We theoretically study the thermoelectric effect in a hybrid device composed by a topological semiconducting nanowire hosting Majorana bound states (MBSs) and a quantum dot (QD) connected to the left and right non-magnetic electrodes held at different temperatures. The electron-electron Coulomb interactions in the QD are taken into account by the non-equilibrium Green's function technique. We find that the sign change of the thermopower, which is useful for detecting the MBSs, will occur by changing the QD-MBS hybridization strength, the direct overlap between the MBSs at the opposite ends of the nanowire, and the system temperature. Large value of 100% spin-polarized or pure spin thermopower emerges even in the absence of Zeeman splitting in the QD or magnetic electrodes because the MBSs are coupled to electrons of only one certain spin direction in the QD due to the chiral nature of the Majorana fermions. Moreover, the magnitude of the thermopower will be obviously enhanced by the existence of MBSs.

This paper presents a theoretical study of the thermoelectric effect in a quantum dot (QD) side-coupled to Majorana bound states (MBSs) formed at the two ends of a Rashba nanowire. In the low-temperature regime favorable for the preparation of MBSs, the magnitude of the thermopower and figure of merit (FOM) are both enhanced by two or three orders of magnitude upon optimizing the QD-MBS coupling strength. In addition, the sign of the thermopower can be reversed by changing the QD-MBS coupling strength, a phenomenon that may be useful for detecting MBSs. The direct overlap between the MBSs also changes the sign of the thermopower and suppresses the magnitude of the FOM at low temperature. However, such an overlap has little influence on the thermopower and FOM at high temperature. In the presence of Zeeman splitting in the QD, the peaks corresponding to spin-up and spin-down thermopowers shift in opposite directions in the QD energy-level space, resulting in a large 100% spin polarization and pure spin thermopower that is crucial in spin caloritronics. Finally, the spin (charge) FOMs are enhanced (reduced) by increasing the Zeeman splitting.

We propose an interferometer composing of a scanning tunneling microscope (STM), double quantum dots (DQDs), and a semiconductor nanowire carrying Majorana bound states (MBSs) at its ends induced by the proximity effect of an s-wave superconductor, to probe the existence of the MBSs in the dots. Our results show that when the energy levels of DQDs are aligned to the energy of MBSs, the zero-energy spectral functions of DQDs are always equal to 1/2, which indicates the formation of the MBSs in the DQDs and is also responsible for the zero-bias conductance peak. Our findings suggest that the spectral functions of the DQDs may be an excellent and convenient quantity for detecting the formation and stability of the spatially separated MBSs in quantum dots.