Microwave resonance in 2D Wigner crystals

TL;DR

This paper explains microwave absorption peaks in 2D Wigner crystals through a model involving electron clusters and fractional charges, linking experimental data with a theoretical formula for the filling factor.

Contribution

It introduces a novel formula for the filling factor based on electron clusters with different l and s values, explaining observed microwave resonance peaks.

Findings

Experimental peaks match the proposed formula when considering electron clusters.

Filling factors can be interpreted as fractional charges.

Zero charge corresponds to a diverging resistivity and an insulating Wigner crystal.

Abstract

Recent experimental measurements of the microwave absorption in the frequency range 1-4 GHz show peaks at several values of the filling factor,\nu=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".