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International Journal of Modern Physics B

HOLON-PAIR CONDENSATION OF HIGH T c CUPRATES: SUPERSYMMETRY CONDITIONS

Sung-Sik Lee, Sung‐Ho Suck Salk

Published Dec 20, 1999• 8 citations
Publisher

Abstract

Based on the t–J Hamiltonian of U(1) slave-boson symmetry it is shown from our derived free energy that symmetry breaking can occur to allow holon-pair bose condensation. Supersymmetry conditions are proposed based on our derived quasiparticle Hamiltonian involving both spinons and holons.
DOI
10.1142/s0217979299003209

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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.
In order to obtain a reasonable phase diagram involving hole-pair condensation for hole-doped cuprate systems, we propose a modified t-J Hamiltonian in which a Coulomb repulsion term between nearest neighbor holes is considered. We show from the investigation of free energy that holon pair condensation can occur as a result of symmetry breaking. In addition, we introduce a possibility of supersymmetry condition at T=0KT=0KT=0K in the intermediate region between the antiferromagnetic phase and the superconducting phase.
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.
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-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.