Anomalous interference in Aharonov-Bohm rings with two Majorana bound states

We investigate the conductance of an Aharonov-Bohm (AB) interferometer coupled to a quantum dot and two Majorana bound states on the edge of the topological superconductor with finite length. When the tunnel couplings between the Majorana bound states and the Aharonov-Bohm interferometer are fixed to the specific phase, the differential conductance becomes zero irrespective of all the parameters as long as the hoppings to the two Majorana fermions on the opposite side are equal. The conductance at the zero bias voltage does not change with the magnetic flux penetrating the ring for all cases. When the energy level of the quantum dot is equal to the energy of the Majorana bound states, the AB oscillation shows \pi periodicity due to the particle-hole symmetry. The breaking of the time-reversal symmetry of the topological superconductor results in 2\pi periodicity of the AB oscillation for the specific phase of the tunnel coupling while the time-reversal symmetry breaking leads to the mixing of the triplet and singlet states in the quantum dot in another specific phase.