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arXiv:cond-mat/9804076 · International Journal of Modern Physics B

Study on Nonmagnetic Impurities in the Superconducting State of Two-Dimensional t-J Model

Hideki Tanaka, Kazuhiro Kuboki, Manfred Sigrist

Published Sep 30, 1998• 11 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1142/s0217979298001435

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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.
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.
We study the effect of magnetic impurities in the d_{x^2-y^2}-wave superconducting (SC) state of the two dimensional t-J model.The spin-orbit and the spin-exchange interactions are examined by treating the impurity as a classical spin. The Bogoliubov de Gennes equation derived within a slave-boson mean-field approximation is solved numerically at T = 0. The spin-exchange scattering induces spin-triplet p-wave SC order parameters near the impurity, while a SC state with broken time-reversal symmetry and a spontaneous current appears in the presence of the spin-orbit interaction. When both interactions coexist, it turns out that a state which carries a spontaneous spin current occurs.
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.
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 ${k}_{F}{\ensuremath{\xi}}_{0}.$
The coexisting phase of the d-wave superconducting and the antiferromagnetic order in the two-dimensional t-JJJ model is reexamined using a variational Monte Carlo method in order to estimate the Gutzwiller factors. A trial wave function is used which is consistent with the mean-field solution. The Gutzwiller factors are determined by comparing the numerically obtained expectation values with the mean-field values. We find the z component of the Gutzwiller factor of exchange interaction is enhanced compared with the xy\mathrm{xy}xy components. This effect does not appear in the conventional Gutzwiller approximation and is essential for the stabilization of the antiferromagnetic order in the presence of d-wave superconductivity. We discuss several applications of the present Gutzwiller factors to the problems with antiferromagnetism and d-wave superconductivity.