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    Zero energy and chiral edge modes in a p-wave magnetic spin model


    Kells, G. and Vala, Jiri (2010) Zero energy and chiral edge modes in a p-wave magnetic spin model. Physical Review B, 82 (125122). pp. 1-8. ISSN 1098-0121

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    Abstract

    In this work we discuss the formation of zero energy vortex and chiral edge modes in a fermionic representation of the Kitaev honeycomb model. We introduce the representation and show how the associated Jordan-Wigner procedure naturally defines the so-called branch cuts that connect the topological vortex excitations. Using this notion of the branch cuts we show how to, in the non-Abelian phase of the model, describe the Majorana zero mode structure associated with vortex excitations. Furthermore we show how, by intersecting the edges between Abelian and non-Abelian domains, the branch cuts dictate the character of the chiral edge modes. In particular we will see in what situations the exact zero energy Majorana edge modes exist. On a cylinder, and for the particular instances where the Abelian phase of the model is the full vacuum, we have been able to exactly solve for the systems edge energy eigensolutions and derive a recursive formula that exactly describes the edge mode structure. Penetration depth is also calculated and shown to be dependent on the momentum of the edge mode. These solutions also describe the overall character of the fully open non- Abelian domain and are excellent approximations at moderate distances from the corners.

    Item Type: Article
    Additional Information: This article is available at DOI: 10.1103/PhysRevB.82.125122 . We thank Steve Simon, Joost Slingerland and Ivan Rodriguez for interesting discussions. This work has been supported by Science Foundation Ireland through the President of Ireland Young Researcher Award 05/YI2/I680.
    Keywords: Zero energy; chiral edge modes; p-wave; magnetic spin model;
    Academic Unit: Faculty of Science and Engineering > Mathematical Physics
    Item ID: 4492
    Depositing User: Dr. Jiri Vala
    Date Deposited: 16 Sep 2013 15:41
    Journal or Publication Title: Physical Review B
    Publisher: American Physical Society
    Refereed: Yes
    URI:

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