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

TL;DR

This paper explores how temperature affects the quantum Hall effect in FISDW states of Bechgaard salts, showing a gradual loss of quantization with increasing temperature, supported by theory and experiments.

Contribution

It introduces a two-fluid model for the quantum Hall effect in FISDW states, linking the temperature dependence to a condensate fraction similar to superfluid density.

Findings

Temperature dependence of Hall conductivity matches experimental data.

Quantum Hall effect diminishes with increasing temperature, disappearing at T_c.

Theoretical model aligns with resistivity measurements on (TMTSF)_2PF_6.

Abstract

We discuss the temperature dependence of the Hall conductivity $\sigma_{xy}$ 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 $\sigma_{xy}(T)$ 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 Fr\"ohlich 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)_2PF_6 sample and then reconstructing the conductivity tensor.