Electron - hole asymmetry and activation energy in quantum Hall ferromagnets

We argue that the dissipative transport in ferromagnetic quantum Hall effect liquids at $\nu =2N+1$ is dominated by the thermal activation of pairs consisting of an electron and an antiskyrmion (topological texture which represents a hole with ‘screened’ exchange interaction), thus manifesting the lack of electron-hole symmetry in quantum Hall ferromagnets. We find that the activation energy of such a pair is not the exchange energy, but is determined by the interplay between the excess Zeeman energy of a skyrmion and the charging energy of its topological texture: $$\mathcal{E}=a{ϵ}_{\mathrm{Z}}^{1\mathrm{/}3}{E}_{\mathrm{C}}^{2\mathrm{/}3}{\ln }^{1\mathrm{/}3}(\frac{{\mathrm{\Im }}_i}{E_{\mathrm{C}}^{2\mathrm{/}3}{ϵ}_{\mathrm{Z}}^{1\mathrm{/}3}}),E_{\mathrm{C}}=\frac{e^2}{\chi \lambda },$$ with $a\approx 1.75$.