Exponential protection of zero modes in Majorana islands

S.M. Albrecht, A.P. Higginbotham, T. Jespersen, M. Madsen, F. Kuemmeth, J. Nygård, P. Krogstrup, C. Marcus, Nature 531 (2016) 206–209.

Journal Article | Published | English
Albrecht, S M; Higginbotham, Andrew PIST Austria ; Jespersen, Thomas; Madsen, Morten; Kuemmeth, Ferdinand; Nygård, Jesper; Krogstrup, Peter; Marcus, Charles
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.
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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.
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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
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
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.
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.
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.
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.
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