---
_id: '101'
abstract:
- lang: eng
text: Majorana zero modes are quasiparticle excitations in condensed matter systems
that have been proposed as building blocks of fault-tolerant quantum computers.
They are expected to exhibit non-Abelian particle statistics, in contrast to the
usual statistics of fermions and bosons, enabling quantum operations to be performed
by braiding isolated modes around one another. Quantum braiding operations are
topologically protected insofar as these modes are pinned near zero energy, with
the departure from zero expected to be exponentially small as the modes become
spatially separated. Following theoretical proposals, several experiments have
identified signatures of Majorana modes in nanowires with proximity-induced superconductivity
and atomic chains, with small amounts of mode splitting potentially explained
by hybridization of Majorana modes. Here, we use Coulomb-blockade spectroscopy
in an InAs nanowire segment with epitaxial aluminium, which forms a proximity-induced
superconducting Coulomb island (a â ∼ Majorana islandâ (tm)) that is isolated
from normal-metal leads by tunnel barriers, to measure the splitting of near-zero-energy
Majorana modes. We observe exponential suppression of energy splitting with increasing
wire length. For short devices of a few hundred nanometres, sub-gap state energies
oscillate as the magnetic field is varied, as is expected for hybridized Majorana
modes. Splitting decreases by a factor of about ten for each half a micrometre
of increased wire length. For devices longer than about one micrometre, transport
in strong magnetic fields occurs through a zero-energy state that is energetically
isolated from a continuum, yielding uniformly spaced Coulomb-blockade conductance
peaks, consistent with teleportation via Majorana modes. Our results help to explain
the trivial-to-topological transition in finite systems and to quantify the scaling
of topological protection with end-mode separation.
acknowledgement: This research was supported by Microsoft Project Q, the Danish National
Research Foundation, the Lundbeck Foundation, the Carlsberg Foundation and the European
Commission. C.M.M. acknowledges support from the Villum Foundation.
author:
- first_name: S M
full_name: Albrecht, S M
last_name: Albrecht
- first_name: Andrew P
full_name: Higginbotham, Andrew P
id: 4AD6785A-F248-11E8-B48F-1D18A9856A87
last_name: Higginbotham
orcid: 0000-0003-2607-2363
- first_name: Thomas
full_name: Jespersen, Thomas
last_name: Jespersen
- first_name: Morten
full_name: Madsen, Morten
last_name: Madsen
- first_name: Ferdinand
full_name: Kuemmeth, Ferdinand
last_name: Kuemmeth
- first_name: Jesper
full_name: Nygård, Jesper
last_name: Nygård
- first_name: Peter
full_name: Krogstrup, Peter
last_name: Krogstrup
- first_name: Charles
full_name: Marcus, Charles
last_name: Marcus
citation:
ama: Albrecht SM, Higginbotham AP, Jespersen T, et al. Exponential protection of
zero modes in Majorana islands. Nature. 2016;531(7593):206-209. doi:10.1038/nature17162
apa: Albrecht, S. M., Higginbotham, A. P., Jespersen, T., Madsen, M., Kuemmeth,
F., Nygård, J., … Marcus, C. (2016). Exponential protection of zero modes in Majorana
islands. Nature. Nature Publishing Group. https://doi.org/10.1038/nature17162
chicago: Albrecht, S M, Andrew P Higginbotham, Thomas Jespersen, Morten Madsen,
Ferdinand Kuemmeth, Jesper Nygård, Peter Krogstrup, and Charles Marcus. “Exponential
Protection of Zero Modes in Majorana Islands.” Nature. Nature Publishing
Group, 2016. https://doi.org/10.1038/nature17162.
ieee: S. M. Albrecht et al., “Exponential protection of zero modes in Majorana
islands,” Nature, vol. 531, no. 7593. Nature Publishing Group, pp. 206–209,
2016.
ista: Albrecht SM, Higginbotham AP, Jespersen T, Madsen M, Kuemmeth F, Nygård J,
Krogstrup P, Marcus C. 2016. Exponential protection of zero modes in Majorana
islands. Nature. 531(7593), 206–209.
mla: Albrecht, S. M., et al. “Exponential Protection of Zero Modes in Majorana Islands.”
Nature, vol. 531, no. 7593, Nature Publishing Group, 2016, pp. 206–09,
doi:10.1038/nature17162.
short: S.M. Albrecht, A.P. Higginbotham, T. Jespersen, M. Madsen, F. Kuemmeth, J.
Nygård, P. Krogstrup, C. Marcus, Nature 531 (2016) 206–209.
date_created: 2018-12-11T11:44:38Z
date_published: 2016-03-10T00:00:00Z
date_updated: 2021-01-12T06:47:37Z
day: '10'
doi: 10.1038/nature17162
extern: '1'
external_id:
arxiv:
- '1603.03217'
intvolume: ' 531'
issue: '7593'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1603.03217
month: '03'
oa: 1
oa_version: Submitted Version
page: 206 - 209
publication: Nature
publication_status: published
publisher: Nature Publishing Group
publist_id: '7953'
quality_controlled: '1'
status: public
title: Exponential protection of zero modes in Majorana islands
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 531
year: '2016'
...