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Physical Review Letters

Impurities and Quantum Interference in the Chains of YBa2Cu3O6+x

Dirk K. Morr, Alexander V. Balatsky

Published Feb 14, 2003• 20 citations
Publisher

Abstract

Motivated by recent experiments, we study the electronic structure near impurities in the chains of YBa2Cu3O6+x. Using a model of proximity induced chain superconductivity, we show that a resonance state in the chain density of states is induced only by a magnetic impurity. The spatial form of the resonance reflects the particle-hole nature of chain superconductivity and therefore distinguishes it from other broken symmetry phases. Because of quantum interference effects between impurities, the chains can undergo a quantum phase transition into a polarized state.

DOI
10.1103/physrevlett.90.067005

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Electronic Structure near Impurities in the Chains of YBa2_22​Cu3_33​O6+x_{6+x}6+x​
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The quasiparticle resonant states around a single nonmagnetic impurity with unitary scattering in a d-wave superconductor is studied by solving the Bogoliubov--de Gennes equations based on a $t\ensuremath{-}J$ model. Both the spatial variation of the order parameter and the local density of states (LDOS) around the impurity have been investigated. We find that (i) a particle-hole symmetric system has a single symmetric zero-energy peak in the LDOS regardless of the size of the superconducting coherence length ${\ensuremath{\xi}}_{0};$ (ii) for the particle-hole asymmetric case, an asymmetric splitting of the zero-energy peak is intrinsic to a system with a small value of ${k}_{F}{\ensuremath{\xi}}_{0}.$
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.
We study the local density of states around potential scatterers in d-wave superconductors, and show that quantum interference between impurity states is not negligible for experimentally relevant impurity concentrations. The two-impurity model is used as a paradigm to understand these effects analytically and in interpreting numerical solutions of the Bogoliubov--de Gennes equations on fully disordered systems. We focus primarily on the globally particle-hole symmetric model which has been the subject of considerable controversy, and give evidence that a zero-energy delta function exists in the density of states. The anomalous spectral weight at zero energy is seen to arise from resonant impurity states belonging to a particular sublattice, exactly as in the two-impurity version of this model. We discuss the implications of these findings for realistic models of the cuprates. In particular, we show how apparently isolated impurity states can be observed in STM experiments, despite long-range interference, due to averaging over a finite energy range within the impurity band.