  Helical symmetry of massive Dirac fermions is broken explicitly in the
presence of electric and magnetic fields. Here we present two equations for the
divergence of helical and axial-vector currents following the Jackiw-Johnson
approach to the anomaly of the neutral axial vector current. We discover the
contribution from the helical symmetry breaking is attributed to the occupancy
of the two states at the top of the valence band and the bottom of the
conduction band. The explicit symmetry breaking fully cancels the anomalous
correction from the quantum fluctuation in the band gap. The chiral anomaly can
be derived from the helical symmetry breaking. It provides an alternative route
to understand the chiral anomaly from the point of view of the helical symmetry
breaking. The pertinent physical consequences in condensed matter are the
helical magnetic effect which means a charge current circulating at the
direction of the magnetic field, and the mass-dependent positive longitudinal
magnetoconductivity as a transport signature. The discovery not only reflects
anomalous magneto-transport properties of massive Dirac materials but also
reveals the close relation between the helical symmetry breaking and the
physics of chiral anomaly in quantum field theory and high energy physics.
