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Journal of the Korean Physical Society

A Detailed Numerical Analysis for High-Tc Superconductivity and Physical Analysis of the High-Tc Phase Diagram Based on the U(1) Slave-Boson Approach to the t − J Hamiltonian

Sul-Ah Ahn, Hyeyoung Cho, Sung‐Ho Suck Salk

Published Jun 1, 2020• 1 citation
Publisher

Abstract

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.

DOI
10.3938/jkps.76.1020

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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.
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 TcT_cTc​ 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 TcT_cTc​ and the pseudogap (spin gap) temperature T∗T^*T∗ tangential to TcT_cTc​ in the overdoped region in the observed phase diagram of high TcT_cTc​ cuprates. A universal parabolic scaling behavior of T∗/TcT^*/T_cT∗/Tc​ (or Tc/T∗T_c/T^*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 TcT_cTc​ 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.
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{T}_{c}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.
High TcT_cTc​ Phase Diagram based on the SU(2) Slave-Boson Approach to the t-J Hamiltonian
Based on an improved SU(2) slave-boson approach to the t-J Hamiltonian, we derive a phase diagram of high TcT_cTc​ cuprates which displays both the superconducting and pseudogap phases in the plane of temperature vs. hole doping rate. It is shown that the inclusion of phase fluctuations in the order parameters results in a closer agreement with the observed superconducting temperature(bose condensation line) of an arch shape as a function of hole doping rate.
A possibility of holon (boson) pair condensation is explored for hole-doped high-Tc{T}_{c}Tc​ cuprates, by using the U(1)U(1)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{T}_{c}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 Δ0Δ_0Δ0​ to both the superconducting temperature Tc and the pseudogap temperature T∗T^*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, 2Δ0kBTc∼x−α\frac{2 Δ_0}{k_B T_c} \sim x^{-α}kB​Tc​2Δ0​​∼x−α with α∼2α\sim 2α∼2 and near doping independence of the latter, 2Δ0kBT∗≈4∼6\frac{2 Δ_0}{k_B T^*} \approx 4 \sim 6kB​T∗2Δ0​​≈4∼6 are found.
We outline the basic ideas involved in a recently proposed [17] derivation of a gauge theory for underdoped cuprates in the “spin gap phase”, performed essentially step by step starting from the t — J model, considered as a model Hamiltonian for the CuO2 layers. The basic tool is the U(1) x SU(2) Chern-Simons bosonization, to which it is dedicated a somewhat detailed discussion. The basic output is a “spingap” not vanishing in any direction and an antiferromagnetic correlation length proportional to the inverse square root of doping concentration, in agreement with data deduced from the neutron experiments. The model also exhibits a small half-pocket Fermi surface around (±π/2, ±π/2) and a linear in temperature dependence of in-plane resistivity in certain temperature range.