Electronic states and persistent current of nanographite ring

We present the electronic states and persistent current of nanographite ring based on the nearest-neighbor tight-binding model under periodic or Möbius boundary conditions. It is found that the parity of transverse mode and edge structures are decisive to determine the electronic spectrum of nanographite ring under the Möbius boundary condition. The electronic states Möbius strip with zigzag edges are derived in the same way as the free-electron case. However, the Möbius strip with armchair edges has loop quantization rule of wave vector due to the characteristics of their parity. The difference of electronic states between edge structures can crucially affect the behavior of the persistent current caused by Aharonov–Bohm magnetic flux passing through the nanographite ring. We also present some scaling properties concerning the persistent current and the zero-field susceptibility.