Described is a flavour of the RVB theory of high Tc materials which uses the “slave boson” method. Holes are added by SU(3) rotation in the auxiliary particle space in a manner which does not violate the constraint Qi = 1. The effective spinon hopping matrix element J − 2xt is reduced by doping. The local SU(3) maps to S. C. Zhang’s SO(5) on two sites but has different π‐operators. Kondo like infrared divergences occur. The ARPES humb‐dip‐peak structure is reproduced.
Described is a flavour of the RVB theory of high Tc materials which uses the “slave boson” method. Holes are added by SU(3) rotation in the auxiliary particle space in a manner which does not violate the constraint Qi = 1. The effective spinon hopping matrix element J − 2xt is reduced by doping. The local SU(3) maps to S. C. Zhang’s SO(5) on two sites but has different π‐operators. Kondo like infrared divergences occur. The ARPES humb‐dip‐peak structure is reproduced.
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.
The interaction between the bosonic excitations as well as between the fermionic ones in the RVB systems with the (extended) Hubbard Hamiltonian were studied by means of the slave boson technique and the perturbation theory. The corresponding effective Hamiltonians have been found. It was shown, in particular, that in the RVB system with two interpenetrating sublattices there exists the effective attraction between two holons of different kinds as well as between two spinions of different kinds in the singlet state.
A Hamiltonian for the motion of oxygen holes strongly coupled to the Cu spins in a one-dimensional (1D) Cu-O lattice is solved exactly for all dopings. This Hamiltonian retains the dominant O-hole hopping term, that is, spin-exchange hopping of the hole spin with the intervening Cu spin and neglects the weaker non-spin-exchange hopping term. The excitations naturally separate into two independent quasiparticles: spinons and holons. It is this Hamiltonian that should be taken as the correct zeroth-order Hamiltonian from which perturbation theory should be applied. We show that the spinon spectrum is the spectrum of the 1D antiferromagnet incommensurate with the Cu lattice and the holons are spinless noninteracting fermions in a cosine band. The Cu-Cu spin correlation in the ground state increases linearly with doping from antiferromagnetic (-0.443) at x=0 to ferromagnetic (\ensuremath{\approxeq}0.19) at x=1.
This thesis deals with different aspects of high temperature superconductivity in hole-doped cuprates. We assume the t - J model to describe the CuO2 planes of cuprates and we use a spin-charge gauge approach with spin-charge separation to describe holes in terms of a spinless fermion carrying the charge (holon) and a neutral boson carrying spin 1/2 (spinon), coupled by a slave-particle gauge field. In this framework we consider the effects of the presence of a finite density of incoherent holon pairs in the normal state as a precursor of superconductivity. We show that it is possible to take such pairs into account through a strongly direction dependent spectral weight for holons, which suppresses quasi-particles starting from the anti-nodal directions, and a wave function renormalization for the slave particle gauge field. In this way we prove that, when temperature is reduced, the formation of holon pairs causes both the deviation from linearity of the resistivity and the deviation from the constant value of the Knight shift. Moreover we point out the need for a negative next-nearest-neighbor hopping term ((t - t' - J model) to get a good continuum limit and to evaluate the Knight shift. These results are obtained through a Green's function, which follows naturally from the formalism and analytically interpolates between a Fermi liquid-like behavior and a d-wave superconductor when the coherence length of the holon pair order parameter is increased. The system preserves a finite Fermi surface until the superconducting transition, where it reduces to four nodes. Finally when, at lower temperatures, both the holon pairs and the RVB spinon pairs condense we enter the superconducting phase. In this phase we study the magnetic excitations showing how to extend to spin waves the hourglass-shape dispersion, found for spinons near the antiferromagnetic vector, if a suitable local mechanism of attraction between spinon and anti-spinon is assumed. The resulting spin wave Green's function, whose imaginary part is directly comparable with experiments, generates the hourglass with a finite gap between the two branches. Since the U(1) slave-particle gauge field gains mass in the superconducting phase via Anderson-Higgs mechanism, we propose the necessary mechanism of attraction comes from the unbroken Z2 subgroup of the U(1) gauge group.
A possibility of holon (boson) pair condensation is explored for hole-doped high-Tc cuprates, by using the U(1) slave-boson representation of the $t\ensuremath{-}J$ Hamiltonian with the inclusion of hole-hole repulsion. A phase diagram of the hole doped high-Tc cuprates is deduced by allowing both the holon pairing and spinon pairing channels. It is shown that the spin gap size remains nearly unchanged below the holon pair condensation temperature. We find that the s-wave holon pairing under the condition of d-wave spin singlet pairing is preferred, thus allowing d-wave hole pairing.
We study a system of doped antiferromagnet in three dimensions at finite temperatures using the t-J model, a canonical model of strongly correlated electrons. We employ the slave-fermion representation of electrons, in which an electron is described as a composite of a charged spinless holon and a chargeless spinon. We introduce two kinds of U(1) gauge fields on links as auxiliary fields, one describing resonating valence bonds of antiferromagnetic nearest-neighbor spin pairs and the other for nearest-neighbor hopping amplitudes of holons and spinons in the ferromagnetic channel. To perform a numerical study of the system, we integrate out the fermionic holon field by using the hopping expansion in powers of the hopping amplitude, which is legitimate for the region in and near the insulating phase. The resultant effective model is described in terms of bosonic spinons, two U(1) gauge fields, and a collective field for hole pairs. We study this model by means of Monte Carlo simulations, calculating the specific heat, spin correlation functions, and instanton densities. We obtain a phase diagram in the hole concentration-temperature plane, which is in good agreement with that observed recently for clean and homogeneous underdoped samples.