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Physical review. B, Condensed matter

Topology of the resonating valence-bond state: Solitons and high- T c superconductivity

Steven Allan Kivelson, Daniel S. Rokhsar, James P. Sethna

Published Jun 1, 1987• 885 citations
Publisher

Abstract

We study the topological order in the resonating valence-bond state. The elementary excitations have reversed charge-statistics relations: There are neutral spin-1/2 fermions and charge \ifmmode\pm\else\textpm\fi{}e spinless bosons, analogous to the solitons in polyacetylene. The charged excitations are very light, and form a degenerate Bose gas even at high temperatures. We discuss this model in the context of the recently discovered oxide superconductors.

DOI
10.1103/physrevb.35.8865

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arXiv:cond-mat/0507452•Physical Review B•Jul 18, 2005•1 citation
We study the topological order in the resonating valence-bond state. The elementary excitations have reversed charge-statistics relations: There are neutral spin-1/2 fermions and charge \ifmmode\pm\else\textpm\fi{}e spinless bosons, analogous to the solitons in polyacetylene. The charged excitations are very light, and form a degenerate Bose gas even at high temperatures. We discuss this model in the context of the recently discovered oxide superconductors.
We derive the neutral fermion excitation spectrum in the resonating-valence-bond state based on a fermion-boson field theory. It is formally shown that charge-eee bosons are created upon doping while the neutral fermion excitation remains gapless, predicting a linear low-temperature specific heat $C\ensuremath{\propto}\ensuremath{\gamma}T$ in the superconducting state. Bose condensation in doped samples leads to the observed superconductivity with true "off-diagonal long-range order."
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The energy associated with bosonic and fermionic pairs of topological spin defects in doped antiferromagnetic quantum spin-1∕21∕21∕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-Tc{T}_{c}Tc​ 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-Tc{T}_{c}Tc​ superconductivity.