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Journal of the Physical Society of Japan

Effect of the Medium-Range Transfer Energies to the Superconductivity in the Two-Chain Hubbard Model

Soh Koike, Yamaji K., Takashi Yanagisawa

Published May 15, 1999• 33 citations
Publisher

Abstract

We investigate the two-chain Hubbard model including the next nearest-neighbor transfer energies both in the interchain and intrachain directions by use of the exact-diagonalization and the variational Monte Carlo methods. We find that superconducting correlation functions are enhanced in such a situation where the density of states of the antibonding band in the neighborhood of the Fermi level enlarges due to the above-mentioned transfer energies, especially, in the situation where the Fermi level is located a little above the bottom of the antibonding band. In such a situation we find from the calculated momentum distribution function that this system is in almost one-band situation close to the two-band one. The relevance to ladder-type superconductor Sr 14- x Ca x Cu 24 O 41 is asserted.

DOI
10.1143/jpsj.68.1657

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We investigate the two-chain Hubbard model including the next nearest-neighbor transfer energies both in the interchain and intrachain directions by use of the exact-diagonalization and the variational Monte Carlo methods. We find that superconducting correlation functions are enhanced in such a situation where the density of states of the antibonding band in the neighborhood of the Fermi level enlarges due to the above-mentioned transfer energies, especially, in the situation where the Fermi level is located a little above the bottom of the antibonding band. In such a situation we find from the calculated momentum distribution function that this system is in almost one-band situation close to the two-band one. The relevance to ladder-type superconductor Sr 14- x Ca x Cu 24 O 41 is asserted.
We have studied on the possibility of superconductivity in the two-chain Hubbard model by using the variational Monte Carlo method changing the interchain transfer energy t d . The energy gain per site Δ E in the variational BCS state in reference to the normal state energy, which is nothing but the superconducting condensation energy, was computed. We have fitted Δ E as a function of the inverse of the lattice size by a power-law function and found that in the bulk limit Δ E remains finite in a certain narrow range of t d . Calculated momentum distribution functions reveal that the superconductivity is most stable in the case where the electron distribution in k -space is in a one-band-like situation, on the brink of transition to a two-band-like one. The SDW-type trial wave function was also examined but we did not obtain any energy gain with it in the above-mentioned superconducting region.
We have studied the superconducting, magnetic, and charge correlation functions and the spin excitation spectrum in the doped two-chain Hubbard model by projector Monte Carlo and Lanczos diagonalization methods. The exponent of the interchain singlet superconducting correlation function, \ensuremath{\gamma}, is found to be close to 2.0 as long as two distinct noninteracting bands cross the Fermi level. Magnetic and charge correlation functions decay more rapidly than or as fast as the interchain singlet superconducting correlation function along the chains. The superconducting correlation in the doped two-chain Hubbard model is the most long-range correlation studied here. Implications of the results for the possible universality class of the doped two-chain Hubbard model are discussed.
By means of the exact-diagonalization method we have studied the finite-size two-band model with the interband pair-transfer interaction by calculating the superconducting (SC) correlation function P s etc. in the ground state. Occurrence of SC was clearly indicated by the increase of P s . The diagram of the observed SC region was constructed in the plane of the relative position of the second band versus on-site Coulomb energy U . In the low-density limit it proved close to the region where a negative- U situation is realized by the pair-transfer interaction. On the high-density side, the SC region was found to be more extended than the latter in accord with the previous interband-ladder-diagram results. Inclusion of the exchange interaction was found to reduce the SC region in a restricted region where two bands substantially share electrons. The two-band situations in cuprates are argued to be relevant to the high T c through the present mechanism.
The possibility of superconductivity in the ground state of the two-dimensional Hubbard model was investigated by means of the variational Monte Carlo method. With slight hole doping on the 6 ×6 and 10 ×10 lattices, a clear minimum was obtained on the curve of the total energy versus the amplitude of the d -wave gap function for large on-site Coulomb energies. Superconducting pair correlations were observed to be well developed. The-next-nearest-neighbor transfer was found to appreciably affect the minimum depth.
Calculations of the single-particle spectral function for the two-band Hubbard model as a function of doping and nearest-neighbor Coulomb repulsion are performed on finite-size clusters. It is shown that for hole doping the effect of the nearest-neighbor Coulomb repulsion leads to the effective pinning of the Fermi energy, and to the creation of new states in the charge-transfer gap. For electron doping, however, the model behaves as a one-band Hubbard model with the Fermi energy moving into the conduction band. The results of this calculation are in qualitative agreement with some of the spectroscopic studies of the electronic structure at the Fermi energy of the high-temperature cuprate superconductors.
Numerical results obtained from Monte Carlo simulation in the ground state and at finite temperatures as well as the exact diagonalization and the transfer matrix method are reported. Efficiency of the Monte Carlo method in the ground state is examined. Spin, charge and superconducting correlations are investigated for the Hubbard and the t - J model in one and two dimensions. The momentum distribution in the one-dimensional Hubbard model shows fermi-liquid-like behavior at least in two orders of magnitude smaller energy scale than the band width. The short-range incommensurate spin correlation is observed and analyzed in the doped Hubbard and the t - J model both in one and two dimensions. In the ground state, the superconducting correlation shows the absence of system size dependence in two dimensions at the filling smaller than 0.8 and in one dimension at any filling. The binding energy of two fermions and the spin and charge distortion around an itinerant fermion are also discussed in the t - J and the coupled spin-fermion model.