Disordered Majorana nanowires: Studying disorder without any disorder

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 (MZM). Disorder effectively segments the nanowire into isolated patches of quantum dots (QD) which act as subgap Andreev bound states often mimicking MZMs. In this work, we propose and develop a new theoretical approach to model disorder, effectively a spatially varying effective mass model, which does not rely on incorporating unknown microscopic details of disorder into the Hamiltonian. This model effectively segments the wire into multiple QDs, characterized by highly enhanced effective mass at impurity sites leading to the segmentation of the wire into effective random QDs. We find that this model can reproduce 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 (TI) in predicting MZMs. We find that TIs alone may yield a significant false positive rate as indicators for topology in the actual wire with increasing disorder strength. Therefore, we propose new indicators to characterize the spatial distribution of the zero-energy state, emphasizing the key necessity for isolated MZMs localized at 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 TI, in identifying topological MZMs. 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.

61 pages, 78 figures

References in corpus (12)

• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Scaling of Majorana Zero-Bias Conductance Peaks
• A Majorana smoking gun for the superconductor-semiconductor hybrid topological system
• Proximity effect at the superconductor - topological insulator interface
• Splitting of Majorana modes due to intervortex tunneling in a p + ip superconductor
• Andreev rectifier: a nonlocal conductance signature of topological phase transitions
• Machine Learning the Disorder Landscape of Majorana Nanowires

Cited by in corpus (9)

• Effect of impurities and disorder on the braiding dynamics of Majorana zero modes
• Characterizing Dynamic Majorana Hybridization for Universal Quantum Computing
• Josephson effect and critical currents in trivial and topological full-shell hybrid nanowires
• Vision transformer based Deep Learning of Topological indicators in Majorana Nanowires
• Majorana zero modes in semiconductor-superconductor hybrid structures: Defining topology in short and disordered nanowires through Majorana splitting
• Mitigating disorder and optimizing topological indicators with vision-transformer-based neural networks in Majorana nanowires
• Rashba spin-orbit coupling and artificially engineered topological superconductors
• Ballistic transport in 1D Rashba systems in the context of Majorana nanowires
• Distinguishing Majorana bound states from accidental zero-energy modes with a microwave cavity