Spatial dependence of local density of states in semiconductor-superconductor hybrids

Majorana bound states are expected to appear in one-dimensional semiconductor-superconductor hybrid systems, provided they are homogenous enough to host a global topological phase. In order to experimentally investigate the uniformity of the system, we study the spatial dependence of the local density of states in multiprobe devices where several local tunnelling probes are positioned along a gate-defined wire in a two-dimensional electron gas. Spectroscopy at each probe reveals a hard induced gap, and an absence of subgap states at zero magnetic field. However, subgap states emerging at finite magnetic field are not always correlated between different probes. Moreover, we find that the extracted critical field and effective $g$-factor of the lowest energy subgap state varies significantly across the length of the wire. Upon studying several such devices we do however find examples of striking correlations in the local density of states measured at different tunnel probes. We discuss possible sources of variations across devices.