Quantum Hall effect in a multi-valley two-dimensional electron system

Two-dimensional electrons in an AlAs quantum well occupy multiple conduction-band minima at the X-points of the Brillouin zone. These valleys have large effective mass and g-factor compared to the standard GaAs electrons, and are highly anisotropic. With proper choice of well width and by applying symmetry-breaking strain in the plane, one can control the occupation of different valleys thus rendering a system with tuneable effective mass, g-factor, Fermi contour anisotropy and valley degeneracy. Here we review some of the rich physics that this system has allowed us to explore.