Quantum Hall Skyrmions with higher topological charge

Abstract

We have investigated quantum Hall Skyrmions at filling factor $\ensuremath{\nu}=1$ 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 $[g{\ensuremath{\mu}}_{B}{B/(e}^{2}/\ensuremath{\epsilon}\mathcal{l})<8.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$], 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.