Spin and charge dynamics in the 2-D systems of strongly correlated ele…

"For the last two decades since the advent of high temperature superconductivity, noticeable progress

has been made to understand both normal and superconducting states by paying attention to phase

diagrams[1], electronic structures[2], thermal properties, super°uidity[3] and both spin[4, 5] and

charge dynamics[6]. Despite the progress there exists no satisfactory theory which consistently repr

oduces various physical properties of cuprate oxides in association with the phase diagram. High Tc

superconductivity is involved with low (two) dimensional systems of strongly correlated electrons,

namely the cuprate oxides acting as Mott insulators. To tackle this problem, theoretical efforts have

been made using either the Hubbard Hamiltonian or the t-J Hamiltonian. Electrons have three ""faces"":

namely, the spin, charge and quantum phase. To meet the three essential faces, earlier we[7] propo

sed both U(1) and SU(2) gauge theoretic slave-boson theories of the t . J Hamiltonian in which coup

ling between the spin pairing and charge paring orders are properly taken care of, contrary to other

slave-boson theories[8, 9]. Thanks to the fact that the Cooper pair is realized as a composite of the

spinon (spin) and holon (charge) pairing orders in our slave-boson treatment, not only the dome-shap

ed phase diagram but other physical properties are consistently reproduced in agreements with meas

urements : superfluid weight, spectral function[10], optical conductivity[11], magnetic susceptibility

and the universal scaling behavior of T ¤=Tc[12]. In this talk we present a study of spin dynamics and

charge dynamics. We explain how the two different dynamics are coupled to cause various exotic

physical phenomena such as the dome-shaped bose condensation temperature, the boomerang

behavior of superfluid weight and peak-dip-hump structures of both spectral function and optical

conductivity. Regarding the charge dynamics we .find that the peak-dip-hump structure in optical

conductivity is attributed to coupling between the spin and charge degrees of freedom, but not to

the spin-charge separation. Further, quantum critical point will found in light of charge dynamics.

Regarding the spin dynamics we unveil physics involved with both temperature and doping depen

dence of magnetic resonance. We find from this study that the onset temperature of magnetic reso

nance which occurs in spin-exciton channel is the pseudogap (spin gap) temperature T . in agree

ment with measurements of Mook and coworkers[4]. The resonance peak energy Eres is shown to

have a linear scaling behavior with the superconducting transition temperature, Tc, in agreements

with observations of Keimer and coworkers[5]. We demonstrate that the spin pairing correlations are

responsible for both the linear scaling of Eres ∼ Tc and the universal scaling behavior of T ¤=Tc[12].

Finally an integrated view of physics of the above novel features will be highlighted in the language of

coupling between the spin and charge degrees of freedom and the spin and charge dynamics. "