  In this study, Rashba coupling induced Aharonov-Casher effect in a graphene
based nano ring is investigated theoretically. The graphene based nano ring is
considered as a central device connected to semi-infinite graphene nano
ribbons. In the presence of the Rashba spin-orbit interaction, two armchair
shaped edge nano ribbons are considered as semi-infinite leads. The
non-equilibrium Green's function approach is utilized to obtain the quantum
transport characteristics of the system. The relaxation and dephasing
mechanisms within the self-consistent Born approximation is scrutinized. The
Lopez-Sancho method is also applied to obtain the self-energy of the leads. We
unveil that the non-equilibrium current of the system possesses measurable
Aharonov-Casher oscillations with respect to the Rashba coupling strength. In
addition, we have observed the same oscillations in dilute impurity regimes in
which amplitude of the oscillations is shown to be suppressed as a result of
the relaxations.
