▎ 摘　　要

We present a theory of the electronic properties of gated graphene nanoribbon rings with zigzag edges in Mobius and cylindrical configurations. The finite width opens a gap and nontrivial topology of the Mobius ring leads to a single edge with edge states with an induced, effective gauge field, in analogy to topological insulators. The single zigzag edge leads to a shell of degenerate states at the Fermi level and a ferromagnetic (FM) ground state at half-filling, i.e., at charge neutrality, due to electron-electron interactions. For fractional fillings, both the magnetic moment and the energy gap are found to oscillate as a function of the shell filling. In cylindrical rings, the two edges lead to AF ground state at half-filling but FM ground state at fractional fillings. DOI: 10.1103/PhysRevB.87.035435