Influence of magnetic-field-induced spin-density-wave motion and finite temperature on the quantum Hall effect in quasi-one-dimensional conductors: A quantum field theory

We derive the effective action for a moving magnetic-field-induced spin-density wave (FISDW) in quasi-one-dimensional conductors at zero and nonzero temperatures by taking the functional integral over the electron field. The effective action consists of the (two plus one)-dimensional [(2+1)D] Chern-Simons term and the (1+1)D chiral anomaly term, both written for a sum of the electromagnetic field and the chiral field associated with the FISDW phase. The calculated frequency dependence of Hall conductivity interpolates between the quantum Hall effect at low frequencies and zero Hall effect at high frequencies, where the counterflow of FISDW cancels the Hall current. The calculated temperature dependence of the Hall conductivity is interpreted within the two-fluid picture, by analogy with the BCS theory of superconductivity.