Charged bosons in a doped Mott insulator: Electronic properties of domain-wall solitons and meron vortices

Abstract

We demonstrate from first principles that when a charge carrier is added to a $\mathrm{spin}\ensuremath{-}1/2$ antiferromagnetic Mott insulator in either a one- or two-dimensional lattice, the self-consistent, Hartree-Fock ground state consists of a magnetic soliton texture with a doubly degenerate electronic level at the center of the Mott-Hubbard charge gap. This model is appropriate to systems with weak interchain or interlayer magnetic couplings in which long-range antiferromagnetic order is observed in the absence of charge carriers (doping). These magnetic solitons mediate the destruction of the magnetic order as the charge carrier concentration is increased. In a one-dimensional lattice with nearest-neighbor hopping $t$, on-site Coulomb repulsion $U,$ and self-consistent, antiferromagnetic moment amplitude $S$, we find that a charged, fermionic, magnetic domain wall soliton with a weakly ferromagnetic core, centered between two sites, has lower Hartree-Fock energy than a corresponding charged quasiparticle in one of the Mott-Hubbard bands. However, for $US/tg2$, this soliton is unstable to the formation of a lower energy charged, bosonic domain wall soliton, centered on a single site. For $US/tl2$, both of the above solitons are charged bosons. The self-consistent structure of these solitons exhibits no rotation of the local magnetic moments, but only a local suppression of the local moment amplitude in the vicinity of the hole. In the absence of doping, charge neutral domain wall solitons exhibit spin rotation within their core region. The equilibrium core size $\ensuremath{\rho}$ is determined by the degree of magnetic anisotropy. The ferromagnetic core soliton exhibits a pair of nondegenerate near-midgap electronic states. The antiferromagnetic core soliton exhibits a pair of nondegenerate electronic states that are symmetric about the midgap energy and that merge into the continuum as the anisotropy effects are made small and the soliton core radius $\ensuremath{\rho}$ becomes very large. The two-dimensional antiferromagnetic Mott insulator exhibits analogous behavior to the one-dimensional model. This analogy is precise for a 2D antiferromagnet exhibiting spin flux. For the undoped Mott insulator, the ferromagnetic core meron vortex (``lotus flower'' configuration of local magnetic moments) exhibits a doubly degenerate electronic midgap state in the continuum model and is the analog of the 1D neutral domain wall soliton. We demonstrate that a hole added to the 2D system can form a charged bosonic collective excitation, in which the spin background around the hole forms a planar vortex with local antiferromagnetic correlations at infinity and vanishing local-moment amplitude at the core of the soliton.