  Electronic localization in narrow graphene constrictions is theoretically
studied, and it is found that long-lived quasibound states (QBSs) can exist in
a class of ultrashort graphene quantum point contacts (QPCs). These QBSs are
shown to originate from the dispersionless edge states that are characteristic
of the electronic structure of generically terminated graphene, in which
pseudo-time-reversal symmetry is broken. The QBSs can be regarded as interface
states confined between two graphene samples, and their properties can be
modified by changing the sizes of the QPC and the interface geometry. In the
presence of bearded sites, these QBSs can be converted into bound states.
Experimental consequences and potential applications are discussed.
