Interacting two dimensional systems with a discrete degree of freedom

This thesis considers several two dimensional and quasi-two dimensional systems in AlAs and GaAs with discrete electronic degrees of freedom, such as spin, valley, and layer indices. Each discrete degree of freedom responds to an externally applied field, allowing us control over the occupation of the levels. Each also enables a new measurement technique, with which we can probe these strongly interacting systems.;We confine holes in closely spaced bilayer GaAs quantum well (QW) samples. In this system the holes possess a layer degree of freedom, which we easily manipulate using electric fields from electrostatic gates on the surface and substrate of the sample. Tunneling through the narrow insulating barrier between the QWs couples the two layers, and allows us to use tunneling measurements to probe the energetics of the two dimensional hole system above and below the Fermi energy. By applying a large magnetic field parallel to the system, we probe the in-plane dispersion of strongly interacting holes. We find a striking departure from the expected dispersion for large magnetic fields.;Electrons in wide AlAs QWs occupy two degenerate minima in the conduction band, called valleys. We break the degeneracy of these valleys with applied strain in the plane of the QW, applied in-situ using a piezoelectric stack. It is well known that changing valley occupation shows clearly in the changing strength of integer quantum Hall resistance minima. We find analogous behavior in the fractional quantum Hall effect (FQHE) minima around Landau level filling factor nu = 32 . In light of the composite fermion model of the FQHE, we deduce that composite fermions in AlAs have a valley degree of freedom, and determine the valley susceptibility and valley polarization energy.