Temperature evolution of the quantum Hall effect in the FISDW state : Theory vs. experiment

Abstract
We discuss the temperature dependence of the Hall conductivity σ_xy in the magnetic-field- induced spin-density-wave (FISDW) state of the quasi-one-dimensional Bechgaard salts (TMTSF)₂X. Electronic thermal excitations across the FISDW energy gap progressively destroy the quantum Hall effect, so σ_xy(T) interpolates between the quantized value at zero temperature and zero value at the transition temperature T_c, where FISDW disappears. This temperature dependence is similar to that of the superfluid density in the BCS theory of superconductivity. More precisely, it is the same as the temperature dependence of the Fröhlich condensate density of a regular CDW/SDW. This suggests a two-fluid picture of the quantum Hall effect, where the Hall conductivity of the condensate is quantized, but the condensate fraction of the total electron density decreases with increasing temperature. The theory appears to agree with the experimental results obtained by measuring all three components of the resistivity tensor simultaneously on a (TMTSF)₂PF₆ sample and then reconstructing the conductivity tensor.