Fano effect in an AB interferometer with a quantum dot side-coupled to a single Majorana bound state

We study the conductance and interference effects through an AB interferometer with an embedded quantum dot (QD) side-coupled to a single Majorana bound state (MBS) by using non-equilibrium Green's function method. The energy levels appearing in the QD are calculated by diagonalizing the Hamiltonian of the embedded QD-MBS system. When the single QD energy level ϵ0 is set to 0, there are three discrete energy levels in the QD appearing at around ω=0, ±ϵM2+2λ2 due to the coupling with MBS where ϵM is the coupling strength between the two MBSs at the two ends of the nanowire and λ is the coupling strength between the MBS and the QD. Asymmetric Fano lineshapes are found around these levels in the conductance due to the interference between electrons traversing through different paths. The phase shift of electrons through the QD changes from π/2 to −π/2 at each of these three energy values. However, the phase does not vary smoothly between these three energy levels but shows severe changes from −π/2 to π/2 at ω=±ϵM2+λ2. As a comparison, we also study the similar AB interferometer in which the QD-MBS system is replaced by a normal QD-QD system or a simple single QD system, which shows only two or one Fano peak and the phase shifts from π/2 to −π/2 only at the Fano peaks. These differences reflect the distinct influences of Majorana bound state on the transport properties of AB interferometer.