Random-phase Approximation Treatment Of Edge Magnetoplasmons: Edge-state Screening And Nonlocality

TL;DR

This paper develops an RPA-based theoretical framework for edge magnetoplasmons in strong magnetic fields, accounting for edge-state screening, nonlocal effects, and Landau level coupling, revealing new dispersion relations for different filling factors.

Contribution

It introduces a comprehensive RPA approach that includes nonlocality and edge-state screening effects for EMPs, providing new insights into their dispersion relations at various filling factors.

Findings

Fundamental EMP mode with   dispersion at u>2.

Existence of a dipole mode with   dispersion at u=1,2.

Identification of nonlocal responses affecting EMP behavior.

Abstract

A random-phase approximation (RPA) treatment of edge magnetoplasmons (EMP) is presented for strong magnetic fields, low temperatures, and integer filling factors \nu. It is valid for negligible dissipation and lateral confining potentials smooth on the scale of the magnetic length \ell_{0} but sufficiently steep that the Landau-level (LL) flattening can be neglected. LL coupling, screening by edge states, and nonlocal contributions to the current density are taken into account. In addition to the fundamental mode with typical dispersion relation \omega\sim q_x \ln(q_{x}), fundamental modes with {\it acoustic} dispersion relation \omega\sim q_x are obtained for \nu>2. For \nu=1,2 a {\bf dipole} mode exists, with dispersion relation \omega\sim q_x^3, that is directly related to nonlocal responses.