Theory of Shubnikov--De Haas Oscillations Around the $\nu=1/2$ Filling Factor of the Landau Level: Effect of Gauge Field Fluctuations

TL;DR

This paper develops a quasiclassical theory for magnetooscillations near the $ u=1/2$ Landau level, revealing an unconventional exponential decay of oscillation amplitude due to gauge field fluctuations, aligning qualitatively with experiments.

Contribution

It introduces a novel quasiclassical model incorporating gauge field fluctuations to explain Shubnikov--De Haas oscillations near $ u=1/2$.

Findings

Unconventional exponential decay of oscillation amplitude with a $(rac{ ext{constant}}{ ext{field}})^4$ dependence

Qualitative agreement with experimental observations

Highlights the role of gauge field fluctuations in quantum Hall phenomena

Abstract

We present a theory of magnetooscillations around the $\nu =1/2$ Landau level filling factor based on a model with a fluctuating Chern--Simons field. The quasiclassical treatment of the problem is appropriate and leads to an unconventional $\exp\left[-(\pi/\omega_c\tau^*_{1/2})^4\right]$ behavior of the amplitude of oscillations. This result is in good qualitative agreement with available experimental data.