Aharonov-Bohm Phase and Valley Splitting in Strained Graphene P-N Junction

Veselago lens focusing on a graphene P-N junction is promising for the realizations of electron-optical devices such as electron lenses and electron beam splitters. We study two effects in a strained graphene layer with P-N junction: the Lorentz force due to fictitious magnetic fields and Aharonov-Bohm (AB) phase. In a strained P-N junction graphene layer, the strain induced magnetic field modifies the electron trajectories. Furthermore, the Lorentz force on electrons engenders the valley-splitting of electron beams as well as the shifting of caustics formed by refracted electron waves. We also calculate a non-zero AB phase associated with the electron beams due to a localized in-plane strain produced by a ripple. This non-zero phase is accumulated from the electrons that avoid traversing through the locally strained region and experience a non-vanishing vector potential associated with the fictitious magnetic field induced by the localized strain. We believe that these effects can be realized in a simple ballistic experiment and might be useful for mapping strain profiles by analyzing the interference pattern observed in electron-optical devices.