N‐band Hubbard models II: Cooperative mechanisms of electron–phonon, electron correlation, and many‐band effects toward high‐T_c superconductors

Abstract

Discoveries of superconductivity of MgB 2 by Akimitsu et al. and high-T c cupurate superconductors by Bednorz and Muller have raised great interest for elucidation of the superconducting mechanism from both experimental and theoretical grounds. The transition temperature (T c ) was found to be 40 K for MgB 2 , while the very high-T c over 130 K was reported for doped copper oxides with layer structures. A crucial role of the electron-phonon (EP) interaction was pointed out as a common mechanism of the superconductivity of both materials. However, such high-T c superconductivity may indicate the possibility of cooperative mechanism of the EP interaction with others such as electron correlation (EC) and multiband (MB) effects discussed in part I (Int J Quantum Chem 1990, 37, 167) of this series. Here, as a continuation of part I, theoretical backgrounds are briefly described to select active orbital space for superconductivity and elucidate the nature of EP, EC, and MB effects for cooperative mechanisms. Next, molecular orbital calculations of Mg m B n and cagetype carbon cluster are carried out to elucidate contributions of the EP interaction using McMillan equation. The relative contributions of the EP and EC interactions are also discussed in relation to the screening of the Coulomb repulsion. Pair binding energies are calculated for cage-type carbon clusters. Finally, the cooperative mechanisms of the EP, EC, and MB effects are discussed to realize the high-T c superconductivity in molecule-based materials such as cage compounds and nanotubes. Several possible candidates are proposed on both experimental and theoretical grounds.

N‐bands Hubbard models. IV. Comparisons of electron‐ or hole‐doped quaternary oxypictides LaOMPn superconductors with cuprates

“…As shown in this series of articles [33], charge density wave (CDW) type state becomes the ground state if U 0 Ͻ Ͻ U 1 , though it is eliminated in the LaOFeAs system. On the other hand, the unconventional superconductivity such as p-wave is feasible if K Ͼ U 1 in the case of two-band model [33], but spin density wave (SDW) state arises if K Ͻ U 1 .…”

“…On the other hand, the unconventional superconductivity such as p-wave is feasible if K Ͼ U 1 in the case of two-band model [33], but spin density wave (SDW) state arises if K Ͻ U 1 . In the strong correlation regime with magnetic phases, the Hubbard model can be reduced to the Heisenberg spin Hamiltonian model [51] H͑Heisenberg͒ ϭ Ϫ 2 J ab S a S b (6) where J ab is the effective exchange integral.…”

“…As shown in this series of articles (I-III), the magnetic model [15] enables us to propose isoelectronic p-d, -d, -R, and -R conjugated systems on the basis of N-band Hubbard model [33]. LaOMPn is one of p-d conjugated systems in our terminology.…”

“…Nband Hubbard models have been derived for a possible theoretical model of describing these requirements on the basis of quantum chemical calculations of cuprates and isoelectronic p-d, -d, -R, and -R conjugated systems. Past decades magnetic models such as spin (SF) fluctuation model are possible working hypotheses for molecular design of high-T c superconductors [33,53]. Indeed, several kinds of SF models have been proposed on the experimental and theoretical grounds in Part II [33].…”

“…Past decades magnetic models such as spin (SF) fluctuation model are possible working hypotheses for molecular design of high-T c superconductors [33,53]. Indeed, several kinds of SF models have been proposed on the experimental and theoretical grounds in Part II [33]. However, a unified theory describing phase diagrams in an intermediate (near Mott transition) regime as well as both weak and strong correlation limits is not established yet [54], partly because serious disorder and defects in each CuO 2 plane (BEC-BCS crossover problem in part III [35]).…”