  We performed a series of theoretical transport studies on Y-branch electron
waveguides which are embedded in mid-size armchair graphene nanoribbons
(AGNRs). Non-equilibrium Greens function (NEGF) with different approximations
of tight-binding (TB) Hamiltonian has been employed. Using the first nearest
hopping approximation, we observed very pronounced conductance quantization,
the structure of which depends on geometrical design and shows a spacing of
$4e^2/h$, indicating the existence of valley degree of freedom. Moreover, by
incorporating the third nearest approximation, we observed seminal plateaus
deviated from multiples of $4e^2/h$ conductance, suggesting the lift of valley
degeneracy. Finally, Quasi-one dimensional band structure calculations have
been performed to study the availability of energy channels and the role of the
major geometrical parameters on the transport.
