(A) study of electron-electron interactions in a two-dimensional quantum dot in the fractional quantum hall regime

Abstract

We examine the effect of electron-electron interactions on the ground state property of a two-dimensional quantum dot in the fractional quantum Hall regime. For quantum dots containing up to six electrons at filling factors between 1 and $\frac{1}{3}$, the many-body wave functions are made of the lowest Landau levels and the higher Landau levels are effectively included by a Jastrow factor. We find that some bumps observed in Single Electron Capacitance Spectroscopy (SECS) experiments are related to the chemical potential discontinuity, $\Delta\mu$, which was shown in the fractional quantum Hall system. We find the precursor of the incompressibility at a filling factor $\nu = \frac{1}{3}$, which is responsible for the fractional quantum Hall effect. A quasi-hole creation results in the phase transition from the $\nu = 1$ state to the $\nu < 1$state. The effect of a quasi-hole creation on compressibility is also discussed. In order to avoid the problem with the tunneling rate decrease in SECS experiments, which makes the quasi-hole creation hardly detectable, we suggest that weaker confining potentials are important.