Abstract. We study the thermoelectric transport properties in the three-dimensional Anderson model of localization near the metal-insulator transition (MIT). In particular, we investigate the dependence of the thermoelectric power S, the thermal conductivity K, and the Lorenz number L0 on temperature T . We first calculate the T dependence of the chemical potential µ from the number density n of electrons at the MIT using an averaged density of states obtained by diagonalization. Without any additional approximation, we determine from µ(T ) the behavior of S, K and L0 at low T as the MIT is approached. We find that σ and K decrease to zero at the MIT as T → 0 and show that S does not diverge. Both S and L0 become temperature independent at the MIT and depend only on the critical behavior of the conductivity.

By varying the orientation of the applied magnetic field with respect to the normal of a twodimensional electron gas, the chemical potential and the specific heat reveal persistent spin splitting in all field ranges. The corresponding shape of the thermodynamic quantities distinguishes whether the Rashba spin-orbit interaction (RSOI), the Zeeman term or both dominate the splitting. The interplay of the tilting of the magnetic field and RSOI resulted to an amplified splitting even in weak fields. The effects of changing the RSOI strength and the Landau level broadening are also investigated.

This work investigates the influence of low temperature and broadened Landau levels on the thermodynamic properties of twodimensional electron systems. The interplay between these two physical parameters on the magnetic field dependence of the chemical potential, the specific heat and the magnetization is calculated. In the absence of a complete theory that explains the Landau level broadening, experimental and theoretical studies in literature perform different model calculations of this parameter. Here it is presented that different broadening parameters of Gaussian-shaped Landau levels cause width variations in their contributions to interlevel and intralevel excitations. Below a characteristic temperature, the interlevel excitations become negligible. Likewise, at this temperature range, the effect of the Landau level broadening vanishes.

We study the behavior of the thermal transport properties in three-dimensional disordered systems close to the metal-insulator transition within linear response. Using a suitable form for the energy-dependent conductivity , we show that the value of the dynamical scaling exponent for noninteracting disordered systems such as the Anderson model of localization can be reproduced. Furthermore, the values of the thermopower S have the right order of magnitude close to the transition as compared to the experimental results. A sign change in the thermoelectric power S -as is often observed in experiments -can also be modeled within the linear response formulation using modified experimental data as input.

A two-dimensional electron gas exposed to a tilted magnetic field is considered with the Rashba spin-orbit interaction and the Zeeman effect. An exact solution for the eigenvalues was obtained assuming that two opposite spin states of adjacent Landau levels have equal probability. No crossings between adjacent eigenenergies were observed, for the tilt angles studied here (θ ≤ 80 • ), unlike in the perpendicular-magnetic-field case. The absence of crossings lead to quenched beating structures in the oscillations of the density of states (DOS). Persistent spin-splittings were observed at the weak magnetic field region. The splittings, however, can be effectively screened by an increased Landau level broadening. The results shed light on how spins can be controlled through the Rashba interaction strength, the disorder-related broadening and the magnetic field tilt angle.