Spin-skyrmion in graphene

In the presence of a magnetic field, the band structure of the two-dimensional electron gas in graphene consists in a series of Landau levels with energy $E_{n}=\pm \sqrt{2} v_{F}\sqrt{\left\vert n\right\vert }/\ell .$ Each Landau level is 4-fold degenerate including valley and spin degrees of freedom. Working in the Hartree-Fock approximation and a finite Zeeman coupling, we compute the energy required to excite a spin-skyrmion (or antiskyrmion) in Landau levels $n=1,2$ at filling factors $\nu =4,8.$ We show that a skyrmion-antiskyrmion pair has lower energy than an electron-hole pair at these two filling factors. We compare our results with a field-theoretical calculation [1] and with a recent experimental measurement of the transport activation gap in this system. \\[4pt] [1] Kun Yang, S. Das Sarma and A. H. MacDonald, Phys. Rev. B \textbf{74}, 075423 (2006).