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arXiv:0812.2420 · Physical Review B

Many-body calculation of the spatial extent of the wave function of a nonmagnetic impurity in a d -wave high-temperature superconductor using the t−J model

Manuela Capello, Didier Poilblanc

Published Jun 8, 2009• 1 citation
arXivHTMLPDF

Abstract

Scanning tunneling microscopy (STM) by providing images of the effects of individual zinc impurities in cuprate superconductors with unprecedented atomic resolution offers a stringent test to models of correlated fermions for high-temperature superconductors. Using a $t\text{\ensuremath{-}}J$ model supplemented by variational Monte Carlo many-body techniques, the spatial dependence of the hole density and of the valence bond and superconducting pairing amplitudes around the impurity are computed. Our calculation supplemented by the theory of interlayer tunneling by I. Martin et al. [Phys. Rev. Lett. 88, 097003 (2002)] can explain most features of the STM experiments including the cross-shaped spatial structure and the impurity ``resonant'' peak.

DOI
10.1103/physrevb.79.224507

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Scanning tunneling microscopy (STM) by providing images of the effects of individual zinc impurities in cuprate superconductors with unprecedented atomic resolution offers a stringent test to models of correlated fermions for high-temperature superconductors. Using a t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model supplemented by variational Monte Carlo many-body techniques, the spatial dependence of the hole density and of the valence bond and superconducting pairing amplitudes around the impurity are computed. Our calculation supplemented by the theory of interlayer tunneling by I. Martin et al. [Phys. Rev. Lett. 88, 097003 (2002)] can explain most features of the STM experiments including the cross-shaped spatial structure and the impurity ``resonant'' peak.
Scanning tunneling microscopy (STM) by providing images of the effects of individual zinc-impurities in cuprate superconductors with unprecedented atomic-resolution offers a stringent test to models of correlated fermions for high-temperature superconductors. Using a t-J model supplemented by Variational Monte Carlo many-body techniques, the spatial dependence of the hole density and of the valence bond and superconducting pairing amplitudes around the impurity are computed. A cross-shaped four-fold symmetric structure very similar to the observed STM observation is found, giving strong credit to the model.
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.
In pursuit of the elusive mechanism of high- T C superconductors (HTSC), spectroscopic imaging scanning tunneling microscopy (SI-STM) is an indispensable tool for surveying local properties of HTSC. Since a conventional STM utilizes metal tips, which allow the examination of only quasiparticles and not superconducting (SC) pairs, Josephson tunneling using STM has been demonstrated by many authors in the past. An atomically resolved scanning Josephson tunneling microscopy (SJTM), however, was realized only recently on Bi 2 Sr 2 CaCu 2 O 8+ x (Bi-2212) below 50 mK and on the Pb(110) surface at 20 mK. Here we report the atomically resolved SJTM on Bi 2 Sr 2 CaCu 2 O 8+ x at 4.2 K using Bi-2212 tips created in situ . The I - V characteristics show clear zero bias conductance peaks following Ambegaokar-Baratoff (AB) theory. A gap map was produced for the first time using an atomically resolved Josephson critical current map I C ( r ) and AB theory. Surprisingly, we found that this new gap map is anticorrelated to the gap map produced by a conventional method relying on the coherence peaks. Quasiparticle resonance due to a single isolated zinc atom impurity was also observed by SJTM, indicating that atomically resolved SJTM was achieved at 4.2 K. Our result provides a starting point for realizing SJTM at even higher temperatures, rendering possible investigation of the existence of SC pairs in HTSC above the T C .
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.
We study the two-dimensional Hubbard model with nonmagnetic Zn impurities modeled by binary diagonal disorder using quantum Monte Carlo within the dynamical cluster approximation. With increasing Zn content we find a strong suppression of d-wave superconductivity and an enhancement of antiferromagnetic spin correlations. T(c) vanishes linearly with Zn impurity concentration. The spin susceptibility changes from pseudogap to Curie-Weiss-like behavior indicating the existence of free magnetic moments in the Zn doped system. We interpret these results within the resonating-valence-bond picture.
Recent scanning tunneling microscopy (STM) experiments on underdoped cuprates have displayed modulations in the local electronic density of states, which are centered on a Cu-O-Cu bond [Kohsaka et al., Science 315, 1380 (2007)]. As a paradigm of the pinning of such bond-centered ordering in strongly correlated systems, we present the theory of valence bond solid (VBS) correlations near a single impurity in a square lattice antiferromagnet. The antiferromagnet is assumed to be in the vicinity of a quantum transition from a magnetically ordered N\'eel state to a spin-gap state with long-range VBS order. We identify two distinct classes of impurities: (i) local modulation in the exchange constants and (ii) a missing or additional spin, for which the impurity perturbation is represented by an uncompensated Berry phase. The ``boundary'' critical theory for these classes is developed. In the second class, we find a VBS pinwheel around the impurity, accompanied by a suppression in the VBS susceptibility. Implications for numerical studies of quantum antiferromagnets and for STM experiments on the cuprates are noted.