Robustness of vortex-bound Majorana zero modes against correlated disorder

Casey Christian; Eugene F. Dumitrescu; Gábor B. Halász

doi:10.1103/PhysRevB.104.L020505

Robustness of vortex-bound Majorana zero modes against correlated disorder

Casey Christian, Eugene F. Dumitrescu, Gábor B. Halász

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2 Scopus citations

Abstract

We investigate the effect of correlated disorder on Majorana zero modes (MZMs) bound to magnetic vortices in two-dimensional topological superconductors. By starting from a lattice model of interacting fermions with a px±ipy superconducting ground state in the disorder-free limit, we use perturbation theory to describe the enhancement of the Majorana localization length at weak disorder and a self-consistent numerical solution to understand the breakdown of the MZMs at strong disorder. We find that correlated disorder has a much stronger effect on the MZMs than uncorrelated disorder and that it is most detrimental if the disorder correlation length ℓ is on the same order as the superconducting coherence length ζ. In contrast, MZMs can survive stronger disorder for ℓ≪ζ as random variations cancel each other within the length scale of ζ, while an MZM may survive up to very strong disorder for ℓ≫ζ if it is located in a favorable domain of the given disorder realization.

Original language	English
Article number	L020505
Journal	Physical Review B
Volume	104
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevB.104.L020505
State	Published - Jul 1 2021

Funding

Acknowledgments. We thank Cristian Batista for useful discussions. This research was sponsored by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. Preliminary modeling by G.B.H. was supported by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the US Department of Energy. C.C. was partially supported by the DOE Science Undergraduate Laboratory Internships (SULI) program. This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the US Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan .

Funders	Funder number
DOE Science Undergraduate Laboratory Internships
SULI
U.S. Department of Energy
Office of Science
Basic Energy Sciences
Oak Ridge National Laboratory
Division of Materials Sciences and Engineering

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abstract = "We investigate the effect of correlated disorder on Majorana zero modes (MZMs) bound to magnetic vortices in two-dimensional topological superconductors. By starting from a lattice model of interacting fermions with a px±ipy superconducting ground state in the disorder-free limit, we use perturbation theory to describe the enhancement of the Majorana localization length at weak disorder and a self-consistent numerical solution to understand the breakdown of the MZMs at strong disorder. We find that correlated disorder has a much stronger effect on the MZMs than uncorrelated disorder and that it is most detrimental if the disorder correlation length ℓ is on the same order as the superconducting coherence length ζ. In contrast, MZMs can survive stronger disorder for ℓ≪ζ as random variations cancel each other within the length scale of ζ, while an MZM may survive up to very strong disorder for ℓ≫ζ if it is located in a favorable domain of the given disorder realization.",

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AB - We investigate the effect of correlated disorder on Majorana zero modes (MZMs) bound to magnetic vortices in two-dimensional topological superconductors. By starting from a lattice model of interacting fermions with a px±ipy superconducting ground state in the disorder-free limit, we use perturbation theory to describe the enhancement of the Majorana localization length at weak disorder and a self-consistent numerical solution to understand the breakdown of the MZMs at strong disorder. We find that correlated disorder has a much stronger effect on the MZMs than uncorrelated disorder and that it is most detrimental if the disorder correlation length ℓ is on the same order as the superconducting coherence length ζ. In contrast, MZMs can survive stronger disorder for ℓ≪ζ as random variations cancel each other within the length scale of ζ, while an MZM may survive up to very strong disorder for ℓ≫ζ if it is located in a favorable domain of the given disorder realization.

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Robustness of vortex-bound Majorana zero modes against correlated disorder

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