Surface spectra of Weyl semimetals through self-adjoint extensions

Babak Seradjeh and Michael Vennettilli
Phys. Rev. B 97, 075132 – Published 15 February 2018

Abstract

We apply the method of self-adjoint extensions of Hermitian operators to the low-energy, continuum Hamiltonians of Weyl semimetals in bounded geometries and derive the spectrum of the surface states on the boundary. This allows for the full characterization of boundary conditions and the surface spectra on surfaces both normal to the Weyl node separation as well as parallel to it. We show that the boundary conditions for quadratic bulk dispersions are, in general, specified by a U(2) matrix relating the wave function and its derivatives normal to the surface. We give a general procedure to obtain the surface spectra from these boundary conditions and derive them in specific cases of bulk dispersion. We consider the role of global symmetries in the boundary conditions and their effect on the surface spectrum. We point out several interesting features of the surface spectra for different choices of boundary conditions, such as a Mexican-hat shaped dispersion on the surface normal to Weyl node separation. We find that the existence of bound states, Fermi arcs, and the shape of their dispersion, depend on the choice of boundary conditions. This illustrates the importance of the physics at and near the boundaries in the general statement of bulk-boundary correspondence.

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  • Received 14 December 2017

DOI:https://doi.org/10.1103/PhysRevB.97.075132

©2018 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Babak Seradjeh1,2 and Michael Vennettilli3,4

  • 1Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
  • 2Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden Germany
  • 3Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
  • 4Department of Physics and Astronomy, Ursinus College, Collegeville, Pennsylvania 19426, USA

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Issue

Vol. 97, Iss. 7 — 15 February 2018

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