Theory of Josephson-Type Oscillations in a Moving Charge-Density Wave

A theory of Josephson-type phenomena is presented, in which the two macroscopic quantum states are the two components of an incommensurate charge-density wave with opposite wave vectors. The Fermi levels of these two states are split for a moving charge-density wave and impurity scattering induces quantum oscillations. Such oscillations may be responsible for the observed narrow-band noise in materials such as Nb${\mathrm{Se}}_3$ and Ta${\mathrm{S}}_3$.