Probing the microscopic structure of the stripe phase at filling factor 5/2

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.

Dynamic ordering transitions in charged solid

The phenomenon of group motion is common in nature, ranging from the schools of fish, birds and insects, to avalanches, landslides and sand drift. If we treat objects as collectively moving particles, such phenomena can be studied from a physical point of view, and the research on many-body systems has proved that marvelous effects can arise from the simplest individuals. The motion of numerous individuals presents different dynamic phases related to the ordering of the system. However, it is usually difficult to study the dynamic ordering and its transitions through experiments. Electron bubble states formed in a two-dimensional electron gas, as a type of electron solids, can be driven by an external electric field and provide a platform to study the dynamic collective behaviors. Here, we demonstrate that the noise spectrum is a powerful method to investigate the dynamics of bubble states. We observed not only the phenomena of dynamically ordered and disordered structures, but also unexpected alternations between them. Our results show that a dissipative system can convert between chaotic structures and ordered structures when tuning global parameters, which is concealed in conventional transport measurements of resistance or conductance. Moreover, charging the objects to study the electrical noise spectrum in collective motions can be an additional approach to revealing dynamic ordering transitions.

Domain Textures in the Fractional Quantum Hall Effect

Impacts of domain textures on low-lying neutral excitations in the bulk of fractional quantum Hall effect (FQHE) systems are probed by resonant inelastic light scattering. We demonstrate that large domains of quantum fluids support long-wavelength neutral collective excitations with well-defined wave vector (momentum) dispersion that could be interpreted by theories for uniform phases. Access to dispersive low-lying neutral collective modes in large domains of FQHE fluids such as long wavelength magnetorotons at filling factor v=1/3 offer significant experimental access to strong electron correlation physics in the FQHE.

Observation of new plasmons in the fractional quantum Hall effect: Interplay of topological and nematic orders

Collective modes of exotic quantum fluids reveal underlying physical mechanisms responsible for emergent quantum states. We observe unexpected new collective modes in the fractional quantum Hall (FQH) regime: intra-Landau-level plasmons measured by resonant inelastic light scattering. The plasmons herald rotational-symmetry-breaking (nematic) phases in the second Landau level and uncover the nature of long-range translational invariance in these phases. The intricate dependence of plasmon features on filling factor provides insights on interplays between topological quantum Hall order and nematic electronic liquid crystal phases. A marked intensity minimum in the plasmon spectrum at Landau level filling factor v = 5/2 strongly suggests that this paired state, which may support non-Abelian excitations, overwhelms competing nematic phases, unveiling the robustness of the 5/2 superfluid state for small tilt angles. At v = 7/3, a sharp and strong plasmon peak that links to emerging macroscopic coherence supports the proposed model of a FQH nematic state.

Pomeranchuk Instability of Composite Fermi Liquids

Nematicity in quantum Hall systems has been experimentally well established at excited Landau levels. The mechanism of the symmetry breaking, however, is still unknown. Pomeranchuk instability of Fermi liquid parameter F_{ℓ}≤-1 in the angular momentum ℓ=2 channel has been argued to be the relevant mechanism, yet there are no definitive theoretical proofs. Here we calculate, using the variational Monte Carlo technique, Fermi liquid parameters F_{ℓ} of the composite fermion Fermi liquid with a finite layer width. We consider F_{ℓ} in different Landau levels n=0, 1, 2 as a function of layer width parameter η. We find that unlike the lowest Landau level, which shows no sign of Pomeranchuk instability, higher Landau levels show nematic instability below critical values of η. Furthermore, the critical value η_{c} is higher for the n=2 Landau level, which is consistent with observation of nematic order in ambient conditions only in the n=2 Landau levels. The picture emerging from our work is that approaching the true 2D limit brings half-filled higher Landau-level systems to the brink of nematic Pomeranchuk instability.

Scanning nuclear resonance imaging of a hyperfine-coupled quantum Hall system

Nuclear resonance (NR) is widely used to detect and characterise nuclear spin polarisation and conduction electron spin polarisation coupled by a hyperfine interaction. While the macroscopic aspects of such hyperfine-coupled systems have been addressed in most relevant studies, the essential role of local variation in both types of spin polarisation has been indicated in 2D semiconductor systems. In this study, we apply a recently developed local and highly sensitive NR based on a scanning probe to a hyperfine-coupled quantum Hall (QH) system in a 2D electron gas subject to a strong magnetic field. We succeed in imaging the NR intensity and Knight shift, uncovering the spatial distribution of both the nuclear and electron spin polarisation. The results reveal the microscopic origin of the nonequilibrium QH phenomena, and highlight the potential use of our technique in microscopic studies on various electron spin systems as well as their correlations with nuclear spins.

A review of the quantum Hall effects in MgZnO/ZnO heterostructures

This review visits recent experimental efforts on high mobility two-dimensional electron systems (2DES) hosted at the Mg _x Zn[Formula: see text]O/ZnO heterointerface. We begin with the growth of these samples, and highlight the key characteristics of ozone-assisted molecular beam epitaxy required for their production. The transport characteristics of these structures are found to rival that of traditional semiconductor material systems, as signified by the high electron mobility ([Formula: see text] cm² Vs^-1) and rich quantum Hall features. Owing to a large effective mass and small dielectric constant, interaction effects are an order of magnitude stronger in comparison with the well studied GaAs-based 2DES. The strong correlation physics results in robust Fermi-liquid renormalization of the effective mass and spin susceptibility of carriers, which in turn dictates the parameter space for the quantum Hall effect. Finally, we explore the quantum Hall effect with a particular emphasis on the spin degree of freedom of carriers, and how their large spin splitting allows control of the ground states encountered at ultra-low temperatures within the fractional quantum Hall regime. We discuss in detail the physics of even-denominator fractional quantum Hall states, whose observation and underlying character remain elusive and exotic.

Competing Charge Density Waves Probed by Nonlinear Transport and Noise in the Second and Third Landau Levels

Charge density waves (CDWs) in the second and third Landau levels (LLs) are investigated by both nonlinear electronic transport and noise. The use of a Corbino geometry ensures that only bulk properties are probed, with no contribution from edge states. Sliding transport of CDWs is revealed by narrow band noise in reentrant quantum Hall states R2a and R2c of the second LL, as well as in pinned CDWs of the third LL. Competition between various phases-stripe, pinned CDW, or fractional quantum Hall liquid-in both LLs are clearly revealed by combining noise data with maps of conductivity versus magnetic field and bias voltage.

Current Flow in the Bubble and Stripe Phases

The spontaneous ordering of spins and charges in geometric patterns is currently under scrutiny in a number of different material systems. A topic of particular interest is the interaction of such ordered phases with itinerant electrons driven by an externally imposed current. It not only provides important information on the charge ordering itself but potentially also allows manipulating the shape and symmetry of the underlying pattern if current flow is strong enough. Unfortunately, conventional transport methods probing the macroscopic resistance suffer from the fact that the voltage drop along the sample edges provides only indirect information on the bulk properties because a complex current distribution is elicited by the inhomogeneous ground state. Here, we promote the use of surface acoustic waves to study these broken-symmetry phases and specifically address the bubble and stripe phases emerging in high-quality two-dimensional electron systems in GaAs/AlGaAs heterostructures as prototypical examples. When driving a unidirectional current, we find a surprising discrepancy between the sound propagation probing the bulk of the sample and the voltage drop along the sample edges. Our results prove that the current-induced modifications observed in resistive transport measurements are in fact a local phenomenon only, leaving the majority of the sample unaltered. More generally, our findings shed new light on the extent to which these ordered electron phases are impacted by an external current and underline the intrinsic advantages of acoustic measurements for the study of such inhomogeneous phases.

Reorientation of the Stripe Phase of 2D Electrons by a Minute Density Modulation

Interacting two-dimensional electrons confined in a GaAs quantum well exhibit isotropic transport when the Fermi level resides in the first excited (N=1) Landau level. Adding an in-plane magnetic field (B_{||}) typically leads to an anisotropic, stripelike (nematic) phase of electrons with the stripes oriented perpendicular to the B_{||} direction. Our experimental data reveal how a periodic density modulation, induced by a surface strain grating from strips of negative electron-beam resist, competes against the B_{||}-induced orientational order of the stripe phase. Even a minute (<0.25%) density modulation is sufficient to reorient the stripes along the direction of the surface grating.

Disorder-Induced Stabilization of the Quantum Hall Ferromagnet

We report on an absolute measurement of the electronic spin polarization of the ν=1 integer quantum Hall state. The spin polarization is extracted in the vicinity of ν=1 (including at exactly ν=1) via resistive NMR experiments performed at different magnetic fields (electron densities) and Zeeman energy configurations. At the lowest magnetic fields, the polarization is found to be complete in a narrow region around ν=1. Increasing the magnetic field (electron density) induces a significant depolarization of the system, which we attribute to a transition between the quantum Hall ferromagnet and the Skyrmion glass phase theoretically expected as the ratio between Coulomb interactions and disorder is increased. These observations account for the fragility of the polarization previously observed in high mobility 2D electron gas and experimentally demonstrate the existence of an optimal amount of disorder to stabilize the ferromagnetic state.

Localized NMR Mediated by Electrical-Field-Induced Domain Wall Oscillation in Quantum-Hall-Ferromagnet Nanowire

We present fractional quantum Hall domain walls confined in a gate-defined wire structure. Our experiments utilize spatial oscillation of domain walls driven by radio frequency electric fields to cause nuclear magnetic resonance. The resulting spectra are discussed in terms of both large quadrupole fields created around the wire and hyperfine fields associated with the oscillating domain walls. This provides the experimental fact that the domain walls survive near the confined geometry despite of potential deformation, by which a localized magnetic resonance is allowed in electrical means.

Optical Emission Spectroscopy Study of Competing Phases of Electrons in the Second Landau Level

Quantum phases of electrons in the filling factor range 2≤ν≤3 are probed by the weak optical emission from the partially populated second Landau level and spin wave measurements. Observations of optical emission include a multiplet of sharp peaks that exhibit a strong filling factor dependence. Spin wave measurements by resonant inelastic light scattering probe breaking of spin rotational invariance and are used to link this optical emission with collective phases of electrons. A remarkably rapid interplay between emission peak intensities manifests phase competition in the second Landau level.

W line shape in the resistively detected nuclear magnetic resonance

The resistively detected nuclear magnetic resonance (RDNMR) performed on a two-dimensional electron gas is known to exhibit a peculiar 'dispersive' line shape at some filling factors, especially around ν = 1. Here, we study in detail the inversion of the dispersive line shape as a function of the filling factor from ν = 1 to 2/3. The RDNMR spectra show a new characteristic W line shape in the longitudinal resistance, whereas dispersive lines detected in the Hall resistance remain unchanged. This W resonance, like the dispersive line, can be fitted correctly by a model of two independent response functions, which are the signatures of polarized and unpolarized electronic sub-systems.

Electron spin polarization by isospin ordering in correlated two-layer quantum Hall systems

Enhancement of the electron spin polarization in a correlated two-layer, two-dimensional electron system at a total Landau level filling factor of 1 is reported. Using resistively detected nuclear magnetic resonance, we demonstrate that the electron spin polarization of two closely spaced two-dimensional electron systems becomes maximized when interlayer Coulomb correlations establish spontaneous isospin ferromagnetic order. This correlation-driven polarization dominates over the spin polarizations of competing single-layer fractional quantum Hall states under electron density imbalances.