Exponential protection of zero modes in Majorana islands
Abstract
Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of faulttolerant quantum computers. They are expected to exhibit nonAbelian 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 proximityinduced superconductivity and atomic chains, with small amounts of mode splitting potentially explained by hybridization of Majorana modes. Here, we use Coulombblockade spectroscopy in an InAs nanowire segment with epitaxial aluminium, which forms a proximityinduced superconducting Coulomb island (a ‘Majorana island’) that is isolated from normalmetal leads by tunnel barriers, to measure the splitting of nearzeroenergy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometres, subgap 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 zeroenergy state that is energetically isolated from a continuum, yielding uniformly spaced Coulombblockade conductance peaks, consistent with teleportation via Majorana modes. Our results help to explain the trivialtotopological transition in finite systems and to quantify the scaling of topological protection with endmode separation.
 Publication:

Nature
 Pub Date:
 March 2016
 DOI:
 10.1038/nature17162
 arXiv:
 arXiv:1603.03217
 Bibcode:
 2016Natur.531..206A
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Superconductivity;
 Quantum Physics
 EPrint:
 main text and methods section