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International Journal of Modern Physics B

Asymmetry in the Hole-Doped and Electron-Doped t-J Model

P. W. Leung, Kwai-Kong Ng

Published Aug 10, 2003• 1 citation
Publisher

Abstract

We model electron-doped high Tc materials using the t-t′-t′′-J model. This model is solved on a cluster with 32 sites using the method of exact diagonalization. Our purpose is to study the symmetry and asymmetry between hole- and electron-doped high Tc materials by comparing the results with those of the t-J model. In the electron-doped model with one charge carrier, we find a strong quasiparticle peak at (π,0). Compared to the t-J model, the bandwidth is larger, reflecting the fact that the charge carrier moves more freely in the electron-doped model. In the two-carrier model the ground state has robust dx2-y2 symmetry. This is in contrary to the two-hole t-J model whose ground state is a competition between low-energy states with dx2-y2 and p symmetries. The spatial distribution function of the carriers shows that they move almost freely on different sublattices.

DOI
10.1142/s0217979203021009

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We systematically examine the asymmetry of the electronic states in the hole- and electron-doped cuprates by using a $t\text{\ensuremath{-}}J$ model with the second-neighbor hopping ${t}^{\ensuremath{'}}$ and third one ${t}^{\ensuremath{''}}$ (the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}{t}^{\ensuremath{''}}\text{\ensuremath{-}}J$ model). Numerically exact diagonalization method is employed for a 20-site square lattice. We impose twisted boundary conditions (BC) instead of standard periodic BC. For static and dynamical correlation functions, averaging procedure over the twisted BC is used to reduce the finite-size effect. We find that antiferromagnetic spin correlation remains strong in electron doping in contrast to the case of hole doping, being similar to the case of the periodic BC. This leads to a remarkable electron-hole asymmetry in the dynamical spin structure factor and two-magnon Raman scattering. By changing the twist, the single-particle spectral function is obtained for all momenta in the Brillouin zone. Examining the spectral function in detail, we find a gap opening at around the $\mathbf{k}=(\ensuremath{\pi},0)$ region for 10% doping of holes (the carrier concentration x=0.1x=0.1x=0.1), leading to a Fermi arc that is consistent with experiments. In electron doping, however, a gap opens at around $\mathbf{k}=(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)$ and persists up to x=0.2x=0.2x=0.2, being correlated with the strength of the antiferromagnetic correlation. We find that the magnitude of the gaps is sensitive to ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$. A pseudogap is also seen in the optical conductivity for electron doping, and its magnitude is found to be the same as that in the spectral function. We compare calculated quantities with corresponding experimental data, and discuss similarities and differences between them as well as their implications.
We carry out a systematic study of collective spin and charge excitations for the canonical single-band Hubbard, t–J–U, and t–J models of high-temperature copper-oxide superconductors, both on electron- and hole-doped side of the phase diagram. A~recently developed variational wave function approach, combined with the expansion in the inverse number of fermionic flavors, is employed. All three models exhibit a substantial electron–hole asymmetry of magnetic excitations, with a robust paramagnon emerging for hole-doping, in agreement with available resonant inelastic X-ray scattering data for the cuprates. The t–J model yields additional high-energy peak in the magnetic spectrum that is not unambiguously identified in spectroscopy. For all considered Hamiltonians, the dynamical charge susceptibility contains a coherent mode for both hole- and electron doping, with overall bandwidth renormalization controlled by the on-site Coulomb repulsion. Away from the strong-coupling limit, the antiferromagnetic ordering tendency is more pronounced on the electron-doped side of the phase diagram.
We study the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}{t}^{\ensuremath{''}}\text{\ensuremath{-}}J$ model with parameters chosen to model an electron-doped high-temperature superconductor. The model with one, two, and four charge carriers is solved on a 32-site lattice using exact diagonalization. Our results demonstrate that at doping levels up to x=0.125x=0.125x=0.125 the model possesses robust antiferromagnetic correlation. When doped with one charge carrier, the ground state has momenta $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0)$ and $(0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi})$. On further doping, charge carriers are unbound and the momentum distribution function can be constructed from that of the single-carrier ground state. The Fermi surface resembles that of small pockets at single-charge-carrier ground-state momenta, which is the expected result in a lightly doped antiferromagnet. This feature persists upon doping up to the largest doping level we achieved. We therefore do not observe the Fermi surface changing shape at doping levels up to 0.125.
Asymmetric features of various physical quantities in the normal and superconducting states between hole- and electron-doped cuprate high-temperature superconductors have been an issue of debate for a long time. Their exploration is very important for the understanding not only of the mechanism of high-Tc superconductivity but also of the nature of doped-Mott insulators. Presented in this review is the present status of theoretical understanding of the electronic states in hole- and electron-doped high- Tc cuprates as well as the origin of the electron-hole asymmetry of the electronic states. In particular, it is shown that numerically exact diagonalization calculations for small clusters in a t-J model with long-range hoppings, t and t nicely reproduce the electron-hole asymmetry observed experimentally in various quantities and thus make it possible to extract the physical origin of the asymmetry. These results give a deep insight on the asymmetric behaviors in hole- and electron-doped high-Tc cuprates and on the nature of doped Mott insulators.
We examine the electronic states in the hole- and electron-doped cuprates by using the t-t′-t″-J model. Numerically exact diagonalization method is employed for a 20-site square lattice under twisted boundary conditions. The density of states in the underdoped region clearly shows a pseudogap behavior near the Fermi level in both hole and electron dopings. In hole doping, the edge of the pseudogap in the occupied side exhibits a large weight that comes from a flat band near k=(π,0). In contrast, the weight near the gap edge in electron doping is larger for the unoccupied side than for the occupied side.
A model to describe electronic correlations in energy bands is considered. The model is a generalization of the conventional Hubbard model that allows for the fact that the wave function for two electrons occupying the same Wannier orbital is different from the product of single-electron wave functions. We diagonalize the Hamiltonian exactly on a four-site cluster and study its properties as a function of band filling. The quasiparticle weight is found to decrease and the quasiparticle effective mass to increase as the electronic band filling increases, and spectral weight in one- and two-particle spectral functions is transferred from low to high frequencies as the band filling increases. Quasiparticles at the Fermi energy are found to be more ``dressed'' when the Fermi level is in the upper half of the band (hole carriers) than when it is in the lower half of the band (electron carriers). The effective interaction between carriers is found to be strongly dependent on band filling becoming less repulsive as the band filling increases and attractive near the top of the band in certain parameter ranges. The effective interaction is most attractive when the single-hole carriers are most heavily dressed, and in the parameter regime where the effective interaction is attractive, hole carriers are found to ``undress,'' hence become more like electrons, when they pair. It is proposed that these are generic properties of electronic energy bands in solids that reflect a fundamental electron-hole asymmetry of condensed matter. The relation of these results to the understanding of superconductivity in solids is discussed.