Existence and stability of Weyl points
Weyl points are quasimomentum-energy pairs in the band structure of three-dimensional periodic media at which two dispersion surfaces touch conically. They first arose in a model introduced by H. Weyl in 1929, but were first observed only recently in condensed matter physics and photonics experiments. Weyl points have been explored theoretically via numerical computation and via tight binding (discrete) models. In this article we present the first analytical treatment of Weyl points in a continuum PDE-type model. Starting with a Schrödinger operator whose electric potential is periodic with respect to the body-centered cubic (BCC) lattice, we introduce a small BCC-periodic magnetic vector potential that is equivariant with respect to a specific abelian group of symmetries. For magnetic Schrödinger operators of this type, we prove (i) that a pair of Weyl points bifurcates from a threefold degeneracy in the band structure of the underlying non-magnetic operator, and (ii) that these Weyl points are stable against small self-adjoint BCC-periodic perturbations of both the electric and magnetic vector potentials.