime, protected by associated crystalline symmetries. This is in sharp contrast to a featureless screening phase in the usual Kondo effect. We demonstrate this symmetry-protected topological degeneracy by an exactly solvable model and by the large-N theory. Based on this effect, we discuss how thermodynamic measurements in the limit of dilute magnetic impurities can be used to detect symmetry fractionalization in gapped Z2 spin liquids.
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Local magnetic moments induced by a nonmagnetic impurity in the two-dimensional $t\ensuremath{-}J$ model are investigated by use of a Green function method in a finite-size system (50\ifmmode\times\else\texttimes\fi{}50=2500 sites). Local electron number and nearest-neighbor correlation functions are calculated self-consistently at each lattice point. A local electron number distribution shows that electrons form a bound state around an impurity site and the magnitude of the local moment is enhanced, whereas doped holes can be distributed only apart from the impurity site and destroy an antiferromagnetic spin configuration by their motion. This result is consistent with experimental results of Zn-doped high-Tc{T}_{c}Tc​ superconductors.
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