Chiral symmetry and chiral anomaly in an incommensurate charge-density-wave system

It is shown that chiral symmetry and chiral anomaly are inherent to the incommensurability of a quasi one-dimensional charge-density-wave system. The chiral anomaly induced by the applied electric field is interpreted as an acceleration mechanism of the sliding charge-density wave and is connected with the Thomas-Fermi screening effect. The explicit breaking of chiral symmetry due to the external potential is proved to have sinusoidal dependence on the phase order parameter. Possible observable effects are also discussed.