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Journal of Physics Conference Series

Anti-phase superconducting domain structures in thet-t'-t"-Jmodel

Hiroki Tsuchiura, Masao Ogata

Published Mar 1, 2009• 2 citations
Publisher

Abstract

We study spatially modulated d -wave superconducting states in the two-dimensional t-t'-t"-J model within the Bogoliubov-de Gennes theory based on an extended Gutzwiller approximation. We find fully self-consistent solutions involving domain walls with vanishing pairing amplitudes Δ separated by four lattice spacing when the system is about 12.5% hole doping, while five at about 15%. The adjacent superconducting domains are in the anti-phase patterns, that is, the relative phase difference between them is π. The Δ = 0 domain walls involve concentration of mobile holes due to the loss of the condensation energy. We also find that the superconducting coherence peaks at the energy of the d -wave gap in the local densities of states are strongly suppressed in these states with anti-phase superconducting domain structures.

DOI
10.1088/1742-6596/150/5/052272

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We study spatially modulated d -wave superconducting states in the two-dimensional t-t'-t"-J model within the Bogoliubov-de Gennes theory based on an extended Gutzwiller approximation. We find fully self-consistent solutions involving domain walls with vanishing pairing amplitudes Δ separated by four lattice spacing when the system is about 12.5% hole doping, while five at about 15%. The adjacent superconducting domains are in the anti-phase patterns, that is, the relative phase difference between them is π. The Δ = 0 domain walls involve concentration of mobile holes due to the loss of the condensation energy. We also find that the superconducting coherence peaks at the energy of the d -wave gap in the local densities of states are strongly suppressed in these states with anti-phase superconducting domain structures.
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.
Motivated by the recently observed pattern of unidirectional domains in high-Tc{T}_{c}Tc​ superconductors [Y. Kohsaka et al., Science 315, 1380 (2007)], we investigate the emergence of spontaneous modulations in the ddd-wave superconducting resonating valence bond phase using the ttt-JJJ model at x=1∕8x=1∕8x=1∕8 doping. Half-filled charge domains separated by four lattice spacings are found to form along one of the crystal axes, leading to modulated superconductivity with out-of-phase ddd-wave order parameters in neighboring domains. Both renormalized mean-field theory and variational Monte Carlo calculations reveal that the energies of modulated and uniform phases are very close to each other.
Using the density matrix renormalization group, we study domain wall structures in the t-J model at a hole doping of x=1/8. We find that the domain walls are composed of d_{x^2-y^2} pairs and that the regions between the domain walls have antiferromagnetic correlations that are pi phase shifted across a domain wall. At x=1/8, the hole filling corresponds to one hole per two domain wall unit cells. When the pairs in a domain wall are pinned by an external field, the d_{x^2-y^2} pairing response is suppressed, but when the pinning is weakened, d_{x^2-y^2} pair-field correlations can develop.
We report on a numerical study of disorder effects in 2D d-wave BCS superconductors. We compare exact numerical solutions of the Bogoliubov-de Gennes (BdG) equations for the density of states rho(E) with the standard T-matrix approximation. Local suppression of the order parameter near impurity sites, which occurs in self-consistent solutions of the BdG equations, leads to apparent power-law behavior rho(E) approximately |E|(alpha) with nonuniversal alpha over an energy scale comparable to the single-impurity resonance energy Omega(0). We show that the novel effects arise from static spatial correlations between the order parameter and the impurity distribution.
The ground state of two-dimensional t – J model including superconductivity and antiferromagnetism is studied using a new type of analytic estimation of the effect of strong correlation. The method is an extension of the Gutzwiller approximation which gives renormalization of parameters, t and J , due to the Gutzwiller projection operator excluding double occupancies. It is shown that the essential point of the renormalization is its dependence on the expectation values of superconductivity and antiferromagnetic moment. In special the renormalization factor is anisotropic in spin space, which leads to a reliable estimate of antiferromagnetic order parameters in the phase diagram, in contrast to the conventional slave-boson mean-field theory. The obtained phase diagram shows the coexistence of antiferromagnetism and d x 2 - y 2 -wave superconductivity for the doping rate, δ, less than 10%. At half-filling, the renormalization of the J -term represents some aspects of quantum spin nature. For the finite doping case, there are two kinds of superconducting order parameters. The variational order parameter of the d-wave superconductivity increases as the doping rate decreases, which will correspond to the experimentally observed superconducting gap. In contrast, the actual expectation value of superconducting order parameter is proportional to δ in underdoped region and has a maximum near δ=0.11, which probably determines T c . We also speculate that the ground-state antiferromagnetic order, being destroyed at finite temperatures, gives the energy and temperature scale of the pseudogap. Applications to the inhomogeneous systems such as the vortex state and stripe state are discussed.
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.