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arXiv:cond-mat/0005503 · Journal of the Physical Society of Japan

Effect of Spin-Orbit Impurity Scattering in the Superconducting State oft–JModel

Toshifumi Yagi, Kazuhiro Kuboki

Published Apr 15, 2001• 1 citation
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Abstract

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.

DOI
10.1143/jpsj.70.1075

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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.
Using an extended dynamical cluster approximation we study superconductivity in the two-dimensional t-J model. In analogy to the extended dynamical mean field theory, non-local spin fluctuations are treated self-consistently with an additional Bosonic bath. To solve the effective cluster problem, we employ an extended non-crossing approximation which allows for transitions to the symmetry-broken state. At sufficiently low temperatures we find a stable superconducting solution with d-wave order parameter. Upon pairing, the exchange energy is lowered, consistent with an exchange-based pairing mechanism.
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 effects of nonmagnetic strong scatterers (unitary limit) on magnetic and transport properties are studied for resonating-valence-bond states in both the slave-boson and slave-fermion mean-field theories with the gap for the triplet excitations. In the d-wave pairing state of the slave-boson mean-field theory in two dimensions, there is no true gap for spinons, but the Anderson localization occurs, which leads to the local moment when the repulsive interaction is taken into account. In the slave-fermion mean-field theory, local moments are found bound to nonmagnetic impurities as a result of (staggered) gauge interaction. However, in both theories, localization of spinon does not appear in the resistivity, which shows the classical value for the holon.
Spin ordering and its effect on low-energy quasiparticles in a p-wave superconducting liquid are investigated. We study the properties of a two-dimensional (2D) p-wave superconducting liquid where the ground state is spin rotation invariant. In quantum spin disordered liquids, the low-energy quasiparticles are bound states of the bare Bogolubov--De Gennes (BdeG) quasiparticles and zero energy skyrmions, which are charge neutral bosons at the low-energy limit. Further more, spin collective excitations are fractionalized ones carrying a half-spin and obeying fermionic statistics. In thermally spin disordered limits, the quasiparticles are bound states of bare BdeG quasiparticles. The latter situation can be realized in some layered p-wave superconductors where the spin-orbit coupling is weak.