Vortex, Skyrmion, and elliptical domain-wall textures in the two-dimensional Hubbard model

Abstract

The spin and charge texture around doped holes in the two-dimensional Hubbard model is calculated within an unrestricted spin rotational invariant slave-boson approach. In the first part, we examine in detail the spin structure around two holes doped in the half-filled system where we have studied cluster sizes up to $10\ifmmode\times\else\texttimes\fi{}10.$ It turns out that the most stable configuration corresponds to a vortex-antivortex pair that has lower energy than the N\'eel-type bipolaron even when one takes the far field contribution into account. We also obtain Skyrmions as local minima of the energy functional but with higher total energy than the vortex solutions. Additionally, we have investigated the stability of elliptical domain walls for commensurate hole concentrations. We find that (i) these phases correspond to local minima of the energy functional only in case of partially filled walls, (ii) elliptical domain walls are only stable in the low-doping regime.