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 spin-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 ͑doping͒. 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/tϾ2, this soliton is unstable to the formation of a lower energy charged, bosonic domain wall soliton, centered on a single site. For US/tϽ 2, 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 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 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 moments͒ 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.

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“…This is more straightforward to see in a simpler, continuum version of the model, obtained by letting the lattice constant a → 0 (see Ref. 17,18). Since the dispersion relation near the Fermi point q = ( π 2a , π 2a ) is isotropic, the dependence on k = K − q → −i∇ r of the continuum HF equations is such that it preserves rotational invariance.…”

“…As a result, the 2D HF equation reduces trivially to a 1D radial equation, with a structure very similar to that of the 1D differential HF equation obtained for the 1D Hubbard model. 17,18 Once this radial 1D solution is found, the 2D configuration is simply generated through a 2π rotation about an axis perpendicular to the 2D plane. As a result, there is a close analogy between solutions obtained for the 1D Hubbard model and for the 2D spin-flux model, in all our investigations.…”

“…The doping hole is trapped in the core of a magnetic vortex, which indeed has azimuthal symmetry. The bound level on which the hole is trapped can be shown 18,14 to be split from the top of the valence band and drawn deep inside the Mott-Hubbard gap. As a result, the meronvortex is a charged boson.…”

“…An argument based on the electronic structure, identical to the one offered for the charged bosonic domain-walls of the polyacetylene, also holds. 17,18,14,20 The parallel to the quasi-one dimensional 1D polyacetylene is again a reflection of azimuthal symmetry which reduces the 2D continuum model to a 1D radial equation. Clearly, the isotropic dispersion about the Fermi points is responsible for the appearance of bosonic charge carriers.…”

“…The charged domain-wall traps the hole on a pair of levels that are localized deep inside the Mott-Hubbard gap, and is a charged boson. 17,18,10 The analog of the spinbag is the spin-polaron, which disturbs the AFM order only locally, trapping the hole in its small FM core. As a result, the spin-polaron carries both charge and spin− 1 2 .…”