Probing Exotic Phases of Interacting Two-dimensional Carriers Using One-dimensional Density Modulation

Abstract

In this Thesis, we present low-temperature magnetotransport studies of two-dimensional (2D) electron and hole systems confined to GaAs quantum wells and subjected to a one-dimensional, periodic density modulation. The modulation is achieved through the piezo-electric effect in GaAs as we fabricate a periodic, strain-inducing superlattice on the sample surface. Under varying perpendicular magnetic field, whenever the carriers' cyclotron orbit becomes commensurate with the modulation period, the magnetoresistance exhibits a minimum value. The resulting oscillations, known as the commensurability oscillations, directly measure the carriers' Fermi wave vector. Imposing a density modulation thus allows us to study the Fermi contour properties of 2D electrons and holes near zero field, and composite fermions (CFs) near the half filling of the lowest Landau level, i.e., filling factor $\nu=1/2$.

The application of a parallel magnetic field ($B_{||}$) also features extensively in the Thesis. First, we use commensurability oscillations to capture the $B_{||}$-induced deformation and the eventual splitting of the Fermi contour of 2D electrons. We also deduce the scattering time anisotropy of hole-flux CFs whose Fermi contour is rendered anisotropic by $B_{||}$. Moreover, we study the anisotropic ($warped$) Fermi contour of 2D holes and hole-flux CFs in wide quantum well samples at $B_{||}=0$. The results provide evidence that CFs inherit Fermi contour properties from their zero-field counterparts.

We further investigate the fate of CFs near the bilayer quantum Hall states at $\nu=1$ and 1/2 induced by a large $B_{||}$. We observe that the commensurability features of CFs near $\nu=1$ are consistent with \textit{half} the total carrier density, implying that CFs prefer to stay in separate layers and show a two-component behavior. In contrast, close to $\nu=1/2$, CFs appear single-layer-like (single-component) as their commensurability features correspond to the \textit{total} density. This finding sheds light on the different nature of the interacting bilayer system at $\nu=1$ and 1/2.

Finally, we focus on the half filling of a higher Landau level, namely $\nu=7/2$, where $B_{||}$ induces an anisotropic stripe phase. We show that a minute external density modulation is sufficient to cause a reorientation of the stripe phase if its wavelength is comparable to the external modulation period.