Transmission function of a system composing of a quantum dot (QD) subjected to a photon field and side-coupled to a topological superconductor nanowire hosting a pair of Majorana bound states (MBSs) is calculated by using the non-equilibrium Green's function technique. We find that a series of photon-induced peaks emerge and are split by the coupling between the QD and the MBSs. Moreover, the peaks' height are suppressed to zero because the MBSs absorb (emit) the photon energy. Under this condition, the MBSs may be shifted to the non-zero energy mode, and thus provide another detection scheme for its existence which is quite different from the currently adopted ones depending on the zero-energy mode of the MBSs. In the presence of MBS-MBS overlaping, the central photon-assisted peaks in the transmission function reappear due to the fact that the photon absorbed (emitted) by one mode of the MBSs are subsequently emitted (absorbed) by another MBSs' mode. We also find that the positions of the additional peaks induced by the MBS-MBS overlaping in the presence of the photon field are quite different from the case of zero photon field.

Non-invasive detection of the Majorana bound state (MBSs), a kind of quasiparticle without charge and mass, is one of the core issues in current condensed matter physics. Here we study in theory the quantum interference effect in parallel-coupled double quantum dots which are connected either by Majorana bound states (MBSs) or regular fermions. We find that the zero-energy conductance develops a sharp peak when the dots are connected by the MBSs, whereas that in the case of the dots are coupled via regular fermions shows a valley. By varying the coupling strength between the dots and the electron reservoirs, the conductance in the two structures changes in different ways. By comparing the properties of the linear conductance in the two systems, the information of the MBSs formed at the two ends of a topological superconductor nanowire then can be inferred. We also find that the MBSs in the present structure also induces the Fano effect, and is favorable in quantum information processing.

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The Seebeck effect is investigated within the framework of a non-equilibrium Green's function technique in a quantum dot (QD) sandwiched between the left and right leads held at different temperatures. We consider that the QD is shelled by a photon field and is side-coupled to a topological superconductor nanowire hosting Majorana zero modes (MZMs). It is found that the thermopower (Seebeck coefficient) can be obviously enhanced by weak QD-MZMs coupling at low temperatures, in addition to its sign reversion that may be used for detecting the existence of MZMs. In the presence of a photon field, the thermopower can be further enhanced due to decreased electrical conductance when electrons' transport probability through each channel is reduced by photon-assisted tunneling (PAT). The hybridization between the MZMs will also induce sign reversion of the thermopower in the absence of a photon field, whereas it has less impact on the thermopower when the QD is shelled by the photon field.