Collapse of the fractional quantum Hall effect in an electron system with large layer thickness

Fractional Quantum Hall Effect Energy Gaps: Role of Electron Layer Thickness

The fractional quantum Hall effect stands as a quintessential manifestation of an interacting two-dimensional electron system. One of the fractional quantum Hall effect's most fundamental characteristics is the energy gap separating the incompressible ground state from its excitations. Yet, despite nearly four decades of investigations, a quantitative agreement between the theoretically calculated and experimentally measured energy gaps is lacking. Here we report a systematic experimental study that incorporates very high-quality two-dimensional electron systems confined to GaAs quantum wells with fixed density and varying well widths. The results demonstrate a clear decrease of the energy gap as the electron layer is made thicker and the short-range component of the Coulomb interaction is weakened. We also provide a quantitative comparison between the measured energy gaps and the available theoretical calculations that takes into account the role of finite layer thickness and Landau level mixing. All the measured energy gaps fall below the calculations, but as the electron layer thickness increases, the results of experiments and calculations come closer. Accounting for the role of disorder in a phenomenological manner, we find better overall agreement between the measured and calculated energy gaps, although some puzzling discrepancies remain.

Fractional quantum Hall effect at ν=1/2 in hole systems confined to GaAs quantum wells

We observe the fractional quantum Hall effect (FQHE) at the even-denominator Landau level filling factor ν=1/2 in two-dimensional hole systems confined to GaAs quantum wells of width 30 to 50 nm and having bilayerlike charge distributions. The ν=1/2 FQHE is stable when the charge distribution is symmetric and only in a range of intermediate densities, qualitatively similar to what is seen in two-dimensional electron systems confined to approximately twice wider GaAs quantum wells. Despite the complexity of the hole Landau level structure, originating from the coexistence and mixing of the heavy- and light-hole states, we find the hole ν=1/2 FQHE to be consistent with a two-component, Halperin-Laughlin (Ψ331) state.

Ferromagnetic fractional quantum Hall states in a valley-degenerate two-dimensional electron system

We study a two-dimensional electron system where the electrons occupy two conduction band valleys with anisotropic Fermi contours and strain-tunable occupation. We observe persistent quantum Hall states at filling factors nu=1/3 and 5/3 even at zero strain when the two valleys are degenerate. This is reminiscent of the quantum Hall ferromagnet formed at nu=1 in the same system at zero strain. In the absence of a theory for a system with anisotropic valleys, we compare the energy gaps measured at nu=1/3 and 5/3 to the available theory developed for single-valley, two-spin systems, and find that the gaps and their rates of rise with strain are much smaller than predicted.

New Quantum Structures

Structures in which electrons are confined to move in two dimensions (quantum wells) have led to new physical discoveries and technological applications. Modification of these structures to confine the electrons to one dimension (quantum wires) or release them in the third dimension, are predicted to lead to new electrical and optical properties. This article discusses techniques to make quantum wires, and quantum wells of controlled size and shape, from compound semiconductor materials, and describes some of the properties of these structures.