In the first part of this project we will study the spin-dependent transport of electrons across a ferromagnet-semiconductor (FS) interface. The presence of a potential barrier (Schottky barrier) at the FS interface will also be addressed. Next, we plan to thoroughly study the injection of spin-polarized electrons into a two dimensional electron gas at the semiconducting side of the interface by considering in detail many-body effects like exchange and correlation. By allowing for spin channel mixing at finite temperatures via electron-magnon scattering our calculations will provide a basis for understanding the room temperature giant magnetoresistance effect.
In the second part we will focus on the localization transition in the Integer Quantum Hall effect. In our calculation both types of disorder (on scalar and vector potential) will be included on equal footing by adopting a lattice model of spin- less fermions the low energy physics of which is described by a free particle Dirac equation. Within our model the edge state problem, and the tunneling among transmission edge channels, will be addressed in detail.