Propagation of Shear in a Two-Dimensional Electron Solid

Abstract

Shear waves are shown to propagate in the two-dimensional electron solid on liquid helium. Their velocity and damping are measured and used to deduce the shear components of the viscoelastic tensor up to melting. A linear temperature variation at low temperatures contrasts with the premelting region, where the sharper renormalization of the elastic component is accompanied by a very rapid increase in the viscous component.PACS 63.20.Dj, 64.70.Dv A material is solid if it returns to its original shape upon removal of an applied shear stress. At finite frequency this property combines with inertia to give rise to shear waves. Shear waves are thus a fundamental attribute of a solid, but no experimental demonstration has been given that they propagate in a two-dimensional (2D) system. 1 The experiment described here on a classical 2D electron solid shows explicitly that shear (transverse phonons) does propagate and the manner in which it ceases to do so as melting is approached.These observations are presented quantitatively in terms of the generalized shear modulus for an isotropic solid, fji(k, co) = /*' +//x" = \i! +i<or}.(1) \x! and TJ describe the elastic and viscous responses to shear at wave vector k and frequency co. The inertia of the particles, of mass m and areal number density n y combines with the restoring_force from (1) to give rise to shear waves exp[/(k* T-wt)) which propagate at velocity v t = <o/k given by v? = ix/mn.(We observe these waves by looking at the response of the system to a transverse excitation of imposed k. A propagating mode is then seen as a welldefined resonance whose peak position o) k -kfx' l/2 and whose width A<o k ~~ k 2 r). We find that both the elastic response, //, and the viscosity, TJ, show important modifications due to thermal excitations as melting is approached, Electrons on helium form a 2D system of (Coulomb) interacting scalar particles subjected to no periodicity, no anisotropy, and only very small, calculable, random potentials. It is probably the simplest and most controllable solid system so far realized in 2D. Furthermore it shows signs of melting by dissociation of the dislocation pairs which are present as a dilute gas of thermal excitations in the solid. This model 2 has proved unusually tractable and considerable theoretical results exist on both static 3 and dynamic 4 properties. A striking qualitative prediction is that the solid should melt, at T m , to an oriented liquid (hexatic) phase with free dislocations and only when these decompose into free disclinations should the liquid become isotropic, at T h The T m transition is now well documented 5 ' 9 but no experiment has been devised to detect T h The quantitative characterization of melting, however, most naturally hinges on the response to shear, even in the hexatic phase. The most direct way to this is to make mechanical shear measurements on a variety of length and time scales. The first attempt in this direction was only able to evaluate the shear modulus averaged over the lengths and times...

Fröhlich polarons from 0D to 3D: concepts and recent developments

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Coulomb disorder in periodic systems: Effect of unscreened charged impurities

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Effect of the classical electron Coulomb crystal on interedge magnetoplasmons

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