  We study the quasi-bound state and the transport properties in the T-shaped
graphene nanoribbon consisting of a metallic armchair-edge ribbon connecting to
a zigzag-edge sidearm. We systematically study the condition under which there
are quasi-bound states in the system for a wide range of the system size. It is
found that when the width of the sidearm is about half of the width of the
armchair leads, there is a quasi-bound state trapped at the intersection of the
T-shape structure. The quasi-bound states are truly localized in the sidearm
but have small continuum components in the armchair leads. The quasi-bound
states have strong effect on the transport between the armchair leads through
the Fano effect, but do not affect the transport between the armchair lead and
the sidearm.
