(A) theoretical study of the electron correlation effects in low-dimensional systems at high magnetic fields

Abstract

We investigate theoretically the physical properties of the low dimensional system for zero-dimensional quantum dot, one-diemnsional quantum Hall edge states, and two-dimensional quantum Hall system especially for the systems at high magnetic fields. In the low dimensional system where the electron-electron interactions are significant, careful theoretical studies are needed for understanding the phenomena which can not be explained in independent-electron models. For the zero-dimensional quantum dot system, through a calculational method developed by us, we investigate the effects of electron correlations on the ground state energy and the chemical potential of a droplet confined by a parabolic potential at high magnetic fields. We demonstrate the importance of correlations in estimating the transition field at which the first edge reconstruction of the maximum density droplet occurs in the spin polarized regime. The spectral weight matrix for quantum dot is also calculated and we find that electron tunneling is strongly spin-related due to electron correlation. Our calculational results are in good agreement with the experiments. For one-dimensional quantum Hall edge states, we investigate the effect of contact hyperfine interaction at the edge of the filling factor ν=2. We find that the contact interaction breaks the U(1) symmetry in the system, so that the compact ground state at ν=2 can be unstable. Due to the electron-electron interactions, there is spontaneous spin polarization at the edge of ν=2. The contact hyperfine interactions can be divided into two parts, static and dynamical parts. The size of the spin-polarized region can be enhanced by the static part of contact interactions, which is an Overhauser effect. The dynamical part of contact interaction is relatively small compared to other interactions and it reduces the size of spin-polarized region. For the two-dimensional quantum Hall system, we study charged spin texture (skyrmion) which have ...