Based on an improved SU(2) slave-boson approach showing coupling between the charge and spin degrees of freedom, we derive a phase diagram of high-
Tc cuprates which displays both the superconducting and pseudogap phases in the plane of temperature vs hole doping rate. It is shown that phase fluctuations in the order parameters result in a closer agreement with the observed phase diagram of an arch shape, by manifesting the presence of an optimal doping rate closer to observation, compared to the U(1) slave-boson theory.
To supplement our recent brief report on the theory of holon-pair boson approach to the t-J Hamiltonian [S.-S. Lee and Sung-Ho Suck Salk, Phys. Rev. B {\bf 64}, 052501(2001)], in this paper we present a full exposure to the theory, detailed physical implications and predicted various physical properties of high
Tc cuprates. We discuss the significance of coupling (interplay) between the spin and charge degrees of freedom in the Heisenberg interaction term of the t-J Hamiltonian. We discuss its importance in causing the arch-shaped superconducting transition temperature
Tc and the pseudogap (spin gap) temperature
T∗ tangential to
Tc in the overdoped region in the observed phase diagram of high
Tc cuprates. A universal parabolic scaling behavior of
T∗/Tc (or
Tc/T∗) with hole doping concentration is predicted in agreement with observations, indicating that there exists correlation between the pseudogap (spin gap) phase and the superconducting phase through antiferromagnetic fluctuations. Our proposed holon-pair boson theory is shown to be self-consistent in that it not only yields the arch (dome) shape structure of
Tc but also reproduces various other physical properties such as superfluid weight, bose condensation energy, spectral function, optical conductivity and spin susceptibility, including their temperature and doping dependence.
One of the major theoretical challenges in high- T c superconductivity is to first reproduce the observed phase diagrams that display the monotonously decreasing pseudogap temperature T * and the dome-shaped superconducting phase transition temperature T c in the plane of temperature vs. hole concentration. Earlier Lee and Salk [J. Korean Phys. Soc. 37, 545 (2000); Phys. Rev. B 64, 052501 (2001)] reported a successful reproduction of the phase diagram by providing a realistic gauge theoretic [SU(2)/U(1)] slave-boson approach to the t - J Hamiltonian. Most recently, we [S.-H. S. Salk, Quantum Studies: Mathematics and Foundations 5, 149 (2018)] presented a comprehensive discussion on both the SU(2) and the U(1) approaches from which one can readily understand the intimate relationship between the two formalisms and discussed that both approaches can lead to room-temperature superconductivity with suitably high values of the antiferromagnetic coupling constant J , owing to the demonstration of identical physical propensities, i.e. , the higher the J is, the higher the superconducting phase transition temperature T c is. Here, we discuss hither-to-unreported detailed numerical computations of the phase diagrams by varying the values of J by using the U(1) gauge slave-boson approach to the t − J Hamiltonian. For the sake of testing convergence, we vary the unit-cell lattice sizes from 10 × 10 to a sufficiently large size of 50 × 50. We find that even a small square lattice size of 20 × 20 is seen to show reliable agreement with the results for higher lattice sizes while the 50 × 50 lattice size displays complete convergence in both T* and T c . In addition, we present a physical analysis of the structure of the high- T c phase diagram, focusing on the role of the spin pairing order in association with the interplay between the pseudo-gap (spin gap) temperature and the bose-condensation temperature/dome-shaped superconducting phase transition temperature.
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.
Based on our improved SU(2) slave-boson approach (Phys. Rev. B 64, 052501(2001)) to the t-J Hamiltonian, we report a scaling behavior of pseudogap with doping and the temperature and doping dependence of spectral functions. In addition we discuss the cause of hump and quasi-particle peak in the observed spectral functions of high Tc cuprates. It is demonstrated that the sharpening of the observed quasi-particle peak below Tc is attributed to the bose condensation of holon pair. From the computed ratios of pseudogap
Δ0 to both the superconducting temperature Tc and the pseudogap temperature
T∗ as a function of hole doping concentration x, we find that there exists a universal scaling of these ratios with doping, that is, the hyperbolic scaling behavior of the former,
kBTc2Δ0∼x−α with
α∼2 and near doping independence of the latter,
kBT∗2Δ0≈4∼6 are found.
We investigate a possibility of holon pairing for bose condensation based on the Bethe-Salpeter equation obtained from the use of the t-J Hamiltonians of both t he U(1) and SU(2) slave-boson symmetries. It is shown that the vertex function contributed from ladder diagram series involving holon-holon scattering channel in the Bethe-Salpeter equation leads to a singular behavior at a critical temperature at each hole doping concentration, showing the instability of the normal state against holon pairing. We find that the holon pairing instability occurs only in a limited range of hole doping, by showing an "arch" shaped bose condensation line in agreement with observation for high
Tc cuprates. It is revealed that this is in agreement with a functional integral approach of the slave-boson theories.