Chiral spin currents and spectroscopically accessible single merons in quantum dots

TL;DR

This paper provides theoretical evidence for the formation of correlation-induced merons in quantum dots, demonstrating their properties, spectroscopic accessibility, and potential for observing topological textures in confined fermion systems.

Contribution

It introduces a novel theoretical framework for unambiguously identifying merons in quantum dots without common approximations, and predicts their spectroscopic accessibility via spin-orbit interactions.

Findings

Merons form in the ground state at low magnetic fields for small fermion numbers.

Degeneracy of meron states is lifted by spin-orbit interactions, enabling spectroscopic detection.

The topological chirality can be characterized by a chiral spin current.

Abstract

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 four-fold degenerate ground-state at $B^*$ corresponds to four orthogonal merons $\ket{QC}$ 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.