Anisotropic conductivity tensor on a half-filled high Landau level

TL;DR

This paper investigates how unidirectional charge density waves in high Landau level electrons induce anisotropic conductivity, with the anisotropy emerging below a critical temperature and persisting above it due to fluctuations.

Contribution

It demonstrates that the anisotropic conductivity tensor arises from charge density wave order and persists above the transition temperature due to fluctuations, aligning with experimental observations.

Findings

Anisotropic conductivity tensor proportional to (T_c - T)/T_c below T_c.

Conductivity anisotropy persists above T_c due to order parameter fluctuations.

Theoretical results agree with experimental data on high Landau level electrons.

Abstract

We study two-dimensional interacting electrons in a weak perpendicular magnetic field with the filling factor $\nu \gg 1$ and in the presence of a quenched disorder. As it is known, the unidirectional charge density wave state can exist near a half-filled high Landau level at low temperatures if disorder is weak enough. We show that the existence of the unidirectional charge density wave state at temperature $T<T_c$ where $T_c$ is the transition temperature leads to the anisotropic conductivity tensor. We find that the anisotropic part of conductivity tensor is proportional to $(T_c-T)/T_c$ below the transition in accordance with the experimental findings. The order parameter fluctuations wash out the mean-field cusp at $T=T_c$ and the conductivity tensor becomes anisotropic even above the mean-field transition temperature $T_c$.