Electronic structure of helicoidal graphene: Massless Dirac particles on a curved surface with a screw symmetry

Masataka Watanabe, Hisato Komatsu, Naoto Tsuji, and Hideo Aoki
Phys. Rev. B 92, 205425 – Published 20 November 2015; Erratum Phys. Rev. B 92, 239902 (2015)

Abstract

Massless Dirac particles on the helicoid are theoretically investigated. With its possible application being helical graphene, we explore how the peculiarities of Dirac particles appear on the curved, screw-symmetric surface. Zweibein is used to derive the massless Dirac equation on the helicoid and on general curved surfaces. We show that bound states of massless Dirac electrons on the helicoid are absent, and thus the system is fully characterized by the scattering probabilities and the phase shifts. We obtain these quantities from numerically calculated wave functions. We find the local density of states and the phase shifts behave characteristically around the axis of the helicoid. Bound states of massive Dirac electrons on the surface are also shown to be absent as an extension of the above result on massless Dirac electrons. A comparison with the nonrelativistic case is also made.

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  • Received 26 May 2015

DOI:https://doi.org/10.1103/PhysRevB.92.205425

©2015 American Physical Society

Erratum

Authors & Affiliations

Masataka Watanabe*

  • Department of Physics, The University of Tokyo, Hongo, Tokyo 133-0033, Japan

Hisato Komatsu

  • Department of Basic Science, The University of Tokyo, Komaba, Tokyo 153-8902, Japan

Naoto Tsuji and Hideo Aoki

  • Department of Physics, The University of Tokyo, Hongo, Tokyo 133-0033, Japan

  • *Present address: Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo, Kashiwa, Chiba 277-8582, Japan; masataka.watanabe@ipmu.jp
  • Present address: RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan.

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Issue

Vol. 92, Iss. 20 — 15 November 2015

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