Spin-valley skyrmions in graphene at filling factor $\nu=-1$
Résumé
We model quantum Hall skyrmions in graphene monolayer at quarter filling by a theory of CP3 fields and study the energy minimizing skyrmions in the presence of valley pseudospin anisotropy and Zeeman coupling. We present a diagram of all types of skyrmions in a wide range of the anisotropy parameters. For each type of skyrmion, we visualize it on three Bloch spheres, and present the profiles of its texture on the graphene honeycomb lattice, thus providing references for the scanning-tunneling microscopy and spectroscopy imaging of spin-pseudospin textures in graphene monolayer in the quantum Hall regime. Besides the spin and pseudospin skyrmions for the corresponding degrees of freedom of an electron in the N=0 Landau level, we discuss two unusual types—the “entanglement skyrmion”, the texture of which lies in the space of the entanglement of spin and pseudospin, as well as the “deflated pseudospin skyrmion” with partial entanglement. For all skyrmion types, we study the dependence of the energy and the size of a skyrmion on the anisotropy parameters and perpendicular magnetic field. We also propose three ways to modify the anisotropy energy, namely, the sample tilting, the substrate anisotropy, and the valley pseudospin analog of Zeeman coupling.