Symmetry of surface states in graphene superlattices terminated with magnetic cap layers

The symmetry of surface states has been investigated with numerical calculations in graphene superlattices (SLs) terminated with magnetic cap layers. It is found that the surface states in SL of pure electric basis with cap layer of magnetic potential A_s≥ 0 are symmetric about the transverse wave vector k_y= 0 plane to those with A_s≤ 0. While those in SL of pure magnetic basis with the same cap layer of magnetic potential A_s are symmetric about the energy origin E= 0 plane. Additionally, the surface states in SL of general complex electric/magnetic basis show no symmetry. These interesting results will provide some important guidelines for the experimental exploration of carbon-based quantum electronic and optoelectronic devices.