Phase diagram of the two-component fractional quantum Hall effect

Origin of Pinning Disorder in Magnetic-Field-Induced Wigner Solids

At low Landau level filling factors (ν), Wigner solid phases of two-dimensional electron systems in GaAs are pinned by disorder and exhibit a pinning mode, whose frequency is a measure of the disorder that pins the Wigner solid. Despite numerous studies spanning the past three decades, the origin of the disorder that causes the pinning and determines the pinning mode frequency remains unknown. Here, we present a study of the pinning mode resonance in the low-ν Wigner solid phases of a series of ultralow-disorder GaAs quantum wells which are similar except for their varying well widths d. The pinning mode frequencies f_{p} decrease strongly as d increases, with the widest well exhibiting f_{p} as low as ≃35  MHz. The amount of reduction of f_{p} with increasing d can be explained remarkably well by tails of the wave function impinging into the alloy-disordered Al_{x}Ga_{1-x}As barriers that contain the electrons. However, it is imperative that the model for the confinement and wave function includes the Coulomb repulsion in the growth direction between the electrons as they occupy the quantum well.

Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids

We investigate the disorder-driven phase transition from a fractional quantum Hall state to an Anderson insulator using quantum entanglement methods. We find that the transition is signaled by a sharp increase in the sensitivity of a suitably averaged entanglement entropy with respect to disorder-the magnitude of its disorder derivative appears to diverge in the thermodynamic limit. We also study the level statistics of the entanglement spectrum as a function of disorder. However, unlike the dramatic phase-transition signal in the entanglement entropy derivative, we find a gradual reduction of level repulsion only deep in the Anderson insulating phase.

Fractionally charged skyrmions in fractional quantum Hall effect

The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeeman energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region.

It is predicted that fractionally charged skyrmions, topologically protected vortex-like spin configurations, may exist in systems exhibiting fractional quantum Hall states. Here, the authors demonstrate the existence of such objects in GaAs single quantum wells.

Luttinger Theorem for the Strongly Correlated Fermi Liquid of Composite Fermions

While an ordinary Fermi sea is perturbatively robust to interactions, the paradigmatic composite-fermion (CF) Fermi sea arises as a nonperturbative consequence of emergent gauge fields in a system where there was no Fermi sea to begin with. A mean-field picture suggests two Fermi seas, of composite fermions made from electrons or holes in the lowest Landau level, which occupy different areas away from half filling and thus appear to represent distinct states. Using the microscopic theory of composite fermions, which satisfies particle-hole symmetry in the lowest Landau level to an excellent approximation, we show that the Fermi wave vectors at filling factors ν and 1-ν are equal when expressed in units of the inverse magnetic length, and are generally consistent with the experimental findings of Kamburov et al. [Phys. Rev. Lett. 113, 196801 (2014)]. Our calculations suggest that the area of the CF Fermi sea may slightly violate the Luttinger area rule.

Microwave spectroscopy of the low-filling-factor bilayer electron solid in a wide quantum well

At the low Landau filling factor termination of the fractional quantum Hall effect series, two-dimensional electron systems exhibit an insulating phase that is understood as a form of pinned Wigner solid. Here we use microwave spectroscopy to probe the transition to the insulator for a wide quantum well sample that can support single-layer or bilayer states depending on its overall carrier density. We find that the insulator exhibits a resonance which is characteristic of a bilayer solid. The resonance also reveals a pair of transitions within the solid, which are not accessible to dc transport measurements. As density is biased deeper into the bilayer solid regime, the resonance grows in specific intensity, and the transitions within the insulator disappear. These behaviours are suggestive of a picture of the insulating phase as an emulsion of liquid and solid components.

In 2D electron gases, insulating behaviour at low fractional quantum Hall filling factors is understood by the formation of an electronic Wigner solid. Here, the authors use microwave spectroscopy to evidence an electron liquid–solid mixed phase in bilayer states of GaAs/AlGaAs wide quantum wells.

Enigmatic 4/11 state: a prototype for unconventional fractional quantum Hall effect

The origin of the fractional quantum Hall effect (FQHE) at 4/11 and 5/13 has remained controversial. We make a compelling case that the FQHE is possible here for fully spin polarized composite fermions, but with an unconventional underlying physics. Thanks to a rather unusual interaction between composite fermions, the FQHE here results from the suppression of pairs with a relative angular momentum of three rather than one, confirming the exotic mechanism proposed by Wójs, Yi, and Quinn [Phys. Rev. B 69, 205322 (2004)]. We predict that the 4/11 state reported a decade ago by Pan et al. [Phys. Rev. Lett. 90, 016801 (2003)] is a conventional partially spin polarized FQHE of composite fermions, and we estimate the Zeeman energy where a phase transition into the unconventional fully spin polarized state will occur.