We probe for statistical and Coulomb induced spin textures among the low-lying states of repulsively-interacting particles confined to potentials that are both rotationally and time-reversal invariant. In particular, we focus on two-dimensional quantum dots and employ configurationinteraction techniques to directly compute the correlated many-body eigenstates of the system. We produce spatial maps of the single-particle charge and spin density and verify the annular structure of the charge density and the rotational invariance of the spin field. We further compute two-point spin correlations to determine the correlated structure of a single component of the spin vector field. In addition, we compute three-point spin correlation functions to uncover chiral structures. We present evidence for both chiral and quasi-topological spin textures within energetically degenerate subspaces in the three-and four-particle system. PACS numbers: 73.21. La, 03.65.Vf

We provide unambiguous theoretical evidence for the formation of correlation-induced isolated merons in rotationally symmetric quantum dots. Our calculations rely on neither the lowest-Landau-level approximation, nor on the maximum-density-droplet approximation, nor on the existence of a spin-polarized state. For experimentally accessible system parameters, unbound merons condense in the ground state at magnetic fields as low as B * = 0.2 T and for as few as N = 3 confined fermions. The fourfold degenerate ground state at B * corresponds to four orthogonal merons |QC characterized by their topological chirality C and charge Q. This degeneracy is lifted by the Rashba and Dresselhaus spin-orbit interaction, which we include perturbatively, yielding spectroscopic accessibility to individual merons. We further derive a closed-form expression for the topological chirality in the form of a chiral spin current and use it to both characterize our states and predict the existence of other topological textures in other regions of phase space, for example, at N = 5. Finally, we compare the spin textures of our numerically exact meron states to ansatz wave functions of merons in quantum Hall droplets and find that the ansatz qualitatively describes the meron states.

We present results on spin and charge correlations in two-dimensional quantum dots as a function of increasing Coulomb strength (dielectric constant). We look specifically at the orbital occupation of both spin and charge. We find that charge and spin evolve separately, especially at low Coulomb strength. For the charge, we find that a hole develops in the core orbitals at strong Coulomb repulsion, invalidating the common segregation of confined electrons into an inert core and active valence electrons. For excitations, we find a total spin-projection Sz = –1/2 breaks apart into separate occupations of net positive and negative spin. This dissociation is caused by spin correlations alone. Quantum fluctuations arising from long-range Coulomb repulsion destroy the spin dissociation and eventually results in all orbitals carrying a negative spin.

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