Majorana bound states in non-homogeneous semiconductor nanowires

We demonstrate that partially overlapping Majorana bound states (MBSs) represent a generic low-energy feature that emerges in non-homogeneous semiconductor nanowires coupled to super conductors in the presence of a Zeeman field. The emergence of these low-energy modes is not correlated with any topological quantum phase transition that the system may undergo as the Zeeman field and other control parameters are varied. Increasing the characteristic length scale of the variations in the potential leads to a continuous evolution from strongly overlapping MBSs, which can be viewed as “regular” Andreev bound states (ABSs) that cross zero energy, to weakly coupled MBSs, which have nearly zero energy in a significant range of parameters and generate signatures similar to the Majorana zero modes (MZMs) that emerge in the topological superconducting phase. We show that using charge (or spin) transport measurements it is virtually impossible to distinguish MZMs from weakly overlapping MBSs emerging in the topologically-trivial regime and suggest a two-lead experiment which will distinguish between these two types of low energy modes in semiconductor-superconductor heterostructures.