We investigate the electronic structure and related equilibrium properties of low dimensional quantum systems in strong magnetic fields. For two-dimensional system, the electronic eigenenergies, magnetization, and heat capacity of multi-quantum well structures under magnetic fields are calculated numerically. The magnetization and heat capacity show characteristic oscillating behavior as a function of chemical potential with much enlarged magnitude compared to the one-well case. We find that the coupling of the magnetic confinement and the band structure of multilayers leads to the hybrid quantization of electron energies which are seen to manifest themselves in the oscillating pattern of the magnetization and heat capacity. We also study anomalous magnetoresistance peaks measured in a narrow Hall conductor, which are positioned in the quantum Hall plateau regions rather than in the plateau transition regions. We show that such peculiar behavior can be explained quantitatively by using a model based on the edge current picture with the non-uniform distribution of the carrier density.
The dependences of the spin Land g-factor($g^*$) on the electron density and the Landau level filling factor are investigated for two-dimensional electron gas. In a treatment of electron-electron interactions, the trial many-body wavefunctions are constructed by multiplying the Jastrow correlation factor to the Laughlin-like wave functions, then, the ground state energy is calculated using a variational Monte Carlo method in the region of the Landau level filling factor, 1<ν<2. For a dimensionless parameter $γ_s=1.33$, $g^*$ is estimated to be about 11 at ν=1, in good agreement with the measured values of 5-10. Considering the Landau level broadening due to impurity and phonon scatterings, a better agreement of $g^*=9$ is found. As in the free electron gas, the kinetic and Coulomb energies of electrons vary roughly such as $1/γ_s^2$ and $1/γ_s$, respectively, however, $g^*$ is found to increase with increasing of $γ_s$ because the Zeeman splitting is proportional to $1/γ_s^2$.
For zero-dimensional system, we investigate the electronic structure of spheroidal- and coupled-quantum dots with two electrons and find that the combined effect of electron-electron interaction and hybrid-magnetoelectric quantization governs the whole energy spectrum. As a result, the spin transition in the ground state is found to strongly depend on the direction of the magnetic field and the confinement-frequency ratio between lateral and vertical confinements. By relaxing the vertical confinement of the spheroidal-quantum dot, it is found that the spin transition in the ground state can be quenched, or can be reentrant by tilting the magnetic field for the spheroidal-quantum dot. We demonstrate that such behavior clearly appears in the heat capacity and magnetization at sufficient low temperature. In the case of the coupled-quantum dot, we calculate the oscillator strengths of various transitions between many-body energy levels and find that both the electron-electron and dot-dot interactions can be observable with far-infrared spectroscopy.
