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Journal of the Physical Society of Japan

Local Density of States near the Surface of ad+s-Wave Superconductorin the Two-Dimensionalt-JModel

Yasunari Tanuma, Yukio Tanaka, Masao Ogata, Satoshi Kashiwaya

Published May 15, 2000• 0 citations
Publisher

Abstract

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 .

DOI
10.1143/jpsj.69.1472

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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 .
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.
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.
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 investigate the quasiparticle spectrum near surfaces in a two-dimensional system with d-density-wave order within a mean-field theory. For Fermi surfaces with perfect nesting for the ordering wavevector (π,π) of the d-density wave, a zero-energy bound state occurs at 110 surfaces, in close analogy with the known effect in d-wave superconducting states or graphite. When the shape of the Fermi surface is changed by doping, the bound-state energy moves away from the Fermi level. Furthermore, away from half-filling we find inhomogeneous phases with domain walls of the d-density-wave order parameter. The domain walls also support low-energy bound states. These phenomena might provide an experimental test for hidden d-density-wave order in the high- T c cuprates.
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 ${k}_{F}{\ensuremath{\xi}}_{0}.$
Two-dimensional t-J model is studied by a variational Monte Carlo method, using Gutzwiller-Jastrow-type wave functions. Various kinds of superconducting pairing symmetries are compared in order to determine the phase diagram of the ground state in the full J/t-n plane. Near the half filling where the high temperature superconductivity is expected, the d_{x^2-y^2} wave pairing state is always the most stable among various symmetries. The three-site term hardly changes the phase diagram in this regime. In the low electron density, the extended s-type wave becomes a quantitatively good state for large J/t, although the energy gain is small. The Gutzwiller wave function is shown to be the exact ground state in the low-electron-density limit for the supersymmetric case (J/t=2).