Self-consistent investigation of exchange and correlation in the two-dimensional electron gas under strong perpendicular magnetic fields

In this thesis, the emergent role of the exchange and thecorrelation effects on a two dimensional electron gas in thepresence of a strong perpendicular magnetic field was studied withinthe Thomas-Fermi-Dirac-Poisson approximation. The effective Lande-gfactor of the two-dimensional system was calculated. In our studies,the exchange functional within a framework of the local spin densityapproximation derived for the homogeneous two-dimensional electrongas and the correlation functionals, which correspond this exchangefunctionals were constructed by using quantum Monte Carlo methods,were used. After investigating the effects of the exchange and thecorrelation on the system, the magnetoconductivity in atwo-dimensional electron system including the exchange andcorrelation interaction was also calculated. In themagnetoconductivity calculations, the short-range disorder wasinvestigated within the Self-consistent Born approximation. Thisapproximation is an appropriate form of broadened Landau density ofstates for strong, quantizing magnetic fields to calculateconductivities in the quantum Hall regime. In the second part of the thesis,the total ground stateenergy of a semiconductor quantum dot which is defined by thetrench gate method was calculated. In our ground state energycalculations, we used a recently developed energy functional calledorbital-free energy functional, Thomas-Fermi approximation andlocal density approximation. We compared the total energies obtainedwith three different approximations for the square quantum slabgeometry with different particle number.