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

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 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 ω∼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.