Fundamental steps of group velocity for slow surface polariton under the quantum hall effect conditions

TL;DR

This paper predicts a new type of surface polariton in a 2D electronic layer under Quantum Hall Effect conditions, revealing unique dispersion, damping, and velocity properties near cyclotron resonance, supported by theoretical calculations matching experimental data.

Contribution

It introduces a novel collective electromagnetic excitation in 2D layers under QHE, detailing its spectrum, damping, polarization, and the fundamental steps in group velocity near cyclotron resonance.

Findings

Surface polaritons exhibit drastically slowed phase velocity near CR.

Negative dispersion occurs near a CR subharmonic.

Calculated CR line-shape and conductance match experimental data.

Abstract

A new type of collective electromagnetic excitations, namely surface polaritons (SP) --- in a 2D electronic layer in a high magnetic field under Quantum Hall Effect (QHE) conditions is predicted. We have found the spectrum, damping, and polarization of the SP in a wide range of frequencies $\omega$ and wavevectors $\bf k$. It is shown that near the Cyclotron Resonance (CR) ($\omega\sim\Omega=\displaystyle eB/mc$) the phase velocity of the SP is drastically slowed down and the group velocity undergoes fundamental steps defined by the Fine Structure Constant $\alpha=e^2/\hbar c$. In the vicinity of a CR subharmonic ($\omega\sim 2 \Omega$) the negative (anomalous) dispersion of the SP occurs. The relaxation of electrons in the 2D layer gives rise to a new dissipative collective threshold-type mode of the SP. We suggest a method for calculating the kinetic coefficients for the 2D electronic layer under QHE condition, using the Wigner distribution function formalism and determine their spatial and frequency dispersion. Using this method we have calculated the line-shape of the CR and the d.c. conductance under the QHE condition, which are in good agreement with experimental data.