Gapless states and current control in strongly distorted gated trilayer graphene

We investigate gated trilayer graphene partially devoid of outer layers and forming a system of two trilayers connected by a single layer of graphene. A difference in the stacking order of trilayers leads to the appearance of gapless states, one of which is mainly localized in the single graphene layer. We demonstrate that by changing the value of the gate voltage applied to the outer layers one can change the slope of E(k) of this state. As a consequence the direction of current flowing in the single layer graphene can also be changed, the effect that could be useful in practical applications.