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We consider theoretically the physics of bulk topological superconductivity accompanied by boundary non- Abelian Majorana zero modes in semiconductor-superconductor (SM-SC) hybrid systems consisting of finite wires in the presence of correlated disorder arising from random charged impurities. We find the system to manifest a highly complex behavior due to the subtle interplay between finite wire length and finite disorder, leading to copious low-energy in-gap states throughout the wire and considerably complicating the interpretation of tunneling spectroscopic transport measurements used extensively to search forMajorana modes. The presence of disorder-induced low-energy states may lead to the nonexistence of end Majorana zero modes even when tunneling spectroscopy manifests zero-bias conductance peaks in local tunneling and signatures of bulk gap closing/reopening in the nonlocal transport. In short wires within the intermediate disorder regime, apparent topology may manifest in small ranges (“patches”) of parameter values, which may or may not survive the longwire limit depending on various details. Because of the dominance of disorder-induced in-gap states, the system may even occasionally have an appropriate topological invariant without manifesting isolated end Majorana zero modes. We discuss our findings in the context of a recent breakthrough experiment from Microsoft reporting the simultaneous observations of zero-bias conductance peaks in local tunneling and gap opening in nonlocal transport within small patches of parameter space. Based on our analysis, we believe that the disorder strength to SC-gap ratio must decrease further for the definitive realization of non-Abelian Majorana zero modes in SM-SC devices.
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Charge-Impurity Effects in Hybrid Majorana Nanowires
We address an outstanding problem that represents a critical roadblock in the development of the Majorana-based topological qubit using semiconductor-superconductor hybrid structures: the quantitative characterization of disorder effects generated by the unintentional presence of charge impurities within the hybrid device. Given that disorder can have far-reaching consequences for the Majorana physics but is intrinsically difficult to probe experimentally in a hybrid structure, providing a quantitative theoretical description of disorder effects becomes essential. To accomplish this task, we develop a microscopic theory that (i) provides a quantitative characterization of the effective potential generated by a charge impurity embedded inside a semiconductor wire proximity coupled to a superconductor layer by solving selfconsistently the associated three-dimensional Schrödinger-Poisson problem, (ii) describes the low-energy physics of the hybrid structure in the presence of s-wave superconductivity, spin-orbit coupling, Zeeman splitting, and disorder arising from multiple charge impurities by using the results of (i) within a standard free-fermion approach, and (iii) links the microscopic results to experimentally observable features by generating tunneling differential-conductance maps as a function of the control parameters (e.g., Zeeman field and chemical potential). We find that charge impurities lead to serious complications regarding the realization and observation of Majorana zero modes, which have direct implications for the development of Majorana-based qubits. More importantly, our work provides a clear direction regarding what needs to be done for progress in the field, including specific materials-quality and semiconductor-purity targets that must be achieved to create a topological qubit.
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- Award ID(s):
- 2014156
- PAR ID:
- 10476249
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review Applied
- Volume:
- 16
- Issue:
- 5
- ISSN:
- 2331-7019
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1103/PhysRevApplied.16.054053
