A low-disorder, two-dimensional electron system (2DES) subjected to a large perpendicular magnetic field and cooled to very low temperatures provides a rich platform for studies of many-body quantum phases. The magnetic field quenches the electrons' kinetic energy and quantizes the energy into a set of Landau levels, allowing the Coulomb interaction to dominate. In excited Landau levels, the fine interplay between short- and long-range interactions stabilizes bubble phases, Wigner crystals with more than one electron per unit cell. Here we present the screening properties of bubble phases, probed via a simple capacitance technique where the 2DES is placed between a top and a bottom gate and the electric field penetrating through the 2DES is measured. The bubbles formed at very low temperatures screen the electric field poorly as they are pinned by the residual disorder potential, allowing a large electric field to reach the top gate. As the temperature is increased, the penetrating electric field decreases and, surprisingly, exhibits a pronounced minimum at a temperature that appears to coincide with the melting temperature of the bubble phase. We deduce a quantitative phase diagram for the transition from bubble to liquid phases for Landau level filling factors 4≤ν≤5.

A sufficiently large perpendicular magnetic field quenches the kinetic (Fermi) energy of an interacting two-dimensional (2D) system of fermions, making them susceptible to the formation of a Wigner solid (WS) phase in which the charged carriers organize themselves in a periodic array in order to minimize their Coulomb repulsion energy. In low-disorder 2D electron systems confined to modulation-doped GaAs heterostructures, signatures of a magnetic-field-induced WS appear at low temperatures and very small Landau level filling factors (ν≃1/5). In dilute GaAs 2D hole systems, on the other hand, thanks to the larger hole effective mass and the ensuing Landau level mixing, the WS forms at relatively higher fillings (ν≃1/3). Here we report our measurements of the fundamental temperature vs. filling phase diagram for the 2D holes' WS-liquid thermal melting. Moreover, via changing the 2D hole density, we also probe their Landau level mixing vs. filling WS-liquid quantum melting phase diagram. We find our data to be in good agreement with the results of very recent calculations, although intriguing subtleties remain.

We studied a bilayer system hosting two-dimensional electron systems (2DESs) in close proximity but isolated from one another by a thin barrier. One 2DES has low electron density and forms a Wigner solid (WS) at high magnetic fields. The other has much higher density and, in the same field, exhibits fractional quantum Hall states (FQHSs). The WS spectrum has resonances which are understood as pinning modes, oscillations of the WS within the residual disorder. We found the pinning mode frequencies of the WS are strongly affected by the FQHSs in the nearby layer. Analysis of the spectra indicates that the majority layer screens like a dielectric medium even when its Landau filling is ~1/2, at which the layer is essentially a composite fermion (CF) metal. Although the majority layer is only ~ one WS lattice constant away, a WS site only induces an image charge of ~0.1e in the CF metal.

One of the most fundamental and yet elusive collective phases of an interacting electron system is the quantum Wigner crystal (WC), an ordered array of electrons expected to form when the electrons' Coulomb repulsion energy eclipses their kinetic (Fermi) energy. In low-disorder, two-dimensional (2D) electron systems, the quantum WC is known to be favored at very low temperatures (T) and small Landau level filling factors (ν), near the termination of the fractional quantum Hall states. This WC phase exhibits an insulating behavior, reflecting its pinning by the small but finite disorder potential. An experimental determination of a T vs ν phase diagram for the melting of the WC, however, has proved to be challenging. Here we use capacitance measurements to probe the 2D WC through its effective screening as a function of T and ν. We find that, as expected, the screening efficiency of the pinned WC is very poor at very low T and improves at higher T once the WC melts. Surprisingly, however, rather than monotonically changing with increasing T, the screening efficiency shows a well-defined maximum at a T that is close to the previously reported melting temperature of the WC. Our experimental results suggest a new method to map out a T vs ν phase diagram of the magnetic-field-induced WC precisely.

One of the most fascinating ground states of an interacting electron system is the so-called Wigner crystal where the electrons, in order to minimize their repulsive Coulomb energy, form an ordered array. Here, we report measurements of the critical filling factor (nu(c)) below which a magnetic-field-induced, quantum Wigner crystal forms in a dilute, two-dimensional electron layer when a second, high-density electron layer is present in close proximity. The data reveal that the Wigner crystal forms at a significantly smaller nu(c) compared to the nu(c) (similar or equal to 0.20) in single-layer two-dimensional electron systems. The measured nu(c) exhibits a strong dependence on the interlayer distance, reflecting the interaction and screening from the adjacent, high-density layer.

Degenerate conduction-band minima, or "valleys", in materials such as Si, AlAs, graphene, and MoS2 allow them to host two-dimensional electron systems (2DESs) that can access a valley degree of freedom. These multivalley 2DESs present exciting opportunities for both pragmatic and fundamental research alike because not only are they a platform for valleytronic devices, but they also provide a tool to tune and investigate the properties of complex many-body ground states. Here, we report ultra-high-quality, modulation-doped AlAs quantum wells containing 2DESs that occupy two anisotropic valleys and have electron mobilities peaking at 2.4 x 10(6) cm(2) V-1 s(-1) at a density of 2.2 x 10(11) cm(-2). This is more than an order of magnitude improvement in mobility over previous results. The unprecedented quality of our samples is demonstrated by magneto-transport data that show high-order fractional quantum Hall minima up to the Landau level filling nu = 8/17, and even the elusive nu = 1/5 quantum Hall state.

An interacting bilayer electron system provides an extended platform to study electron-electron interaction beyond single layers. We report here experiments demonstrating that the layer densities of an asymmetric bilayer electron system oscillate as a function of perpendicular magnetic field that quantizes the energy levels. At intermediate fields, this interlayer charge transfer can be well explained by the alignment of the Landau levels in the two layers. At the highest fields where both layers reach the extreme quantum limit, however, there is an anomalous, enhanced charge transfer to the majority layer. Surprisingly, when the minority layer becomes extremely dilute, this charge transfer slows down as the electrons in the minority layer condense into a Wigner crystal. Furthermore, by examining the quantum capacitance of the dilute layer at high fields, the screening induced by the composite fermions in an adjacent layer is unveiled. The results highlight the influence of strong interaction in interlayer charge transfer in the regime of very high fields and low Landau level filling factors.

The two-dimensional electron system in an InAs quantum well has emerged as a prime candidate for hosting exotic quasiparticles with non-Abelian statistics such as Majorana fermions and parafermions. To attain its full promise, however, the electron system has to be clean enough to exhibit electron-electron interaction phenomena. Here, we report the observation of the fractional quantum Hall effect in a very low disorder InAs quantum well with a well width of 24 nm, containing a two-dimensional electron system with a density $n=7.8\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ and low-temperature mobility $1.8\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{2}$/Vs. At a temperature of $\ensuremath{\simeq}\phantom{\rule{0.16em}{0ex}}35$ mK and $B\ensuremath{\simeq}24$ T, we observe a deep minimum in the longitudinal resistance, accompanied by a nearly quantized Hall plateau at a Landau level filling factor $\ensuremath{\nu}=4/3$.

When the kinetic energy of a collection of interacting two-dimensional (2D) electrons is quenched at very high magnetic fields so that the Coulomb repulsion dominates, the electrons are expected to condense into an ordered array, forming a quantum Wigner crystal (WC). Although this exotic state has long been suspected in high-mobility 2D electron systems at very low Landau level fillings (ν≪1), its direct observation has been elusive. Here we present a new technique and experimental results directly probing the magnetic-field-induced WC. We measure the magnetoresistance of a bilayer electron system where one layer has a very low density and is in the WC regime (ν≪1), while the other ("probe") layer is near ν=1/2 and hosts a sea of composite fermions (CFs). The data exhibit commensurability oscillations in the magnetoresistance of the CF layer, induced by the periodic potential of WC electrons in the other layer, and provide a unique, direct glimpse at the symmetry of the WC, its lattice constant, and melting. They also demonstrate a striking example of how one can probe an exotic many-body state of 2D electrons using equally exotic quasiparticles of another many-body state.

When the kinetic energy of a collection of interacting two-dimensional (2D) electrons is quenched at very high magnetic fields so that the Coulomb repulsion dominates, the electrons are expected to condense into an ordered array, forming a quantum Wigner crystal (WC). Although this exotic state has long been suspected in high-mobility 2D electron systems at very low Landau level fillings (ν << 1), its direct observation has been elusive. Here we present a new technique and experimental results that directly probe the magnetic-field-induced WC. We measure the magneto-resistance of a bilayer electron system with unequal layer densities at high magnetic fields. One layer has a very low density and is in the WC regime (ν << 1), while the other (”probe”) layer is near ν = 1/2 and hosts a sea of composite fermions, quasi-particles formed by attaching two flux-quanta to each interacting electron. The composite fermions feel the periodic electric potential of the WC in the other layer and exhibit magneto-resistance maxima whenever their cyclotron orbit encircles certain integer number of the WC lattice points. The positions of the maxima reveal that the WC has a triangular lattice and yield a direct measure of its lattice constant. Our results provide a striking example of how one can probe an exotic many-body state of 2D electrons using equally exotic quasi-particles of another many-body state.

Magnetotransport measurements on two-dimensional electrons confined to wide GaAs quantum wells reveal a remarkable evolution of the ground state at filling factor ν=1/2 as we tilt the sample in the magnetic field. Starting with a compressible state at zero tilt angle, a strong ν=1/2 fractional quantum Hall state appears at intermediate angles. At higher angles an insulating phase surrounds this state and eventually engulfs it at the highest angles. This evolution occurs because the parallel component of the field renders the charge distribution increasingly bilayer-like.

Magnetotransport measurements on two-dimensional electrons confined to wide GaAs quantum wells reveal a remarkable evolution of the ground state at filling factor $\nu=1/2$ as we tilt the sample in the magnetic field. Starting with a compressible state at zero tilt angle, a strong $\nu=1/2$ fractional quantum Hall state appears at intermediate angles. At higher angles an insulating phase surrounds this state and eventually engulfs it at the highest angles. This evolution occurs because the parallel component of the field renders the charge distribution increasingly bilayer-like.