Surface spectra of Weyl semimetals through self-adjoint extensions

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 $\mathbb{U}(2)$ matrix relating the wavefunction 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.

9 pages, 3 figures; v2: published version with added references and discussion of the limiting relation between the surface spectra of different bulk dispersion models

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Cited by in corpus (6)

• Lorentz violation in Dirac and Weyl semimetals
• Infinite Berry Curvature of Weyl Fermi Arcs
• A new version of the Aharonov-Bohm effect
• Field theory approach to the quantum transport in Weyl semimetals
• Ever-present Majorana bound state in a generic one-dimensional superconductor with odd number of Fermi surfaces
• Berry curvature associated to Fermi arcs in continuum and lattice Weyl systems