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arXiv:cond-mat/9802243 · Journal of the Physical Society of Japan

Theory of Local Density of States ofdx2-y2-Wave Superconducting State Near the Surfaces of thet-JModel

Yasunari Tanuma, Yukio Tanaka, Masao Ogata, Satoshi Kashiwaya

Published Apr 15, 1998• 59 citations
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Abstract

Spatial dependencies of the pair potential and the local density of states near the surfaces of $d_{x^{2}-y^{2}}$-wave superconductors are studied theoretically. The calculation is based on the t-J model within a mean-field theory with Gutzwiller approximation. Various types of surface geometries are considered. Similar to our result in the extended Hubbard model, it is found that the formation of zero-energy states strongly depends on the surface geometry. In addition to this feature, the zero-energy states give peak splitting for the (110) surfaces when the super-exchange interaction $J$ is large. This is due to the induced s-wave component near the surface. The present result explains the microscopic origin of the spontaneous time- reversal symmetry breaking at the surfaces of high-$T_{c}$ superconductors.

DOI
10.1143/jpsj.67.1118

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Journal of Physics Conference Series•Mar 1, 2009•2 citations
Spatial dependencies of the pair potential and the local density of states near the surfaces of dx2−y2d_{x^{2}-y^{2}}dx2−y2​-wave superconductors are studied theoretically. The calculation is based on the t-J model within a mean-field theory with Gutzwiller approximation. Various types of surface geometries are considered. Similar to our result in the extended Hubbard model, it is found that the formation of zero-energy states strongly depends on the surface geometry. In addition to this feature, the zero-energy states give peak splitting for the (110) surfaces when the super-exchange interaction JJJ is large. This is due to the induced s-wave component near the surface. The present result explains the microscopic origin of the spontaneous time- reversal symmetry breaking at the surfaces of high-TcT_{c}Tc​ superconductors.
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 .
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 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.
A new superconducting phase is found in the two-dimensional t - J model near half-filling within the mean-field theory and Gutzwiller approximation. This state has a spatial dependence of order parameters which is interpreted as a mixing of the extended s -wave component with the finite total momentum in addition to the d x 2 - y 2 -wave symmetry. The origin of this peculiar pairing is investigated. There is no node in the gap function in the new state and possible experimental consequences are discussed.
We present a variational Monte Carlo (VMC) study of spontaneous Fermi-surface symmetry breaking in the $t\text{\ensuremath{-}}J$ model. We find that the variational energy of a Gutzwiller projected Fermi sea is lowered by allowing for a finite asymmetry between the xxx and the yyy directions. However, the best variational state remains a pure superconducting state with ddd-wave symmetry, as long as the underlying lattice is isotropic. Our VMC results are in good overall agreement with slave boson mean field theory (SBMFT) and renormalized mean field theory (RMFT), although apparent discrepancies do show up in the half-filled limit, revealing some limitations of mean field theories. VMC and complementary RMFT calculations also confirm the SBMFT predictions that many-body interactions can enhance any anisotropy in the underlying crystal lattice. Thus, our results may be of consequence for the description of strongly correlated superconductors with an anisotropic lattice structure.
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.