Disordered Majorana nanowires: Studying disorder without any disorder

The interplay of disorder and short finite wire length is the crucial physics\nhindering progress in the semiconductor-superconductor nanowire platform for\nrealizing non-Abelian Majorana zero modes (MZM). Disorder effectively segments\nthe nanowire into isolated patches of quantum dots (QD) which act as subgap\nAndreev bound states often mimicking MZMs. In this work, we propose and develop\na new theoretical approach to model disorder, effectively a spatially varying\neffective mass model, which does not rely on incorporating unknown microscopic\ndetails of disorder into the Hamiltonian. This model effectively segments the\nwire into multiple QDs, characterized by highly enhanced effective mass at\nimpurity sites leading to the segmentation of the wire into effective random\nQDs. We find that this model can reproduce disorder physics, providing a\ncrystal clear way to understand the effects of disorder by comparing the mean\nfree path to the superconducting coherence length. In addition, this model\nallows precise control over the disorder regime, enabling us to evaluate the\nreliability of topological invariants (TI) in predicting MZMs. We find that TIs\nalone may yield a significant false positive rate as indicators for topology in\nthe actual wire with increasing disorder strength. Therefore, we propose new\nindicators to characterize the spatial distribution of the zero-energy state,\nemphasizing the key necessity for isolated MZMs localized at wire ends.\nEmploying this set of new indicators for stringent characterizations, we\nexplore their experimental relevance to the measured differential conductance\nspectra. Our findings highlight the critical role of isolated localized states,\nbeyond the TI, in identifying topological MZMs. We believe that this approach\nis a powerful tool for studying realistic Majorana nanowires where disorder and\nshort wire length obfuscate the underlying topological physics.\n