Tunable Fermi Contour Anisotropy in GaAs Electron and Hole Systems

Abstract

This Thesis explores the ballistic transport of quasi two-dimensional (2D) electron and hole systems confined to GaAs quantum wells and subjected to a periodic, strain-induced density modulation. In the presence of an applied perpendicular magnetic field, whenever the diameter of the charged carriers' cyclotron orbit becomes commensurate with the period of the density modulation, the sample's resistance exhibits commensurability features. We use the commensurability effects to directly probe the size of the cyclotron orbit, the Fermi contour, and the spin-polarization of particles at low magnetic field and of composite fermions near even-denominator Landau level filling factors (ν). We establish how the commensurability signatures depend on the sample parameters, including the carrier density, the modulation period, and the width of the confining quantum well.

In the presence of a small perpendicular magnetic field (Bperp), both 2D electrons and holes are essentially spin-unpolarized and their Fermi contours are nearly circular. When an additional parallel component B|| is introduced, it couples to the carriers' out-of-plane motion and leads to a severe distortion of the energy bands and the Fermi contours. The degree of anisotropy is typically stronger in the wider quantum wells but it also depends on the carrier type. For a given QW width, holes become anisotropic more readily than electrons. The application of B|| also affects the spin-polarization of the carriers. Hole samples, for example, become more spin-polarized compared to electrons. We can semi-quantitatively explain the shape and size of the electron and hole Fermi contours with a theoretical calculation with no adjustable parameters based on an 8 x 8 Kane Hamiltonian.

In addition to the electron and hole data at low perpendicular magnetic fields, we observe commensurability features for composite fermions near Landau level filling factors &nu; = 3/2, 1/2, and 1/4. Our data reveal an asymmetry of the composite fermion commensurability features on the two sides of filling factors &nu; = 1/2 and 3/2. The asymmetry is a fascinating manifestation of a subtle breaking of the particle-hole equivalence in the ballistic transport of composite fermions. It is consistent with a transport picture in which the <italic>minority</italic> carriers capture flux quanta to form composite fermions.

We also employ commensurability oscillations as a tool to probe and quantify the effect of B|| on the composite fermion Fermi contours. Our measurements reveal that, thanks to the finite layer thickness of the carriers and the coupling of their out-of-plane motion to B||, the Fermi contours of &nu; = 1/2 and 3/2 composite fermions are significantly distorted. Furthermore, depending on the width of the quantum well and the sample density, in the vicinity of &nu; = 3/2 the spin-polarization of the composite fermions varies while near &nu; = 1/2 they remain fully spin-polarized.