Abnormal electron paths induced by Klein tunneling in graphene quantum point contacts

We study quantum transport in a general graphene system subject to external potential, a situation that can be expected in all kinds of future graphene-based electronic devices with quantum dots and quantum point contacts. We find that electrons tend to take on propagating paths due to Klein tunneling that have absolutely no counterpart in nonrelativistic quantum systems. Strikingly, such abnormal quantum paths can lead to an extreme type of fractal-like of conductance fluctuations, not seen previously in any quantum transport systems. This phenomenon has profound implications to the development of graphene based devices that require stable electronic properties.