Spin-structure on the surface of a sphere

When the kinetic energy of a many-electron system is quenched, as in quantum Hall ferromagnets, electron-electron interactions can drive the system to form interesting manybody states. Such energy degeneracy occurs in quantum Hall systems under high magnetic field and low temperatures. Electrons on the surface of a sphere display similarly degenerate single particle states as a function of magnetic quantum number m for fixed orbital quantum number l. We explore the possibility of novel manybody states in this system by constructing variational wavefunctions using both a Hartree-Fock approach and by a physically motivated ansatz. We calculate a bound on the groundstate energy for the case of a contact interaction and the Coulomb interaction, comparing the energy of states with a spin texture with that of the untextured state. We investigate that the textured-spin structure can result in the lower energy of the system than the non-textured counterparts. We discuss considerations for realizing this system in semiconductor core-shell quantum dots, such as the choice of material, thickness and the role of screening.