Continuum elasticity theory of edge excitations in a two-dimensional electron liquid with finite range interactions

TL;DR

This paper uses continuum elasticity theory to analyze edge excitations in a two-dimensional electron liquid with finite-range interactions, deriving universal and regime-dependent dispersion relations for collective modes.

Contribution

It provides an analytical framework for understanding edge excitations in 2D electron systems considering finite-range interactions and near-incompressibility.

Findings

Universal linear dispersion at small wave vectors

Dispersion form varies with length scales at larger wave vectors

Analytical formulas for mode dispersion and damping

Abstract

We make use of continuum elasticity theory to investigate the collective modes that propagate along the edge of a two-dimensional electron liquid or crystal in a magnetic field. An exact solution of the equations of motion is obtained with the following simplifying assumptions: (i) The system is {\it macroscopically} homogeneous and isotropic in the half-plane delimited by the edge (ii) The electron-electron interaction is of finite range due to screening by external electrodes (iii) The system is nearly incompressible. At sufficiently small wave vector $q$ we find a universal dispersion curve $\omega \sim q$ independent of the shear modulus. At larger wave vectors the dispersion can change its form in a manner dependent on the comparison of various length scales. We obtain analytical formulas for the dispersion and damping of the modes in various physical regimes.