Role of boundary conditions, topology and disorder in the chiral magnetic effect in Weyl semimetals

Abstract

Quantum field theory predicts Weyl semimetals to possess a peculiar response of the longitudinal current density to the application of a DC magnetic field. Such a response function has been shown to be at odds with a general result showing the vanishing of the bulk current in an equilibrium system on any real material with a lattice in an external magnetic field. Here we resolve this apparent contradiction by introducing a model where a current flows in response to a magnetic field even without Weyl nodes. We point out that the previous derivation of a vanishing CME in the limit of vanishing real frequency is a consequence of the assumption of periodic boundary conditions of the system. A more realistic system with open boundary conditions is not subject to these constraints and can have a non-vanishing CME. Consistent with recent work, we found the finite frequency CME to be non-vanishing in general when there was a non-vanishing Berry curvature on the Fermi surface. This does not necessitate having a topological Berry flux as in the case of a Weyl node. Finally, we study how the perturbation theory in magnetic field might be more stable in the presence of disorder. Using the standard diagrammatic treatment of disorder within the Born approximation, we have found that in a realistic disordered system, the chiral magnetic response is really a dynamical phenomena and vanishes in the DC limit.