The S-matrix for surface boundary states: An application to photoemission for Weyl semimetals

We present a new theory of photoemission for Weyl semimetals. We derive this theory using a model with a boundary surface at z=0. Due to the boundary, the self adjoint condition needs to be verified in order to ensure physical solutions. The solutions are given by two chiral zero modes which propaga...

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Bibliographic Details
Published in:Annals of physics 2018-09, Vol.396, p.304-317
Main Author: Schmeltzer, D.
Format: Article
Language:English
Subjects:
[formula omitted] matrix
Boundary states
CHIRALITY
CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
CRYSTALS
GRAPHENE
HAMILTONIANS
MATHEMATICAL SOLUTIONS
monopole–antimonopoles
PHOTOEMISSION
PHOTONS
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
S MATRIX
SCATTERING
SEMIMETALS
SPIN ORIENTATION
TEMPERATURE DEPENDENCE
TWO-DIMENSIONAL CALCULATIONS
VALENCE
VELOCITY
Weyl semimetals
Zero modes
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Summary:We present a new theory of photoemission for Weyl semimetals. We derive this theory using a model with a boundary surface at z=0. Due to the boundary, the self adjoint condition needs to be verified in order to ensure physical solutions. The solutions are given by two chiral zero modes which propagate on the boundary. Due to the Coulomb interaction, the chiral boundary model is in the same universality class as interacting graphene. The interactions cause a temperature dependence of the velocity and life time. Using the principle of minimal coupling, we identify the electron–photon Hamiltonian. The photoemission intensity is computed using the S-matrix formalism. The S-matrix is derived using the initial photon state, the final state of a photoelectron and a hole in the valence band. The photoemission reveals the final valence band dispersion ħv(±ky−k0)+ħΩ after absorbing a photon of frequency Ω (k0 represents the shift in the momentum due to the crystal potential). The momentum in the z direction is not conserved, and is integrated out. As a result, the scattering matrix is a function of the parallel momentum . We observe two dimensional contours, representing the “Fermi arcs”, which for opposite spin polarization have opposite curvature. This theory is in agreement with previous experimental observations.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2018.04.018