Special odd-even effects of electron transport through quantum-dot molecules with side-coupled Majorana zero modes

Abstract

We investigate the electron transport through a serially coupled quantum-dot molecule in which each dot is side-coupled to one Majorana zero mode (MZM) at an end of the topological-superconducting nanowire. Calculation results show that with the increase of dot number, the zero-bias conductance does not display the conventional odd-even effect but always keeps equal to e^{2}/h. On the other hand, if different superconducting phases are added to the dot-MZM couplings with the left-right asymmetry mode, the zero-bias conductances display apparent odd-even effect. Namely, in the odd-dot cases, the zero-bias conductances are less determined by the superconducting phase, whereas they are more dependent on the superconducting phase in the cases of even dots. Regarding the shot-noise Fano factors, they also exhibit clear odd-even effects, mainly manifested as the dependence of the relation between zero-bias Fano factors and superconducting phase difference on the parity of dot number. We believe that these results are helpful to construct mesoscopic cells based on quantum dots and MZMs.