Quantum Hall Skyrmions with Higher Topological Charge

TL;DR

This paper explores quantum Hall skyrmions with higher topological charge, revealing that under very low Zeeman energy, charge two skyrmions become energetically favorable and form stable pairs with increased spin per charge.

Contribution

It demonstrates that at extremely low Zeeman energies, charge two skyrmions are energetically favored and form stable pairs, a novel finding in quantum Hall skyrmion research.

Findings

Charge two skyrmions become less costly to create than two charge one skyrmions at very low Zeeman energy.

Doubly charged skyrmions are stable against further charge addition.

They exhibit approximately 10% more spin per unit charge than single-charge skyrmions.

Abstract

We have investigated quantum Hall skyrmions at filling factor \nu=1 carrying more than one unit of topological, and hence electric, charge. Using a combination of analytic and numerical methods we find the counterintuitive result that when the Zeeman energy is tuned to values much smaller than the interaction energy (g \mu_B B/(e^2/\epsilon\ell) < 9*10^{-5}),the creation energy of a charge two skyrmion becomes less than twice the creation energy of a charge one skyrmion, i.e. skyrmions bind in pairs. The doubly charged skyrmions are stable to further accretion of charge and exhibit a 10% larger spin per unit charge than charge one skyrmions which would, in principle, signal this pairing.