Disordered Majorana nanowires: Studying disorder without any disorder
Haining Pan, S. Das Sarma
Abstract
The interplay of disorder and short finite wire length is the crucial physics hindering progress in the semiconductor-superconductor nanowire platform for realizing non-Abelian Majorana zero modes. Disorder effectively segments the nanowire into isolated patches of quantum dots which act as subgap Andreev bound states often mimicking Majorana zero modes. In this work, we propose and develop a new theoretical approach to model the disorder, effectively a spatially varying effective mass model, which does not rely on incorporating the unknown microscopic details of disorder into the Hamiltonian. This model effectively segments the wire into multiple quantum dots, characterized by highly enhanced effective mass at impurity sites leading to the segmentation of the wire into effective random quantum dots. We find that this model can qualitatively and quantitatively reproduce the disorder physics, providing a crystal clear way to understand the effects of disorder by comparing the mean free path to the superconducting coherence length. In addition, this model allows precise control over the disorder regime, enabling us to evaluate the reliability of topological invariants in predicting Majorana zero modes. We find that topological invariants alone may yield a significant false-positive rate as indicators for topology in the actual wire with increasing disorder strength. Therefore, we propose a set of new indicators to characterize the spatial distribution of the zero-energy state, emphasizing the key necessity for isolated Majorana zero modes localized at the wire ends. Employing this set of new indicators for stringent characterizations, we explore their experimental relevance to the measured differential conductance spectra. Our findings highlight the critical role of isolated localized states, beyond the topological invariant, in identifying topological Majorana zero modes. We believe that this approach is a powerful tool for studying realistic Majorana nanowires where disorder and short wire length obfuscate the underlying topological physics.