Zeeman coupling and screening corrections to skyrmion excitations in graphene

Abstract

At half-filling of the fourfold degenerate Landau levels $|n|\ensuremath{\ge}1$ in graphene, the ground states are spin-polarized quantum Hall states that support spin skyrmion excitations for $|n|=1,2,3$. Working in the Hartree-Fock approximation, we compute the excitation energy of an unbound spin skyrmion-antiskyrmion excitation as a function of the Zeeman coupling strength for these Landau levels. We find for both the bare and screened Coulomb interactions that the spin skyrmion-antiskyrmion excitation energy is lower than the excitation energy of an unbound spin-$1/2$ electron-hole pair in a finite range of Zeeman coupling in Landau levels $|n|=1,2,3$. This range decreases rapidly for increasing Landau level index and is extremely small for $|n|=3.$ For valley skyrmions, which should be present at $1/4$ and $3/4$ fillings of the Landau levels $|n|=1,2,3$, we show that screening corrections are more important in the latter case. It follows that an unbound valley skyrmion-antiskyrmion excitation has lower energy at $3/4$ filling than at $1/4.$ We compare our results with recent experiments on spin and valley skyrmion excitations in graphene.