A Caltech Library Service

Boosting Majorana zero modes

Karzig, Torsten and Refael, Gil and von Oppen, Felix (2013) Boosting Majorana zero modes. Physical Review X, 3 (4). Art. No. 041017. ISSN 2160-3308. doi:10.1103/PhysRevX.3.041017.

PDF - Published Version
Creative Commons Attribution.

PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


One-dimensional topological superconductors are known to host Majorana zero modes at domain walls terminating the topological phase. Their non-Abelian nature allows for processing quantum information by braiding operations that are insensitive to local perturbations, making Majorana zero modes a promising platform for topological quantum computation. Motivated by the ultimate goal of executing quantum-information processing on a finite time scale, we study domain walls moving at a constant velocity. We exploit an effective Lorentz invariance of the Hamiltonian to obtain an exact solution of the associated quasiparticle spectrum and wave functions for arbitrary velocities. Essential features of the solution have a natural interpretation in terms of the familiar relativistic effects of Lorentz contraction and time dilation. We find that the Majorana zero modes remain stable as long as the domain wall moves at subluminal velocities with respect to the effective speed of light of the system. However, the Majorana bound state dissolves into a continuous quasiparticle spectrum after the domain wall propagates at luminal or even superluminal velocities. This relativistic catastrophe implies that there is an upper limit for possible braiding frequencies even in a perfectly clean system with an arbitrarily large topological gap. We also exploit our exact solution to consider domain walls moving past static impurities present in the system.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Karzig, Torsten0000-0003-0834-0547
Additional Information:© 2013 Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Received 20 May 2013; revised 13 August 2013; published 22 November 2013. It is a pleasure to thank L. Glazman, C.-Y. Hou, and D. Pesin for helpful discussions. This work was funded by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation, the Packard Foundation, a Bessel award of the Alexander-von-Humboldt Foundation, SPP 1285 of the Deutsche Forschungsgemeinschaft, as well as the Helmholtz Virtual Institute “New states of matter and their excitations.”
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationGBMF1250
David and Lucile Packard FoundationUNSPECIFIED
Alexander von Humboldt FoundationUNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG)SPP 1285
Helmholtz Virtual InstituteUNSPECIFIED
Subject Keywords:Condensed Matter Physics, Superconductivity, Topological Insulators
Issue or Number:4
Classification Code:PACS: 03.67.Lx, 71.10.Pm, 03.65.Pm, 74.78.Na
Record Number:CaltechAUTHORS:20130603-083248608
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38744
Deposited By: Tony Diaz
Deposited On:07 Jun 2013 22:23
Last Modified:09 Nov 2021 23:39

Repository Staff Only: item control page