Bond-operator theory of doped antiferromagnets: From Mott insulators with bond-centered charge order to superconductors with nodal fermions

Abstract

The ground states and excitations of two-dimensional insulating and doped Mott insulators are described by a bond operator formalism. While the method represents the degrees of freedom of an arbitrary antiferromagnet exactly, it is especially suited to systems in which there is a natural pairing of sites into bonds, as in states with spontaneous or explicit spin-Peierls order (or bond-centered charge order). In the undoped insulator, as discussed previously, we obtain both paramagnetic and magnetically-ordered states. We describe the evolution of superconducting order in the ground state with increasing doping-at low doping, the superconductivity is weak, can co-exist with magnetic order, and there are no gapless spin 1/2 fermionic excitations; at high doping, the magnetic order is absent and we obtain a BCS d-wave superconductor with gapless spin 1/2, nodal fermions. We present the critical theory describing the onset of these nodal fermionic excitations. We discuss the evolution of the spin spectrum, and obtain regimes where a spin 1 exciton contributes a sharp resonance in the dynamic spin susceptiblity. We also discuss the experimental consequences of low-energy, dynamically fluctuating, spin-Peierls order in an isotropic CuO2 plane-we compute consequences for the damping and dispersion of an optical phonon involving primarily the O ions, and compare the results with recent neutron scattering measurements of phonon spectra.

Competition between spin density wave order and superconductivity in the underdoped cuprates

“…(2.20), and so compute H c2 as a function of both α 1 and the SDW tuning parameter α 2 . The natural scale for the magnetic field is 28) where in the last step we have used values from the quantum oscillation experiment 1 quoted in Section I. Our results for H c2 /H m are shown in Fig.…”

“…Numerical studies of models in which the strong local repulsion associated with Mott insulator is implemented in a mean-field manner do appear to restore aspects of the picture of competing orders. 28,29 Here, we shall provide a detailed study of the model of the underdoped cuprates proposed in Refs. 7,8,24,25, and show that it is consistent with the features A, B, and C of the theory of competing orders noted above, which are essential in the interpretation of the experiments.…”

Understanding correlated electron systems by a classification of Mott insulators

“…The fate of the d = 2 bond-ordered paramagnet upon doping with mobile charge carriers has been investigated in a number of studies [4,38,53,54,55]. As stated earlier, the bond order survives for a finite range of doping concentrations.…”

Plaquette boson-fermion model of cuprates

“…For one electron per site (half filling), the short range antiferromagnetic correlations are apparent when diagonalizing (1) and (2) on two sites. The dimer states were used to construct effective models on the ladder 20,21 and for spin-Peierls phases on the square lattice 22 . The projected SO(5) model was defined on a ladder using empty dimer states as the hole pair bosons 6 .…”