A method for obtaining finite electronic systems on a liquid-helium su
rface is proposed. If a thin film of liquid helium lies above a bottom
capacitor plate made in the form of metal rings connected with one an
other, then electrons will accumulate in potential troughs near these
rings. The purity of the helium surface, i.e., the absence of impuriti
es and pinning centers on it, affords an excellent opportunity for inv
estigating the Aharonov-Bohm effect in an ideal ring of a Wigner cryst
al and a Luttinger liquid. (C) 1998 American Institute of Physics. [S0
021-3640(98)01006-8].