Weyl semimetal from non-inertial observers

Abstract

We show that a reference frame transformation could turn a topologically trivial Dirac fermion into a topologically nontrivial Weyl semimetal. This is elucidated by the transformation of the Dirac equation into the equation for Weyl semimetals through specific infinitesimal local Lorentz transformations of the orthonormal basis. This kind of transformation, interpreted as a change of reference frame, could induce an observational effect that an axial gauge field and/or a vector U(1) gauge field appears effectively, which are in fact inertial forces in the non-inertial frame.The precise local Lorentz transformations and the movement of observers needed to realize the two additional fields are provided respectively. This novel effect can be viewed as a generalization of the effect found in relativistic hydrodynamics that topologically trivial modes in an inertial frame could become topologically nontrivial observed by a special non-inertial observer.