Microwave resonance in 2D Wigner crystals

Abstract

Recent experimental measurements of the microwave absorption in the frequency range 1-4 GHz show peaks at several values of the filling factor,ν=nh/eB. Since the filling factor multiplies the magnetic field, it is similar to the Lande's splitting factor, g. By using both signs in j={\it l}\pm s, we obtain a formula for the splitting factor which is equivalent to obtaining the filling factor. The experimentally observed values of 6/5, 4/3, 7/5, 8/5, 5/3, 7/3 and 5/2 are in agreement with our formula provided that we propose that there are "electron clusters". The clusters have {\it l} and s values and vary in size. It is possible to interpret the filling factor as a fractional charge. When charge becomes zero, the transverse resistivity diverges so that large resistivity belongs to an insulator which is called a "Wigner crystal".