Experimental studies of the fractional quantum Hall effect and the Wigner solids

This Ph.D. thesis is composed of two parts: the first part is concerned with electron transport in the higher Landau levels (LL) in a two-dimensional electron system (2DES); the second part is focused on the Wigner Crystal in two-dimensional hole system (2DHS). We report on the high Landau-level (LL) magnetotransport (including tilt-fields) in a high purity modulation-doped GaAs/AlGaAs quantum Well (QW) with twice the electron density of standard samples. A quantized nu = 5/2 Hall plateau is observed at B ∼ 10 T, with an activation gap Delta 5/2 ∼ 125 mK; the plateau can persist up to a ∼ 25° tilt-field. This finding is discussed in the context of proposed Moore-Read Pfaffian (Pf) wave function (or Anti-Pfaffian (APf)) being possible ground states at 5/2. The tilted-fields induce background resistance at 5/2 that could be either isotropic or anisotropic, depending simply on in-plane magnetic field orientation with respect to the GaAs crystalline axis. Such data indicate a substantial coupling between the 5/2 collective phases and the GaAs crystal. In a high hole density (p = 2.0x1011 cm-2), high mobility (micro = lx106 cm2/V s) 20 nm wide GaAs/AlGaAs quantum well, we observed reentrant insulating phases around Landau-level filling factor nu = 1/5 and nu = 2/9 at very high magnetic fields. Previous experiments reported the reentrant insulating phases around the nu = 1/3 FQHE state in dilute 2DHS and around the nu = 1/5 FQH liquid in 2DES, respectively. It is rather interesting that our experimental results in the hole system look like the former electron results at low fields. Our T-dependent conductance measurements exhibit rather intriguing behaviors: the Arrhenius plot of the conductance (vs. 1/T) suggests a certain energy scale in the melting procedure of the solid phase. We also observed a large threshold for electric field in the differential conductance measurements, which is an indication of the sliding motion of Wigner solid driven by an external field. These phenomena are related to the depinning of Wigner solids under various magnetic fields. A possible explanation is that the effective pinning potential increases with the magnetic fields