Using the improved U(1) and SU(2) slave-boson approaches of the $t\ensuremath{-}J$ Hamiltonian [S.-S. Lee and Sung-Ho Suck Salk, Phys. Rev. B 64, 052501 (2001)] that we developed recently, we study the doping and temperature dependence of superfluid weight and spectral function and discuss our finding of the universal scaling behavior of the pseudogap. It is shown that at low hole doping concentrations
x and at low temperatures
T, there exists a propensity of linear decrease in the superfluid weight
ns∕m∗ with temperature
T, and a tendency of doping independence in the linearly decreasing slopes of
(ns∕m∗)(x,T) with
T in qualitative agreement with the experimentally observed relation; that is, $({n}_{s}∕{m}^{*})(x,T)=({n}_{s}∕{m}^{*})(x,0)\ensuremath{-}\ensuremath{\alpha}T$, where $\ensuremath{\alpha}$ is a constant. It is also demonstrated that there exists a boomerang behavior; that is, both
Tc and
ns∕m∗ increase with hole doping concentration
x in the underdoped region, reach a saturation (maximum) at a hole doping above optimal doping, and decrease beyond the saturation point in the overdoped region, in agreement with $\ensuremath{\mu}\mathrm{SR}$ measurements. Based on our improved SU(2) slave-boson approach to the $t\ensuremath{-}J$ Hamiltonian, we further investigate the doping and temperature dependence of the spectral function and discuss our theoretical finding of a scaling behavior of the pseudogap. In addition, we discuss the cause of the hump and quasiparticle peak in the observed spectral functions of high
Tc cuprates. It is demonstrated that the sharpening of the observed quasiparticle peak below
Tc is attributed to the bose condensation of holon pair, in agreement with observations. From the predicted ratios of the pseudogap ${\ensuremath{\Delta}}_{0}$ to both the superconducting temperature
Tc and the pseudogap temperature
T∗, i.e., $2{\ensuremath{\Delta}}_{0}∕{k}_{B}{T}_{c}$ and $2{\ensuremath{\Delta}}_{0}∕{k}_{B}{T}^{*}$, respectively, as a function of hole doping concentration
x, we find that there exists a universal scaling behavior (sample independence) of these ratios with doping, by showing a nonlinearly decreasing behavior of the former; that is, $2{\ensuremath{\Delta}}_{0}∕{k}_{B}{T}_{c}\ensuremath{\sim}{x}^{\ensuremath{-}\ensuremath{\alpha}}$ with $\ensuremath{\alpha}\ensuremath{\sim}2$ and a near doping independence of the latter; that is, $2{\ensuremath{\Delta}}_{0}∕{k}_{B}{T}^{*}\ensuremath{\approx}4--6$.
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.
The phase fluctuations of the condensate in doped antiferromagnets, described by a ${t\ensuremath{-}t}^{\ensuremath{'}}\ensuremath{-}J$ model and a suitable
1/N expansion, provide a mechanism for a Kosterlitz-Thouless (KT) type of transition to a superconducting state below
Tc. In this paper, we present a Monte Carlo study of the corresponding superfluid weight
Ds(T) in the classical (large-
N) limit, as a function of temperature and doping. Consistent with generic experimental trends,
Ds(T) exhibits a T-linear decrease at low temperatures, with the magnitude of the slope ${D}_{s}^{\ensuremath{'}}(0)$ increasing upon doping. Finite-size scaling in the underdoped regime predicts values for the dimensionless ratio
A=kBTc/Ds(0) of order unity, with
A=0.4435(5) in the half filled band limit, thus confirming
Ds(0) as the fundamental energy scale determining
Tc. Our Monte Carlo results for
Ds(T)/Ds(0) vs
kBT/Ds(0), at 10% hole doping, are found to be in reasonable agreement with recent measurements on ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4},$ with
x=0.10, throughout the temperature range below the theoretical KT transition temperature
Tc.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.
Based on our recent holon-pair boson theory of the t-J Hamiltonian (Phys. Rev. B 64, 052501 (2001)) we report the doping dependence of the bose condensation energy, superfluid weight and spectral peak intensity. We find a universality of doping dependence in these physical quantities, by equally showing an arch shape in the variations of their magnitudes with the hole doping concentration. We find that all of these physical quantities scale well with the positive charge carrier (hole) density x, but not with the electron density 1-x for the entire range of hole doping. It is shown that the doping dependence of the condensation energy U at T = 0 K is given by the relation,
U(0)≈αx2∣Δ0∣2 with
Δ0, the pairing gap at 0 K and
α, a constant.