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Physical review. B, Condensed matter

High- Tc phase diagram based on the SU(2) slave-boson approach to the t−J Hamiltonian

Sung-Sik Lee, Sung‐Ho Suck Salk

Published Jun 25, 2001• 23 citations
Publisher

Abstract

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-${T}_{c}$ 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.

DOI
10.1103/physrevb.64.052501

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High $T_c$ Phase Diagram based on the SU(2) Slave-Boson Approach to the t-J Hamiltonian

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Based on an improved SU(2) slave-boson approach to the t-J Hamiltonian, we derive a phase diagram of high $T_c$ 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.

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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.

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SU(2) formulation of the t−J model: Application to underdoped cuprates

Patrick A. Lee, Naoto Nagaosa, Tai Kai Ng +1 more

We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping that respects an SU(2) symmetry: a symmetry previously known to be important at half filling. The mean-field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain $d$-wave superconductor, spin-gap, strange metal, and Fermi-liquid phases. The spin-gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The physical electron spectral function shows small Fermi segments at low doping that continuously evolve into the large Fermi surface at high-doping concentrations. The close relation between the SU(2) and the U(1) slave-boson theory is discussed. The low-energy effective theory for the low-lying fluctuations is derived and additional lying modes [which were overlooked in the U(1) theory] are identified.

arXiv:cond-mat/9701168•Physical review. B, Condensed matter•Mar 1, 1998•213 citations
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.
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.
The SU(2) slave-boson mean-field theory for the ${\mathrm{tt}}^{\ensuremath{'}}J$ model is analyzed. The role of next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ on the phase diagram is studied. We find a pseudogap phase in hole-doped (HD) materials (where ${t}^{\ensuremath{'}}<0).$ The pseudogap phase is a U(1) spin liquid (the staggered-flux phase) with a U(1) gauge interaction and no fractionalization. This agrees with experiments on HD samples. The same calculation also indicates that a positive ${t}^{\ensuremath{'}}$ favors a Z2{Z}_{2}Z2​ state with true spin-charge separation. The Z2{Z}_{2}Z2​ state that exists when ${t}^{\ensuremath{'}}\ensuremath{\gtrsim}0.5J$ can be a candidate for the pseudogap phase of electron-doped (ED) cuprates (if such a phase exists). The experimental situation in ED materials is also addressed.
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.
We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping that respects an SU(2) symmetry: a symmetry previously known to be important at half filling. The mean-field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain ddd-wave superconductor, spin-gap, strange metal, and Fermi-liquid phases. The spin-gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The physical electron spectral function shows small Fermi segments at low doping that continuously evolve into the large Fermi surface at high-doping concentrations. The close relation between the SU(2) and the U(1) slave-boson theory is discussed. The low-energy effective theory for the low-lying fluctuations is derived and additional lying modes [which were overlooked in the U(1) theory] are identified.