Exponential protection of zero modes in Majorana islands

• Published in: Nature (London) Vol. 531; no. 7593; pp. 206 - 209
• Main Authors: Albrecht, S. M., Higginbotham, A. P., Madsen, M., Kuemmeth, F., Jespersen, T. S., Nygård, J., Krogstrup, P., Marcus, C. M.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 10.03.2016; Nature Publishing Group
• Subjects: 142/126; 639/766/1130/1064; 639/766/119/1000/1016; 639/766/259; Aluminum; Dynamics of a particle; Humanities and Social Sciences; letter; Magnetic fields; Molecular beam epitaxy; multidisciplinary; Nanowires; Observations; Particles (Nuclear physics); Properties; Science; Superconductivity; United States
• ISSN: 0028-0836; 1476-4687
• DOI: 10.1038/nature17162

The splitting of zero-energy Majorana modes in a tunnel-coupled InAs nanowire with epitaxial aluminium is exponentially suppressed as the wire length is increased, resulting in protection of these modes; this result helps to establish the robust presence of Majorana modes and quantifies exponential protection in nanowire devices. Majorana modes get more real There are three known fundamental types of fermions called Dirac, Weyl and Majorana. Until recently, the latter two had escaped observation, but evidence for the existence of Weyl and Majorana modes was found in condensed matter systems. In particular, signatures for Majorana modes were identified in semiconductor–superconductor nanowire devices, and this sparked significant interest because non-trivial topological properties had been predicted. Charles Marcus and colleagues present the next essential piece of evidence for the robust presence of Majorana modes in such devices, namely the exponential protection of Majorana modes in the form of a suppression of energy splitting with increasing nanowire length. The observations open a path to the next step of controlling Majorana modes and establishing topological properties. Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of fault-tolerant quantum computers 1 . 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 1 , 2 . 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 3 , 4 . Following theoretical proposals 5 , 6 , several experiments have identified signatures of Majorana modes in nanowires with proximity-induced superconductivity 7 , 8 , 9 , 10 , 11 and atomic chains 12 , with small amounts of mode splitting potentially explained by hybridization of Majorana modes 13 , 14 , 15 . 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 16 , 17 . 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.