Development of the Dimple Instability on Liquid 4

Electrons localized on the surface of liquid helium have been investigated quite extensively as an example of a nearly ideal two-dimensional Coulomb system [1,2]. Recently it has been observed that the homogeneous spatial distribution of the surface charge can be destroyed by self-trapping of the electrons in macroscopic dimples, which appear when the electric field pulling the charges toward the surface exceeds a critical value [3]. These dimples, resulting from an electrohydrodynamic instability of the surface, were found to be arranged in a regular, hexagonal structure, with a lattice constant approximately given by the wavelength of the soft ripplon which drives the instability. Theoretically the electrohydrodynamic instability of the electron-liquid helium system has first been considered by Gorkov and Chernikova. These authors suggested that above a critical electric field bandlike or hexagonal structures should appear on the helium surface, but the stability of such structures was an open question [2,4-61. After the experimental verification of the dimple lattice Ikezi presented a theory which accounted for the observed stable hexagonal configuration and in addition predicted hysterestis effects at the transition from the homogeneous to the dimple state [7]*' . In the present work we report about an experimental investigation of this transition. For the measurements we used an optical sample