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arXiv:cond-mat/9906022 · Journal of the Physical Society of Japan

Quasiparticle Properties around a Nonmagnetic Impurity in the Superconducting State of the Two-Dimensionalt-JModel

Hiroki Tsuchiura, Yukio Tanaka, Masao Ogata, Satoshi Kashiwaya

Published Aug 15, 1999• 41 citations
arXivHTMLPDF

Abstract

The superconducting state around a well isolated nonmagnetic impurity in the high-Tc superconductors is studied using the two-dimensional t-J model. The spatial dependence of the order parameter and the local density of states are obtained from the numerical diagonalization of the Bogoliubov-de Gennes equation derived using the Gutzwiller approximation. We find a zero-energy peak in the local density of states around the impurity. Different from the previous results on a vortex or surfaces in the t-J model, the splitting of zero-energy peak is not found. The zero-energy states corresponding to the zero-energy peak is approximately localized around the impurity.

DOI
10.1143/jpsj.68.2510

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The superconducting state around a well isolated nonmagnetic impurity in the high-Tc superconductors is studied using the two-dimensional t-J model. The spatial dependence of the order parameter and the local density of states are obtained from the numerical diagonalization of the Bogoliubov-de Gennes equation derived using the Gutzwiller approximation. We find a zero-energy peak in the local density of states around the impurity. Different from the previous results on a vortex or surfaces in the t-J model, the splitting of zero-energy peak is not found. The zero-energy states corresponding to the zero-energy peak is approximately localized around the impurity.
The local density of states (LDOS) around two nonmagnetic impurities which are located at different sites is studied within the two-dimensional t-J-U model. The order parameters are determined in a self-consistent way with the Gutzwiller projected mean-field approximation and the Bogoliubov-de Gennes theory. When the two impurities are located one or two sites away, we find the superconductivity coherence peaks are more strongly suppressed and the zero-energy peak (ZEP) has split into two peaks. Whereas when the two impurities are located next to each other, the ZEP vanished, and LDOS does not change a lot compared with the case away from the impurities.
We study the effect of nonmagnetic impurities in the superconducting state of the t–J model. The Bogoliubov de Gennes equation is derived using a slave-boson mean-field approximation, and we solve it numerically at T = 0. The dx2-y2-wave order parameter is suppressed near an impurity and the extended s-wave component is induced. We also find the local CDW-like feature due to the Friedel oscillations. This leads to the splitting of the expected zero-energy Andreev bound state. Therefore the system is unlikely introducing a localized state of other symmetry such as superconductivity with broken time reversal symmetry or antiferromagnetism.
Using the Gutzwiller approximation and Bogoliubov-de Gennes(BdG) theory,the local density of states around many nonmagnetic impurities in cuprate superconductors are studied under the t-J-U model.Results show that away from the impurities,the local density of state presents typical V shape asymmetric curve;zero-energy peaks are induced around the impurities,and the superconducting coherence peaks are strongly suppressed.With the increasing of the distance among the impurities,the superconducting coherence peaks around the impurities are less suppressed,and the intensity of the zero-energy peaks decrease.
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 ${k}_{F}{\ensuremath{\xi}}_{0}.$
Recent calculation found a new type of pairing states, i.e., a spatially oscillating d + s -wave symmetry, in the two-dimensional t - J model [M. Ogata: J. Phys. Soc. Jpn. 66 (1997) 3375.] The d + s -wave state is a possible candidate for electron-doped cuprates because the quasiparticle states in the bulk are fully-gapped reflecting the lack of nodes in k space. We calculate the local density of states near the surface for the case of d + s -wave symmetry. It is shown that a zero-energy peak shows up in the local density of states near a (110) surface, even though there is no nodes in the d + s -wave state. However, due to the absence of the nodes, we find that the zero-energy peak splits. This means that the d + s -wave state has a very unique character. The present result is compared with experimental data on Nd 1.85 Ce 0.15 CuO 4 .
Strong evidence is presented for the localization of low-energy quasiparticle states in disordered ddd-wave superconductors. Within the framework of the Bogoliubov-de Gennes (BdG) theory applied to the extended Hubbard model with a finite concentration of nonmagnetic impurities, we carry out a fully self-consistent numerical diagonalization of the BdG equations on finite clusters containing up to 50\ifmmode\times\else\texttimes\fi{}50 sites. Localized states are identified by probing their sensitivity to the boundary conditions and by analyzing the finite-size dependence of inverse participation ratios.