  It has recently been found that Dirac and Weyl metals are characterized by an
unusual weak-field longitudinal magnetoresistance: large, negative, and
quadratic in the magnetic field. This has been shown to arise from chiral
anomaly, i.e. nonconservation of the chiral charge in the presence of external
electric and magnetic fields, oriented collinearly. In this paper we report on
a theory of this effect in both Dirac and Weyl metals. We demonstrate that this
phenomenon contains two important ingredients. One is the
magnetic-field-induced coupling between the chiral and the total (or vector, in
relativistic field theory terminology) charge densities. This arises from the
Berry curvature and is present in principle whenever the Berry curvature is
nonzero, i.e. is nonspecific to Dirac and Weyl metals. This coupling, however,
leads to a large negative quadratic magnetoresistance only when the second
ingredient is present, namely when the chiral charge density is a nearly
conserved quantity with a long relaxation time. This property is specific to
Dirac and Weyl metals and is realized only when the Fermi energy is close to
Dirac or Weyl nodes, expressing an important low-energy property of these
materials, emergent chiral symmetry.
