Exponential protection of zero modes in Majorana islands

By S. Albrecht, Andrew Higginbotham, M. Madsen, F. Kuemmeth, T. Jespersen, J. Nygård, P. Krogstrup, Charles M. Marcus. Nature, 2016

953 citations recorded by the source corpus.

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 ‘Majorana island’) 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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/8b9e5545782f7380d21211aad3c8394edb640597

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Citations in the corpus

Scalable designs for quasiparticle-poisoning-protected topological quantum computation with Majorana zero modes (2016, methodology): “The combination of material science progress [29,30], device quality and controllability [20,31], and theoretical advances involving semiconductor-superconductor heterostructures [32–36] provides a pathway for topological quantum computation with semiconductor nanowires.”
Odd-frequency superconductivity (2017, result): “Recent experiments (Albrecht et al., 2016; Mourik et al., 2012; Nadj-Perge et al., 2014) have reported measurements which are largely consistent with the theoretical predictions.”
Effects of Gate-Induced Electric Fields on Semiconductor Majorana Nanowires (2018, methodology): “Our results allow one to understand and interpret recent experiments investigating the electric field and disorder dependence of the effective parameters [57,60,62,64,68].”
Topological superconductors: a review (2016, background): “However, recent experiment on InAs nanowire with epitaxially-grown Al superconductor add-layer, which realizes much cleaner proximity-induced superconductivity with a ‘hard’ gap, found convincing evidence for Majorana fermions at the edges of the nanowire through observation of the Majorana teleport”
The physics of quantum materials (2017, neutral): “There are a number of promising experimental results indicating zero-bias peaks in tunnelling 107–109 that could be from Majorana zero modes, but not yet any demonstration of braiding.”