  We investigate electron transport inside a ring system composed of a quantum
dot (QD) coupled to two Majorana bound states confined at the ends of a
one-dimensional topological superconductor nanowire. By tuning the magnetic
flux threading through the ring, the model system we consider can be switched
into states with or without zero-energy modes when the nanowire is in its
topological phase. We find that the Fano profile in the conductance spectrum
due to the interference between bound and continuum states exhibits markedly
different features for these two different situations, which consequently can
be used to detect the Majorana zero-energy mode. Most interestingly, as a
periodic function of magnetic flux, the conductance shows $2\pi$ periodicity
when the two Majorana bound states are nonoverlapping (as in an infinitely long
nanowire) but displays $4\pi$ periodicity when the overlapping becomes nonzero
(as in a finite length nanowire). We map the model system into a QD--Kitaev
ring in the Majorana fermion representation and affirm these different
characteristics by checking the energy spectrum.
