Helical symmetry breaking and quantum anomaly in massive Dirac fermions

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 quantum fluctuation in the band gap. The chiral anomaly can be derived from the helical symmetry breaking. It provides an alternative route to understanding 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 magnetotransport 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.