Quantum Interference In Graphene With Quantum Anomalous Hall Effect System

As a new material, Graphene possesses excellent thermoelectric, electrical and optical properties, and its band structure at low energy is linear. At low energy electrons in graphene perform as Dirac Fermions, and their speeds is one three-hundredth of light, which is the special case in low-energy condensed matter that meet high-energy relativistic quantum mechanics. All these properties make a special material from ordinary ones. Graphene has many special quantum effect, such as, Klein tunneling, half-integer quantum Hall effect, quantum spin Hall effect, and so on. In quantum Hall effect, electrons with specific direction move alone on the edges, and the back scattering is suppressed. As a result, all the electrons move on their own way, and the resistances are zero, which likes the superconductivity. But, to realize the quantum Hall Effect, very strong magnet and extremely low temperature is needed, which makes quantum Hall Effect unavailable in daily life. So, researchers are concentrating to find materials to realize the quantum anomalous quantum Hall effect, which may not needs extremely conditions. Graphene is one of these materials.In the presence of both an external Rashba spin orbital interaction and an exchange field, topological transform and consequently the quantum anomalous Hall effect are expected in graphene. Based on it, considering inequivalent AB sub-lattice with the same on-site energy, graphene’s band structure has a bulk gap, and it has inversion symmetry. What’s more, there are quantum anomalous Hall edge states in the bulk gap. The quantum anomalous Hall edge states are reflected by the left and right boundaries of the graphene cavity. The reflected states will interfere with each other, and the interference is periodic. While, the interference period is inversely with the flux of the cavity. Our simulation results show that the reason is AB effect. On the other way, when the AB sub-lattices’ on-site energy are not equal, the bulk gap will close, and the inversion symmetry will be broken. At this time, the bulk states and the edge states will exist at the same time, which lead to topological Anderson insulator phenomenon. Then, graphene become topological Anderson insulator. At the topological Anderson insulating region, interference exists but not periodic. In addition, there will be disorders in real materials. In this case, interference will disappear. The interference is very sensitive to disorder and bulk state, as showed by our simulation. Therefore, the interference phenomenon can be used to detect whether the real edge states exist or not.In this article, the quantum interference phenomenon in graphene’s quantum anomalous Hall system will be elaborated in sections as follows, calculation backgrounds, theory methods, simulation results, and so on.