Anomalous Magnetic Effects in Three-Dimensional Weyl Semimetals
Gogh, M.A. van
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We calculate the energy spectrum of a Weyl semimetal near the band touching points in the presence of a magnetic field. In this calculation we include the effect of the anomalous magnetic moment, coming from a vertex correction to the action. We show that this effect breaks the spin degeneracy, which is present in all states except the chiral ground state. Additionally, we calculate the effect of introducing a time reversal symmetry breaking vector, which separates the two Weyl nodes in momentum space. We find that having the vector along the direction of the magnetic field yields analytically computable states. In contrast, having the vector perpendicular to the direction of the magnetic field requires numerical computation of the energy levels and leads to a non-linear dispersion relation for the ground state. This conclusion is supported by perturbation theory. Furthermore, we consider the influence of magnetic fields on bound surface states. We show that within a WKB approximation, a magnetic field parallel to the boundary does not affect the surface state dispersion relation. However, the anomalous magnetic moment terms do alter the dispersion relation, as well as the region in reciprocal space in which the dispersion relation is a solution.