  Graphene nanoribbons (GNRs) are promising components in future
nanoelectronics due to the large mobility of graphene electrons and their
tunable electronic band gap in combination with recent experimental
developments of on-surface chemistry strategies for their growth. Here we
explore a prototype 4-terminal semiconducting device formed by two crossed
armchair GNRs (AGNRs) using state-of-the-art first-principles transport
methods. We analyze in detail the roles of intersection angle, stacking order,
inter-GNR separation, and finite voltages on the transport characteristics.
Interestingly, when the AGNRs intersect at $\theta= 60^\circ$, electrons
injected from one terminal can be split into two outgoing waves with a tunable
ratio around 50% and with almost negligible back-reflection. The splitted
electron wave is found to propagate partly straight across the intersection
region in one ribbon and partly in one direction of the other ribbon, i.e., in
analogy of an optical beam splitter. Our simulations further identify realistic
conditions for which this semiconducting device can act as a mechanically
controllable electronic beam splitter with possible applications in
carbon-based quantum electronic circuits and electron optics. We rationalize
our findings with a simple model that suggests that electronic beam splitters
can generally be realized with crossed GNRs.
