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

URL:http://link.aps.org/doi/10.1103/PhysRevB.60.2084 DOI:10.1103/PhysRevB.60.2084We 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.This work was supported by NSF Grant No. DMR- 9706788. G.V. gratefully acknowledges the hospitality of the Institute for Theoretical Physics at the University of California, Santa Barbara, under NSF Grant No. PHY94- 07194, where part of this work was done