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

摘要

We present a new theory of photoemission for Weyl semimetals. We derive thistheory using a model with a boundary surface at $z=0$. Due to the boundary, theself adjoint condition needs to be verified in order to ensure physicalsolutions. The solutions are given by two chiral zero modes which propagate onthe boundary. Due to the Coulomb interaction, the chiral boundary model is in the sameuniversality class as interacting graphene. The interactions cause atemperature dependence of the velocity and and life time. \noindent Using theprinciple of minimal coupling, we identify the electron-photon Hamiltonian. Thephotoemission intensity is computed using the $S$-matrix formalism. The$S$-matrix is derived using the initial photon state, the final state of aphotoelectron and a hole in the valence band. The photoemission reveals thefinal valence band dispersion $ \hbar v(\pm k_{y}-k_{0})+\hbar\Omega$ afterabsorbing a photon of frequency $ \Omega$ ($k_{0}$ represents the shift in themomentum due to the crystal potential). The momentum in the $z$ direction isnot conserved, and is integrated out. As a result, the scattering matrix is afunction of the parallel momentum . We observe two dimensional contours,representing the $^{"}$Fermi arcs $^{"}$, which for opposite spin polarizationhave opposite curvature. This theory is in agreement with previous experimentalobservations.