Magnetoplasma resonances and nonlinear mode coupling in pools of ions trapped below the surface of superfluid helium

Oscillation mode transformation of edge magnetoplasmons in two-dimensional electron system on liquid-helium surface

“…EMPs appear as the lower frequency branch of 2D magnetoplasmons, and the frequency decreases as the external perpendicular magnetic field is increased. Subsequently, EMPs were observed in a wide variety of 2DESs including degenerate 2DESs in semiconductor heterostructures [6], 2DESs in nanostructures [7], and in 2D ion systems trapped under a liquid-helium surface [8]. Taking advantage of the EMP property that the charge oscillation localizes near the edge, researchers have attempt to employ EMPs as sensitive probes to study the structure of edge electronic states and electronic transport along edge channels [9,10].…”

Magnetoplasmons in two-dimensional circular sheets of4He+ions

“…͑Strictly speaking, effects of this type were first observed in an array of small samples of a two-dimensional electron gas in a GaAs/AlGaAs heterojunction. 3 ͒ More recently 4 the effects have been studied by our group in a two-dimensional sheet of ions trapped below the surface of superfluid 4 He. An interesting theoretical development occurred in 1988 when Nazin and Shikin 5 showed that, if proper account is taken of the smooth falloff in the density profile near the edge of the sheet, extra ͑''multipole''͒ edge modes ought to appear in the presence of a magnetic field, and this prediction was verified in a semiquantitative way for the ion sheets by Elliott et al 6 Subsequently, it has been recognized that the new modes had been seen in the electron system by Kirichek et al 7 Edge modes associated with a step from one density n 0 to another have been observed by Sommerfeld et al 8 in the electron sheets.…”

“…Our experimental techniques have been described in detail in previous publications, 12,13,4 to which we refer for details. In brief the ions are trapped below the helium surface by the combined interaction with their images in the surface and a vertical external electric field E 0 .…”

“…The details of this double-drive technique need not concern us here, where we are interested only in resonant mode frequencies; they were described in greater detail in Ref. 4, and they will be described in further detail in a forthcoming publication, concerned with applications where line widths as well as resonant frequencies need to be measured and where therefore the technique needs to be used and analyzed with particular care.…”

“…One such method was described in an earlier publication of our group. 4 To set up a suitable trial function describing the radial variation of the perturbation (r) in the charge density, the sheet is divided into a large number N of annuli, and (r) is taken to have the form…”