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arXiv:cond-mat/0507452 · Physical Review B

Bosonic versus fermionic pairs of topological spin defects in monolayered high- Tc superconductors

M. A. García‐Bach

Published Jul 18, 2005• 1 citation
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Abstract

The energy associated with bosonic and fermionic pairs of topological spin defects in doped antiferromagnetic quantum spin-$1∕2$ square lattice is estimated within a resonating valence bond scenario, as described by a $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$-like model Hamiltonian, plus a ${t}_{\ensuremath{\perp}}$, responsible of a three-dimensional screening of the electrostatic repulsion within the bosonic pairs. For parameters appropriate for monolayered high-${T}_{c}$ superconductors, both fermionic and bosonic pairs show ${x}^{2}\ensuremath{-}{y}^{2}$ symmetry. We find a critical value of doping such that the energy of the bosonic pairs goes below twice the energy of two fermionic pairs at their Fermi level. This finding could be related to the onset of high-${T}_{c}$ superconductivity.

DOI
10.1103/physrevb.72.024530

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We present a strong-coupling approach to the theory of high-temperature superconductivity based on the observation of a quantum critical point in the plaquette within the $t,{t}^{\ensuremath{'}}$ Hubbard model. The crossing of ground-state energies in the N=2−−4N=2--4N=2−−4 sectors occurs for parameters close to the optimal doping. The theory predicts the maximum of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave order parameter at the border between localized and itinerant electron behaviors and gives a natural explanation for the pseudogap formation via the soft-fermion mode related to local singlet states of the plaquette in the environment. Our approach follows the general line of resonating valence-bond theory stressing a crucial role of singlets in the physics of high-Tc{T}_{c}Tc​ superconductors but focuses on the formation of local singlets, similar to phenomena observed in frustrated one-dimensional quantum spin models.
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A connection between quantum antiferromagnetism and high Tc{T}_{c}Tc​ superconductivity is theoretically investigated by analyzing the $t\text{\ensuremath{-}}J$ model and its relationships to the Gutzwiller-projected BCS Hamiltonian. After numerical corroboration via exact diagonalization, it is analytically shown that the ground state of the $t\text{\ensuremath{-}}J$ model at half filling [i.e., the two-dimensional (2D) antiferromagnetic Heisenberg model] is entirely equivalent to the ground state of the Gutzwiller-projected BCS Hamiltonian with strong pairing. Combined with the high wave function overlap between the ground states of the $t\text{\ensuremath{-}}J$ model and the projected BCS Hamiltonian at moderate doping, this equivalence provides strong support for the existence of superconductivity in the $t\text{\ensuremath{-}}J$ model. The relationship between the ground state of the projected BCS Hamiltonian and Anderson's resonating valence bond state (i.e., the projected BCS ground state) is discussed.