Observation of an Anisotropic Wigner Crystal

Highly Anisotropic Even-Denominator Fractional Quantum Hall State in an Orbitally Coupled Half-Filled Landau Level

The even-denominator fractional quantum Hall states (FQHSs) in half-filled Landau levels are generally believed to host non-Abelian quasiparticles and be of potential use in topological quantum computing. Of particular interest is the competition and interplay between the even-denominator FQHSs and other ground states, such as anisotropic phases and composite fermion Fermi seas. Here, we report the observation of an even-denominator fractional quantum Hall state with highly anisotropic in-plane transport coefficients at Landau level filling factor ν=3/2. We observe this state in an ultra-high-quality GaAs two-dimensional hole system when a large in-plane magnetic field is applied. By increasing the in-plane field, we observe a sharp transition from an isotropic composite fermion Fermi sea to an anisotropic even-denominator FQHS. Our data and calculations suggest that a unique feature of two-dimensional holes, namely the coupling between heavy-hole and light-hole states, combines different orbital components in the wave function of one Landau level, and leads to the emergence of a highly anisotropic even-denominator fractional quantum Hall state. Our results demonstrate that the GaAs two-dimensional hole system is a unique platform for the exploration of exotic, many-body ground states.

Robust Quantum Hall Ferromagnetism near a Gate-Tuned ν=1 Landau Level Crossing

In a low-disorder two-dimensional electron system, when two Landau levels of opposite spin or pseudospin cross at the Fermi level, the dominance of the exchange energy can lead to a ferromagnetic, quantum Hall ground state whose gap is determined by the exchange energy and has skyrmions as its excitations. This is normally achieved via applying either hydrostatic pressure or uniaxial strain. We study here a very high-quality, low-density, two-dimensional hole system, confined to a 30-nm-wide (001) GaAs quantum well, in which the two lowest-energy Landau levels can be gate tuned to cross at and near filling factor ν=1. As we tune the field position of the crossing from one side of ν=1 to the other by changing the hole density, the energy gap for the quantum Hall state at ν=1 remains exceptionally large, and only shows a small dip near the crossing. The gap overall follows a sqrt[B] dependence, expected for the exchange energy. Our data are consistent with a robust quantum Hall ferromagnet as the ground state.

Anisotropic Two-Dimensional Disordered Wigner Solid

The interplay between the Fermi sea anisotropy, electron-electron interaction, and localization phenomena can give rise to exotic many-body phases. An exciting example is an anisotropic two-dimensional (2D) Wigner solid (WS), where electrons form an ordered array with an anisotropic lattice structure. Such a state has eluded experiments up to now as its realization is extremely demanding: First, a WS entails very low densities where the Coulomb interaction dominates over the kinetic (Fermi) energy. Attaining such low densities while keeping the disorder low is very challenging. Second, the low-density requirement has to be fulfilled in a material that hosts an anisotropic Fermi sea. Here, we report transport measurements in a clean (low-disorder) 2D electron system with anisotropic effective mass and Fermi sea. The data reveal that at extremely low electron densities, when the r_{s} parameter, the ratio of the Coulomb to the Fermi energy, exceeds ≃38, the current-voltage characteristics become strongly nonlinear at small dc biases. Several key features of the nonlinear characteristics, including their anisotropic voltage thresholds, are consistent with the formation of a disordered, anisotropic WS pinned by the ubiquitous disorder potential.

A Short Review of One-Dimensional Wigner Crystallization

The simplest possible structural transition that an electronic system can undergo is Wigner crystallization. The aim of this short review is to discuss the main aspects of three recent experimets on the one-dimensional Wigner molecule, starting from scratch. To achieve this task, the Luttinger liquid theory of weakly and strongly interacting fermions is briefly addressed, together with the basic properties of carbon nanotubes that are required. Then, the most relevant properties of Wigner molecules are addressed, and finally the experiments are described. The main physical points that are addressed are the suppression of the energy scales related to the spin and isospin sectors of the Hamiltonian, and the peculiar structure that the electron density acquires in the Wigner molecule regime.

Coherent two-dimensional Fourier transform spectroscopy using a 25 Tesla resistive magnet

We performed nonlinear optical two-dimensional Fourier transform spectroscopy measurements using an optical resistive high-field magnet on GaAs quantum wells. Magnetic fields up to 25 T can be achieved using the split helix resistive magnet. Two-dimensional spectroscopy measurements based on the coherent four-wave mixing signal require phase stability. Therefore, these measurements are difficult to perform in environments prone to mechanical vibrations. Large resistive magnets use extensive quantities of cooling water, which causes mechanical vibrations, making two-dimensional Fourier transform spectroscopy very challenging. Here, we report on the strategies we used to overcome these challenges and maintain the required phase-stability throughout the measurement. A self-contained portable platform was used to set up the experiments within the time frame provided by a user facility. Furthermore, this platform was floated above the optical table in order to isolate it from vibrations originating from the resistive magnet. Finally, we present two-dimensional Fourier transform spectra obtained from GaAs quantum wells at magnetic fields up to 25 T and demonstrate the utility of this technique in providing important details, which are obscured in one dimensional spectroscopy.

Geometric Resonance of Composite Fermions near Bilayer Quantum Hall States

Via the application of a parallel magnetic field, we induce a single-layer to bilayer transition in two-dimensional electron systems confined to wide GaAs quantum wells and study the geometric resonance of composite fermions (CFs) with a periodic density modulation in our samples. The measurements reveal that CFs exist close to bilayer quantum Hall states, formed at Landau level filling factors ν=1 and 1/2. Near ν=1, the geometric resonance features are consistent with half the total electron density in the bilayer system, implying that CFs prefer to stay in separate layers and exhibit a two-component behavior. In contrast, close to ν=1/2, CFs appear single-layer-like (single component) as their resonance features correspond to the total density.