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Journal of the Physical Society of Japan

Mean Field Theory of the Holon-Spinon System. I

Sadao Nakajima, Minoru Sato, Yoshimasa Murayama

Published Jul 15, 1991• 13 citations
Publisher

Abstract

Mean field approximation is applied to nonlinear equations of motion in the holon-spinon operator formalism proposed previously. A simple interpolation scheme, which looks very much like the conventional band theory, is thus established between insulating and metallic limits of the tJ model. The transport equation of the normal state is given and critical temperatures of S -wave and D -wave superconducting states are calculated.

DOI
10.1143/jpsj.60.2333

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Mean field approximation is applied to nonlinear equations of motion in the holon-spinon operator formalism proposed previously. A simple interpolation scheme, which looks very much like the conventional band theory, is thus established between insulating and metallic limits of the tJ model. The transport equation of the normal state is given and critical temperatures of S -wave and D -wave superconducting states are calculated.
The U(1) slave-boson mean-field theory of the t - J model has been used by many authors as a starting point for the theoretical analysis of high - Tc cuprate superconductors. With suitable refinements, the theory can explain a lot of qualitative features of cuprates. However, the theory does not produce a correct description of the low-energy quasi-particle properties in the under-doped regime. There exist several possible schemes to resolve this difficulty, among them, one generalizes the U(1) theory to SU(2) formulation and the other introduces confinement between spinons and holons. In this thesis, we generalize the Landau transport equations of the U(1) slave-boson mean-field theory of the t - J model to the SU(2) formulation. We first generalize the SU(2) slave-boson mean-field theory to the time-dependent regime. After eliminating the boson and constraint fields exactly in the linear-response regime at zero-temperature, we obtain a set of transport equations for quasi-particles, which has a similar structure as the Landau transport equations for Fermi-liquid superconductors, with all the Landau parameters explicitly given except that besides the usual effective interaction in the particle-hole channel in Fermi-liquid theory, we find an effective interaction in the particle-particle channel, which reflects the SU(2) symmetry between particles and holes. The transport equation is SU(2) invariant at half-filling. Around q⃗ = 0, the electron density couples only to the transverse part of the external field and the quasi-particle charge is still of order x. Besides the SU(2) formulation approach, we also investigate spinon-holon confinement in the U(1) slave-boson theory. The optical and thermal conduc-tivities of U (1) slave-boson theory with confinement are calculated. For optical conductivity, we consider only the contributions from static impurities. The qualitative behavior of our results agrees with experimental results. However, to explain the experiments quantitatively, we need to study further the con-tributions from phonons. We found a phenomenological effective Hamiltonian for the quasi-particle Green's functions in the U(1) slave-boson theory with spinon-hoion confinement. Starting from this effective Hamiltonian, we exam-ine the thermal conductivity within the theory. In particular, we compare the thermal conductivity for four different situations: (i) the ordinary d-wave su-perconducting state with four Dirac Fermi points; (ii) the normal metal state with a half-pocket Fermi surface; (iii) the spinon-holon confinement supercon-ducting state with a half-pocket Fermi surface; (iv) BCS superconducting state with a half-pocket Fermi surface.
Using a phenomenological model, we discuss the consequences of spinon-holon binding in the U(1)U(1)U(1) slave-boson approach to $t\text{\ensuremath{-}}J$ model in the weak-coupling limit. We find that spinon-holon binding produces a pseudogap normal state with a segmented Fermi surface and the superconducting state is formed by opening an ``additional'' ddd-wave gap on the segmented Fermi surface. The ddd-wave gap merges with the pseudogap smoothly as temperature $T\ensuremath{\rightarrow}0$. The quasiparticles in the superconducting state are coupled to external electromagnetic field with a coupling constant of order ${x}^{\ensuremath{\gamma}∕2}\phantom{\rule{0.3em}{0ex}}(x=\text{hole concentration})$, where $0\ensuremath{\leqslant}\ensuremath{\gamma}\ensuremath{\leqslant}1$.
The recently introduced concept of exact mean-field theories is applied to the extended simplified Hubbard model, which is a one-band extended Hubbard model (including nearest-neighbor interaction) where only the \ensuremath{\downarrow} electrons can hop. An exact mean-field Hamiltonian is derived for the model on a Bethe lattice in the limit of a large coordination number (Z\ensuremath{\rightarrow}\ensuremath{\infty}). The mean-field Hamiltonian is used to calculate the Green functions and the free energy at half-filling. This exact solution is analyzed analytically at small and large values of the on-site (U) and nearest-neighbor (V) interaction strengths. One finds that a phase transition occurs at sufficiently low temperatures for all U,V>0. The low-temperature phase is a charge-density wave for V>1/2U and a spin-density wave for V1/2U. Special attention is paid to (i) the critical temperature as a function of U and V, (ii) the order parameter as a function of temperature, and (iii) the density of states. The density of states shows that the low-temperature phase is an insulator for all U,V provided that V/U\ensuremath{\ne}1/2, while the high-temperature phase is a paramagnetic metal for all V if U2, and a paramagnetic insulator if U>2. Many detailed results are given.
Conventional Hartree-Fock mean field theory is used, for the first time, to investigate the full two-dimensional t-J model. To date, all other nontrivial mean field approaches modify the Hamiltonian or violate the double occupancy constraint. Unlike conventional mean field theory, these methods do not give variational results for the t-J model. The mean field phase diagram of the t-J model predicts enhanced superconductivity at the crossover between an insulating phase at low doping and a metallic phase at moderate doping. This behavior is remarkably similar to that of high temperature superconductors, for which the model is expected to provide a good description. In the mean field approximation, the t-J model is described by self-interacting spinless fermions hopping on a background lattice with spiral antiferromagnetic order. The interaction is attractive and high temperature superconductivity arises from the narrow bandwidth at the insulator to metal crossover.