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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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Feasibility of measurement-based braiding in the quasi-Majorana regime of semiconductor-superconductor heterostructures
We discuss the feasibility of measurement-based braiding in semiconductor-superconductor (SM-SC) heterostructures in the so-called quasi-Majorana regime—the topologically-trivial regime characterized by robust zero-bias conductance peaks (ZBCPs) that are due to partially-separated Andreev bound states (ps-ABSs). These low energy ABSs consist of component Majorana bound states (also called quasi-Majorana modes) that are spatially separated by a length scale smaller than the length of the system, in contrast with the Majorana zero modes (MZMs) emerging in the topological regime, which are separated by the length of the wire. In the quasi-Majorana regime, the ZBCPs appear to be robust to various perturbations as long as the energy splitting of the ps-ABS is less than the typical width Ew of the low-energy conductance peaks (Ew ∼ 10–20 μeV). However, the feasibility of measurement-based braiding depends on a different, much smaller, energy scale Em ∼ 0.1 μeV. This energy scale is given by the typical fermion parity-dependent ground state energy shift due to virtual electron transfer between the SM-SC system and a quantum dot used for parity measurements. In this paper we show that it is possible to prepare the SM-SC system in the quasi-Majorana regime with energy splittings below the Em threshold, so that measurement-based braiding is possible in principle. However, despite the apparent robustness of the corresponding ZBCPs, ps-ABSs are in reality topologically unprotected. Starting with ps-ABSs with energy below Em, we identify the maximum amplitudes of different types of (local) perturbations that are consistent with perturbation-induced energy splittings not exceeding the Em limit.We argue that measurements generating perturbations larger than the threshold amplitudes appropriate for Em cannot realize measurement-based braiding in SM-SC heterostructures in the quasi-Majorana regime. We find that, if possible at all, quantum computation using measurement-based braiding in the quasi-Majorana regime would be plagued with errors introduced by the measurement processes themselves, while such errors are significantly less likely in a scheme involving topological MZMs.
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- Award ID(s):
- 2014156
- PAR ID:
- 10476246
- Publisher / Repository:
- Amesican Physical Society
- Date Published:
- Journal Name:
- Physical Review B
- Volume:
- 102
- Issue:
- 20
- ISSN:
- 2469-9950
- 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/PhysRevB.102.205101
