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Physical review. B, Condensed matter

Holon pairing instability based on the Bethe-Salpeter equation obtained from the t−J Hamiltonians of both U(1) and SU(2) slave-boson symmetries

Sung-Sik Lee, Sung‐Ho Suck Salk

Published Aug 20, 2002• 8 citations
Publisher

Abstract

A Bethe-Salpeter equation is obtained by using of the $t\ensuremath{-}J$ Hamiltonians that satisfy the U(1) and the SU(2) slave-boson symmetries, respectively. Holon-holon scattering channels in the Bethe-Salpeter equation are judiciously examined at a critical temperature to study the instability of the normal state against holon pairing. From the present study of the holon pairing instability, an arch-shaped bose condensation line is revealed in agreement with the observation for high-${T}_{c}$ cuprates over a range of hole doping concentration.

DOI
10.1103/physrevb.66.054427

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A Bethe-Salpeter equation is obtained by using of the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J Hamiltonians that satisfy the U(1) and the SU(2) slave-boson symmetries, respectively. Holon-holon scattering channels in the Bethe-Salpeter equation are judiciously examined at a critical temperature to study the instability of the normal state against holon pairing. From the present study of the holon pairing instability, an arch-shaped bose condensation line is revealed in agreement with the observation for high-Tc{T}_{c}Tc​ cuprates over a range of hole doping concentration.
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 TcT_cTc​ cuprates. It is revealed that this is in agreement with a functional integral approach of the slave-boson theories.
Holon Pair Bose Condensation in High TcT_cTc​ Cuprates; Symmetry Breaking and Supersymmetry Conditions
Using the t-J Hamiltonian of U(1) slave-boson symmetry, bose condensation is discussed by showing the occurrence of symmetry breaking in the hole doped high TcT_cTc​ cuprates. The symmetry breaking is shown to take place with the d-wave hole pairing, but not with the s-wave hole pairing. Based on a derived supersymmetry Hamiltonian we find that there exists a possibility of supersymmetry conditions in association with the pairing order parameters of both spinon and holon.
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.
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.
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.