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What are the ground states of an interacting, low-density electron system? In the absence of disorder, it has long been expected that as the electron density is lowered, the exchange energy gained by aligning the electron spins should exceed the enhancement in the kinetic (Fermi) energy, leading to a (Bloch) ferromagnetic transition. At even lower densities, another transition to a (Wigner) solid, an ordered array of electrons, should occur. Experimental access to these regimes, however, has been limited because of the absence of a material platform that supports an electron system with very high quality (low disorder) and low density simultaneously. Here we explore the ground states of interacting electrons in an exceptionally clean, two-dimensional electron system confined to a modulation-doped AlAs quantum well. The large electron effective mass in this system allows us to reach very large values of the interaction parameter [Formula: see text] , defined as the ratio of the Coulomb to Fermi energies. As we lower the electron density via gate bias, we find a sequence of phases, qualitatively consistent with the above scenario: a paramagnetic phase at large densities, a spontaneous transition to a ferromagnetic state when [Formula: see text] surpasses 35, and then a phase with strongly nonlinear current-voltage characteristics, suggestive of a pinned Wigner solid, when [Formula: see text] exceeds [Formula: see text]. However, our sample makes a transition to an insulating state at [Formula: see text] , preceding the onset of the spontaneous ferromagnetism, implying that besides interaction, the role of disorder must also be taken into account in understanding the different phases of a realistic dilute electron system.

In 1929, Felix Bloch suggested that the paramagnetic Fermi sea of electrons should make a spontaneous transition to a fully magnetized state at very low densities, because the exchange energy gained by aligning the spins exceeds the enhancement in the kinetic energy1. However, experimental realizations of this effect have been hard to implement. Here, we report the observation of an abrupt, interaction-driven transition to full magnetization, highly reminiscent of Bloch ferromagnetism. Our platform utilizes the two-dimensional Fermi sea of composite fermions near half-filling of the lowest Landau level. We measure the Fermi wavevector—which directly provides the spin polarization—and observe a sudden transition from a partially spin-polarized to a fully spin-polarized ground state as we lower the density of the composite fermions. Our theoretical calculations that take Landau level mixing into account provide a semi-quantitative account of this phenomenon. Composite fermions can be tuned to very low effective density in a clean two-dimensional electron gas, which allows the formation of a Bloch ferromagnet.

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., 11 pages, 4 figures, and Supplemental Material

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, as a function of Landau level filling factor (\ensuremath{\nu}) and temperature, for the transition from the bubble to liquid phases for $4\ensuremath{\le}\ensuremath{\nu}\ensuremath{\le}5$.

Domain walls in fractional quantum Hall ferromagnets are gapless helical one-dimensional channels formed at the boundaries of topologically distinct quantum Hall (QH) liquids. Na\"{i}vely, these helical domain walls (hDWs) constitute two counter-propagating chiral states with opposite spins. Coupled to an s-wave superconductor, helical channels are expected to lead to topological superconductivity with high order non-Abelian excitations. Here we investigate transport properties of hDWs in the $\nu=2/3$ fractional QH regime. Experimentally we found that current carried by hDWs is substantially smaller than the prediction of the na\"{i}ve model. Luttinger liquid theory of the system reveals redistribution of currents between quasiparticle charge, spin and neutral modes, and predicts the reduction of the hDW current. Inclusion of spin-non-conserving tunneling processes reconciles theory with experiment. The theory confirms emergence of spin modes required for the formation of fractional topological superconductivity., Comment: 26 pages, 8 figures

Anomalous nematic states, recently discovered in ultraclean two-dimensional electron gas, emerge from quantum Hall stripe phases upon further cooling. These states are hallmarked by a local minimum (maximum) in the hard (easy) longitudinal resistance and by an incipient plateau in the Hall resistance in nearly half-filled Landau levels. Here, we demonstrate that a modest in-plane magnetic field, applied either along $\left < 110 \right >$ or $\left < 1\bar10 \right >$ crystal axis of GaAs, destroys anomalous nematic states and restores quantum Hall stripe phases aligned along their native $\left < 110 \right >$ direction. These findings confirm that anomalous nematic states are distinct from other ground states and will assist future theories to identify their origin., 5 pages, 4 figures

Even-denominator fractional quantum Hall (FQH) states, such as 5/2 and 7/2, have been well known in a two-dimensional electron gas (2DEG) for decades and are still investigated as candidates of non-Abelian statistics. In this paper, we present the observation of a 3/2 FQH plateau in a single-layer 2DEG with lateral confinement at a bulk filling factor of 5/3. The 3/2 FQH plateau is quantized at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\frac{h}{{e^2}}} \right)/\left( {\frac{3}{2}} \right)$$\end{document}he2∕32 within 0.02%, and can survive up to 300 mK. This even-denominator FQH plateau may imply intriguing edge structure and excitation in FQH system with lateral confinement. The observations in this work demonstrate that understanding the effect of the lateral confinement on the many-body system is critical in the pursuit of important theoretical proposals involving edge physics, such as the demonstration of non-Abelian statistics and the realization of braiding for fault-tolerant quantum computation., Fractional quantum Hall states in 2D electron gases arise due to strong electron-electron interactions, which makes a general theoretical understanding difficult. Fu et al. present data showing the ν = 5/3 quantum Hall state has a 3/2 plateau in the diagonal resistance that has not been captured by existing models.

We report complex magnetotransport patterns of the $\ensuremath{\nu}=1$ integer quantum Hall state in a GaAs/AlGaAs sample from the newest generation with a record high electron mobility. The reentrant integer quantum Hall effect in the flanks of the $\ensuremath{\nu}=1$ plateau indicates the formation of the integer quantum Hall Wigner solid, a collective insulator. Moreover, at a fixed filling factor, the longitudinal resistance versus temperature in the region of the integer quantum Hall Wigner solid exhibits a sharp peak. Such sharp peaks in the longitudinal resistance versus temperature so far were only detected for bubble phases forming in high Landau levels but were absent in the region of the Anderson insulator. We suggest that in samples of sufficiently low disorder, sharp peaks in the longitudinal resistance versus temperature traces are universal transport signatures of all isotropic electron solids that form in the flanks of integer quantum Hall plateaus. We discuss possible origins of these sharp resistance peaks and we draw a stability diagram for the insulating phases in the $\ensuremath{\nu}\ensuremath{-}T$ phase space.

Flat bands near M points in the Brillouin zone are key features of honeycomb symmetry in artificial graphene (AG) where electrons may condense into novel correlated phases. Here we report the observation of van Hove singularity doublet of AG in GaAs quantum well transistors, which presents the evidence of flat bands in semiconductor AG. Two emerging peaks in photoluminescence spectra tuned by backgate voltages probe the singularity doublet of AG flat bands, and demonstrate their accessibility to the Fermi level. As the Fermi level crosses the doublet, the spectra display dramatic stability against electron density, indicating interplays between electron-electron interactions and honeycomb symmetry. Our results provide a new flexible platform to explore intriguing flat band physics., 11 pages, 4 figures, and Supplementary Material

A central goal of condensed-matter physics is to understand how the diverse electronic and optical properties of crystalline materials emerge from the wavelike motion of electrons through periodically arranged atoms. However, more than 90 years after Bloch derived the functional forms of electronic waves in crystals [1] (now known as Bloch wavefunctions), rapid scattering processes have so far prevented their direct experimental reconstruction. In high-order sideband generation [2-9], electrons and holes generated in semiconductors by a near-infrared laser are accelerated to a high kinetic energy by a strong terahertz field, and recollide to emit near-infrared sidebands before they are scattered. Here we reconstruct the Bloch wavefunctions of two types of hole in gallium arsenide at wavelengths much longer than the spacing between atoms by experimentally measuring sideband polarizations and introducing an elegant theory that ties those polarizations to quantum interference between different recollision pathways. These Bloch wavefunctions are compactly visualized on the surface of a sphere. High-order sideband generation can, in principle, be observed from any direct-gap semiconductor or insulator. We thus expect that the method introduced here can be used to reconstruct low-energy Bloch wavefunctions in many of these materials, enabling important insights into the origin and engineering of the electronic and optical properties of condensed matter., Total: 27 pages, 12 figures. Main text 13 pages, 4 figures

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 their 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 noise spectrum is a powerful method to investigate the dynamics of bubble states. We observed not only the phenomena from 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 electrical noise spectrum in collective motions can be an additional approach to revealing dynamic ordering transitions., Comment: Main text (13 pages, 3 figures) + SI (12 pages, 11 figures)

The effect of spin-orbit interaction was studied in a high-quality $p$-AlGaAs/GaAs/AlGaAs structure with a square quantum well using acoustic methods. The structure grown on a GaAs (100) substrate was symmetrically doped with carbon on both sides of the quantum well. Shubnikov-de Haas-type oscillations of the ac conductance of two-dimensional holes were measured. At a low magnetic field $B, Comment: 6 pages, 7 figures

We study multielectron bubble phases in the $N=2$ and $N=3$ Landau levels in a high mobility GaAs/AlGaAs sample. We found that the longitudinal magnetoresistance versus temperature curves in the multielectron bubble region exhibit sharp peaks, irrespective of the Landau-level index. We associate these peaks with an enhanced scattering caused by thermally fluctuating domains of a bubble phase and a uniform uncorrelated electron liquid at the onset of the bubble phases. Within the $N=3$ Landau level, onset temperatures of three-electron and two- electron bubbles exhibit linear trends with respect to the filling factor; the onset temperatures of three-electron bubbles are systematically higher than those of two-electron bubbles. Furthermore, onset temperatures of the two-electron bubble phases across $N=2$ and $N=3$ Landau levels are similar, but exhibit an offset. This offset and the dominant nature of the three-electron bubbles in the $N=3$ Landau level reveals the role of the short-range part of the electron-electron interaction in the formation of the bubbles.

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.

Memory or transistor devices based on an electron's spin rather than its charge degree of freedom offer certain distinct advantages and comprise a cornerstone of spintronics. Recent years have witnessed the emergence of a new field, valleytronics, which seeks to exploit an electron's valley index rather than its spin. An important component in this quest would be the ability to control the valley index in a convenient fashion. Here we show that the valley polarization can be switched from zero to 1 by a small reduction in density, simply tuned by a gate bias, in a two-dimensional electron system. This phenomenon, which is akin to Bloch spin ferromagnetism, arises fundamentally as a result of electron-electron interaction in an itinerant, dilute electron system. Essentially, the kinetic energy favors an equal distribution of electrons over the available valleys, whereas the interaction between electrons prefers single-valley occupancy below a critical density. The gate-bias-tuned transition we observe is accompanied by a sudden, twofold change in sample resistance, making the phenomenon of interest for potential valleytronic transistor device applications. Our observation constitutes a quintessential demonstration of valleytronics in a very simple experiment.

Two-dimensional electrons confined to GaAs quantum wells are hallmark platforms for probing electron-electron interaction. Many key observations have been made in these systems as sample quality improved over the years. Here, we present a breakthrough in sample quality via source-material purification and innovation in GaAs molecular beam epitaxy vacuum chamber design. Our samples display an ultra-high mobility of $44\times10^6$ cm$^2$/Vs at an electron density of $2.0\times10^{11}$ /cm$^2$. These results imply only 1 residual impurity for every $10^{10}$ Ga/As atoms. The impact of such low impurity concentration is manifold. Robust stripe/bubble phases are observed, and several new fractional quantum Hall states emerge. Furthermore, the activation gap of the $\nu=5/2$ state, which is widely believed to be non-Abelian and of potential use for topological quantum computing, reaches $\Delta\simeq820$ mK. We expect that our results will stimulate further research on interaction-driven physics in a two-dimensional setting and significantly advance the field., Comment: 15 pages, 4 figures in main text. 4 pages, 2 figures in supplement. Nat. Mater. (2021)

A fundamental concept in physics is the Fermi surface, the constant-energy surface in momentum space encompassing all the occupied quantum states at absolute zero temperature. In 1960, Luttinger postulated that the area enclosed by the Fermi surface should remain unaffected even when electron-electron interaction is turned on, so long as the interaction does not cause a phase transition. Understanding what determines the Fermi surface size is a crucial and yet unsolved problem in strongly interacting systems such as high-$T_{c}$ superconductors. Here we present a precise test of the Luttinger theorem for a two-dimensional Fermi liquid system where the exotic quasi-particles themselves emerge from the strong interaction, namely for the Fermi sea of composite fermions (CFs). Via direct, geometric resonance measurements of the CFs' Fermi wavevector down to very low electron densities, we show that the Luttinger theorem is obeyed over a significant range of interaction strengths, in the sense that the Fermi sea area is determined by the density of the \textit{minority carriers} in the lowest Landau level. Our data also address the ongoing debates on whether or not CFs obey particle-hole symmetry, and if they are Dirac particles. We find that particle-hole symmetry is obeyed, but the measured Fermi sea area differs quantitatively from that predicted by the Dirac model for CFs., 6 pages, 4 figures

Hydrostatic pressure is a useful tool that can tune several key parameters in solid state materials. For example, the Land\'e $g$-factor in GaAs two-dimensional electron systems (2DESs) is expected to change from its bulk value $g\simeq-0.44$ to zero and even to positive values under a sufficiently large hydrostatic pressure. Although this presents an intriguing platform to investigate electron-electron interaction in a system with $g=0$, studies are quite limited because the GaAs 2DES density decreases significantly with increasing hydrostatic pressure. Here we show that a simple model, based on pressure-dependent changes in the conduction band alignment, quantitatively explains this commonly observed trend. Furthermore, we demonstrate that the decrease in the 2DES density can be suppressed by more than a factor of 3 through an innovative heterostructure design., Comment: 4 pages, 3 figures

The spin-polarized even-denominator fractional quantum Hall (FQH) states in the second Landau level (LL), i.e. 5/2 and 7/2, may possess novel quasi-particle excitations obeying non-Abelian statistics. However, the spin polarization of the 7/2 FQH state has not been investigated experimentally and the spin polarization of the 5/2 FQH state from tilted field experiments remains controversial. Using a piezo-driven sample rotator with the lowest electron temperature down to 25 mK, we studied the energy gap of the even-denominator FQH states in the second LL by precise control of the tilted angles with a resolution less than 0.1{\deg}. We observed two different energy gap dependences on the in-plane magnetic field for 5/2, 7/2, other FQH states (7/3 and 8/3) in the second LL and reentrant integer quantum Hall (RIQH) states in the third LL. Though the transition fields vary from states, their corresponding in-plane magnetic lengths are comparable to the quantum well thickness of the sample, which may result from the influence of the finite-thickness effect. At low in-plane magnetic fields, before the conjectured finite-thickness effect starts to dominate, the energy gaps of both 5/2 and 7/2 states show a non-decreasing behavior, supporting spin-polarized ground states. Our results also suggest that the 7/3, 8/3 FQH states, and the RIQH states in the third LL are spin-polarized or partially spin-polarized.

Adopting undoped ultraclean two-dimensional hole systems, we approach a strongly correlated limit by reducing the carrier density down to $1\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. The temperature dependence of the resistivity as a function of the carrier density reveals a characteristic energy scale displaying a benchmark critical behavior near a critical density of ${p}_{c}\ensuremath{\sim}4\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. The insulating state below ${p}_{c}$ exhibits a sharp resistance discontinuity in response to heating across a critical temperature ${T}_{c1}\ensuremath{\sim}30\phantom{\rule{0.16em}{0ex}}\mathrm{mK}$, consistent with a first-order transition. The dc response also identifies a second critical temperature ${T}_{c2}$ where linear IV behavior is recovered. Similar effects are also demonstrated by varying an external electric field. The results support a complex quantum phase transition with intermediate phases.

Suppressing electron scattering is essential to achieve high-mobility two-dimensional electron systems (2DESs) that are clean enough to probe exotic interaction-driven phenomena. In heterostructures it is common practice to utilize modulation doping, where the ionized dopants are physically separated from the 2DES channel. The doping-well structure augments modulation doping by providing additional screening for all types of charged impurities in the vicinity of the 2DES, which is necessary to achieve record-breaking samples. Despite its prevalence in the design of ultra-high-mobility 2DESs, the working principles of the doping-well structure have not been reported. Here we elaborate on the mechanics of electron transfer from doping wells to the 2DES, focusing on GaAs/AlGaAs samples grown by molecular beam epitaxy. Based on this understanding we demonstrate how structural parameters in the doping well can be varied to tune the properties of the 2DES., 6 pages, 5 fitures

Microwave-induced resistance oscillations (MIROs) and zero-resistance states (ZRSs) occur in high-mobility two-dimensional electron gas exposed to microwave (MW). We observe that the velocity shift ($\mathrm{\ensuremath{\Delta}}v/v$) oscillates in anticorrelation with MIRO, and $\mathrm{\ensuremath{\Delta}}v/v$ shows peaks at the minimal resistance of MIRO or at ZRS. The SAW velocity features of ZRS remain robust even in the absence of external driving current, which suggests the involvement of intrinsic mechanism in the nonequilibrium phase. In addition, under high-power MW, the phase (${\ensuremath{\varphi}}_{\mathrm{ac}}$) of ZRS stays constant at about 1/4, whereas the phase of the transitions in MIRO is reduced to below 0.10. We argue that the peaks of SAW velocity at ZRS may result from the inhomogeneity of superposed current domain structures. Moreover, a multiphoton process around $\ensuremath{\varepsilon}=1/2$ is observed in the SAW measurements.

We perform momentum-conserving tunneling spectroscopy using a GaAs cleaved-edge overgrowth quantum wire to investigate adjacent quantum Hall edge states. We use the lowest five wire modes with their distinct wave functions to probe each edge state and apply magnetic fields to modify the wave functions and their overlap. This reveals an intricate and rich tunneling conductance fan structure which is succinctly different for each of the wire modes. We self-consistently solve the Poisson-Schr\"odinger equations to simulate the spectroscopy, reproducing the striking fans in great detail, thus confirming the calculations. Further, the model predicts hybridization between wire states and Landau levels, which is also confirmed experimentally. This establishes momentum-conserving tunneling spectroscopy as a powerful technique to probe edge state wave functions., Comment: 5 pages, 5 figures

We demonstrate two types of waveguide structures that optically confine exciton-polaritons in two dimensions and act as polaritonic channels. We show a strong optical confinement in an etched recta...

The interplay between electron–electron interactions and the honeycomb topology is expected to produce exotic quantum phenomena and find applications in advanced devices. Semiconductor-based artificial graphene (AG) is an ideal system for these studies that combines high-mobility electron gases with AG topology. However, to date, low-disorder conditions that reveal the interplay of electron–electron interaction with AG symmetry have not been achieved. Here, we report the creation of low-disorder AG that preserves the near-perfection of the pristine electron layer by fabricating small period triangular antidot lattices on high-quality quantum wells. Resonant inelastic light scattering spectra show collective spin-exciton modes at the M-point's nearly flatband saddle-point singularity in the density of states. The observed Coulomb exchange interaction energies are comparable to the gap of Dirac bands at the M-point, demonstrating interplay between quasiparticle interactions and the AG potential. The saddle-point exciton energies are in the terahertz range, making low-disorder AG suitable for contemporary optoelectronic applications., Artificial nanostructures designed to simulate models of materials such as graphene provide insights into the material physics but can also have practical advantages. Du et al. create low-disorder artificial graphene devices, and present evidence of terahertz spin-exciton modes and large Coulomb interactions.

The plateau-plateau transition in the integer quantum Hall effect is studied in three Hall bars with different widths. The slopes of the Hall resistance as a function of magnetic field follow the scaling power law as expected in the plateau-plateau transition, and saturate at the low temperature limit. Surprisingly, the saturation temperature is irrelevant with the Hall bar size, which suggests that the saturation of the coherence length is intrinsic.

The single-particle spectral function measures the density of electronic states (DOS) in a material as a function of both momentum and energy, providing central insights into phenomena such as superconductivity and Mott insulators. While scanning tunneling microscopy (STM) and other tunneling methods have provided partial spectral information, until now only angle-resolved photoemission spectroscopy (ARPES) has permitted a comprehensive determination of the spectral function of materials in both momentum and energy. However, ARPES operates only on electronic systems at the material surface and cannot work in the presence of applied magnetic fields. Here, we demonstrate a new method for determining the full momentum and energy resolved electronic spectral function of a two-dimensional (2D) electronic system embedded in a semiconductor. In contrast with ARPES, the technique remains operational in the presence of large externally applied magnetic fields and functions for electronic systems with zero electrical conductivity or with zero electron density. It provides a direct high-resolution and high-fidelity probe of the dispersion and dynamics of the interacting 2D electron system. By ensuring the system of interest remains under equilibrium conditions, we uncover delicate signatures of many-body effects involving electron-phonon interactions, plasmons, polarons, and a novel phonon analog of the vacuum Rabi splitting in atomic systems.

Exciton–polariton condensates have garnered interest as a means to access macroscopic displays of quantum phenomena such as Bose–Einstein condensation and superfluidity. In this work, a direct measure of the polariton–polariton interaction is obtained.

Quantum fluids of light are realized in semiconductor microcavities using exciton-polaritons, solid-state quasi-particles with a light mass and sizeable interactions. Here, we use the microscopic analogue of oceanographic techniques to measure the excitation spectrum of a thermalised polariton condensate. Increasing the fluid density, we demonstrate the transition from a free-particle parabolic dispersion to a linear, sound-like Goldstone mode characteristic of superfluids at equilibrium. Notably, we reveal the effect of an asymmetric pumping by showing that collective excitations are created with a definite direction with respect to the condensate. Furthermore, we measure the critical sound speed for polariton superfluids close to equilibrium., Polariton condensates undergo continuous driving and dissipation, posing challenges for investigating their collective behaviour. Ballarini et al. adapt an oceanographic technique to measure the asymmetric occupation of the Goldstone mode and identify similarities with equilibrium condensates.

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 ($\nu\simeq1/5$). In dilute GaAs 2D \textit{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 ($\nu\simeq1/3$). Here we report our measurements of the fundamental temperature vs. filling phase diagram for the 2D holes' WS-liquid \textit{thermal melting}. Moreover, via changing the 2D hole density, we also probe their Landau level mixing vs. filling WS-liquid \textit{quantum melting} phase diagram. We find our data to be in good agreement with the results of very recent calculations, although intriguing subtleties remain., Comment: Phys. Rev. Lett. (in press) (2020)

What is the fate of the ground state of a two-dimensional electron system (2DES) at very low Landau level filling factors ($\nu$) where interaction reigns supreme? An ordered array of electrons, the so-called Wigner crystal, has long been believed to be the answer. It was in fact the search for the elusive Wigner crystal that led to the discovery of an unexpected, incompressible liquid state, namely the fractional quantum Hall state at $\nu=1/3$. Understanding the competition between the liquid and solid ground states has since remained an active field of fundamental research. Here we report experimental data for a new two-dimensional system where the electrons are confined to an AlAs quantum well. The exceptionally high quality of the samples and the large electron effective mass allow us to determine the liquid-solid phase diagram for the two-dimensional electrons in a large range of filling factors near $\simeq 1/3$ and $\simeq 1/5$. The data and their comparison with an available theoretical phase diagram reveal the crucial role of Landau level mixing and finite electron layer thickness in determining the prevailing ground states.

Quantum Hall stripe phases near half-integer filling factors $\ensuremath{\nu}\ensuremath{\ge}9/2$ were predicted by Hartree-Fock (HF) theory and confirmed by discoveries of giant resistance anisotropies in high-mobility two-dimensional electron gases. A theory of such anisotropy was proposed by MacDonald and Fisher, although they used parameters whose dependencies on the filling factor, electron density, and mobility remained unspecified. Here, we fill this void by calculating the hard-to-easy resistivity ratio as a function of these three variables. Quantitative comparison with experiment yields very good agreement, which we view as evidence for the ``plain vanilla'' smectic stripe HF phases.

We study the magnetoresistance of an ultrahigh mobility GaAs/AlGaAs two-dimensional electron system (2DES) in a weak magnetic field under low-frequency $(fl20$ GHz) microwave (MW) irradiation. We observe that, with decreasing MW frequency, microwave induced resistance oscillations (MIRO) are damped and multiphoton processes become dominant. At very low MW frequency $(fl4$ GHz), MIRO disappear gradually and an SdH-like oscillation develops. Our analysis indicates that the oscillation may originate from alternating Hall-field induced resistance oscillations (ac-HIRO), due to the transition from the elastic scattering in real space. On the other hand, from the view of photon energy, the oscillations can be understood as a multiphoton process of MIRO in the low MW frequency limit. We show that the two different nonequilibrium mechanisms of MIRO and HIRO can be unified under low-frequency MW irradiation.

We report on detailed experimental studies of a high-quality heterojunction insulated-gate field-effect transistor (HIGFET) to probe the particle-hole symmetry of the fractional quantum Hall effect (FQHE) states about half-filling in the lowest Landau level. The HIGFET is specially designed to vary the density of a two-dimensional electronic system under constant magnetic fields. We find in our constant magnetic field, variable density measurements that the sequence of FQHE states at filling factors ν=1/3,2/5,3/7… and its particle-hole conjugate states at filling factors 1-ν=2/3,3/5,4/7… have a very similar energy gap. Moreover, a reflection symmetry can be established in the magnetoconductivities between the ν and 1-ν states about half-filling. Our results demonstrate that the FQHE states in the lowest Landau level are manifestly particle-hole symmetric.

We investigate the photon-dressed state of excitons in bulk GaAs by optical pump-probe spectroscopy. We reveal that the high-energy branch of the dressed states continuously evolves into a singular enhancement at the absorption edge in the high-density region where the exciton picture is no longer valid. Comparing the experimental result with a simulation based on semiconductor Bloch equations, we show that the dressed state in such a high-density region is better viewed as a Bardeen-Cooper-Schrieffer-like state, which has been theoretically anticipated to exist over decades. Having seen that the dressed state can be regarded as a macroscopic coherent state driven by an external light field, we also discuss the decoherence from the dressed state to an incoherent state after the photoexcitation in view of the Coulomb enhancement in the transient absorption.

The field of THz mixers for astrophysics is dominated by superconducting hot-electron bolometers (HEBs), whereas Schottky-diode mixers have been the only devices suitable for planetary instruments. The Schottky mixers operate at ambient temperature, which is a great advantage for planetary applications, but are much less sensitive than the state-of-the art HEBs and require a 103 higher local oscillator (LO) power. Here, we have demonstrated a novel THz mixer which offers the best of both worlds: it operates at $\sim60\mathrm{K}$ (accessible by passive cooling on space), requires $\sim {\mu} \mathrm{W}$ LO power, and has a potential to be as sensitive as the HEB mixer.

Exciton-polaritons (polaritons herein) offer a unique nonlinear platform for studies of collective macroscopic quantum phenomena in a solid state system. Shaping of polariton flow and polariton confinement via potential landscapes created by nonresonant optical pumping has gained considerable attention due to the degree of flexibility and control offered by optically-induced potentials. Recently, large density-dependent energy shifts (blueshifts) exhibited by optically trapped polaritons at low densities, below the bosonic condensation threshold, were interpreted as an evidence of strong polariton-polariton interactions [Nat. Phys. 13, 870 (2017)]. In this work, we further investigate the origins of these blueshifts in optically-induced circular traps and present evidence of significant blueshift of the polariton energy due to reshaping of the optically-induced potential with laser pump power. Our work demonstrates strong influence of the effective potential formed by an optically-injected excitonic reservoir on the energy blueshifts observed below and up to the polariton condensation threshold and suggests that the observed blueshifts arise due to interaction of polaritons with the excitonic reservoir, rather than due to polariton-polariton interaction., 10 pages, 8 figures

Two-dimensional interacting electrons exposed to strong perpendicular magnetic fields generate emergent, exotic quasiparticles phenomenologically distinct from electrons. Specifically, electrons bind with an even number of flux quanta, and transform into composite fermions (CFs). Besides providing an intuitive explanation for the fractional quantum Hall states, CFs also possess Fermi-liquid-like properties, including a well-defined Fermi sea, at and near even-denominator Landau level filling factors such as $��=1/2$ or $1/4$. Here, we directly probe the Fermi sea of the rarely studied four-flux CFs near $��=1/4$ via geometric resonance experiments. The data reveal some unique characteristics. Unlike in the case of two-flux CFs, the magnetic field positions of the geometric resonance resistance minima for $��1/4$ are symmetric with respect to the position of $��=1/4$. However, when an in-plane magnetic field is applied, the minima positions become asymmetric, implying a mysterious asymmetry in the CF Fermi sea anisotropy for $��1/4$. This asymmetry, which is in stark contrast to the two-flux CFs, suggests that the four-flux CFs on the two sides of $��=1/4$ have very different effective masses, possibly because of the proximity of the Wigner crystal formation at small $��$., 7 pages, 4 figures, supplemental materials

Recent progress in condensed matter physics, such as for graphene, topological insulators, and Weyl semimetals, often originate from the specific topological symmetries of their lattice structures. Quantum states with different degrees of freedom, e.g., spin, valley, layer, etc., arise from these symmetries, and the coherent superposition of these states form multiple energy subbands. The pseudospin, a concept analogous to the Dirac spinor matrices, is a successful description of such multisubband systems. When the electron-electron interaction dominates, many-body quantum phases arise. They usually have discrete pseudospin polarizations and exhibit sharp phase transitions at certain universal critical pseudospin energy splittings. In this Letter, we present our discovery of hydrostatic-pressure-induced degeneracy between the two lowest Landau levels. This degeneracy is evidenced by the pseudospin polarization transitions of the fragile correlated quantum liquid phases near the Landau level filling factor $\ensuremath{\nu}=3/2$. Benefitting from the constant hole concentration and the sensitive nature of these transitions, we study the fine-tuning effect of the hydrostatic pressure at the order of $10\text{ }\text{ }\ensuremath{\mu}\mathrm{eV}$, well beyond the meV-level state-of-the-art resolution of other techniques.

We have developed a scanning photoluminescence technique that can directly map out the local two-dimensional electron density with a relative accuracy of $\sim2.2\times10^8$ cm$^{-2}$. The validity of this approach is confirmed by the observation of the expected density gradient in a high-quality GaAs quantum well sample that was not rotated during the molecular beam epitaxy of its spacer layer. In addition to this global variation in electron density, we observe local density fluctuations across the sample. These random density fluctuations are also seen in samples that were continuously rotated during growth, and we attribute them to residual space charges at the substrate-epitaxy interface. This is corroborated by the fact that the average magnitude of density fluctuations is increased to $\sim9\times10^{9}$ cm$^{-2}$ from $\sim1.2\times10^9$ cm$^{-2}$ when the buffer layer between the substrate and the quantum well is decreased by a factor of seven. Our data provide direct evidence for local density inhomogeneities even in very high-quality two-dimensional carrier systems., 6 pages, 3 figures

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 ($\nu$), 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 $\nu$ 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 $\nu$. 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 $T$ which is close to the previously-reported melting temperature of the WC. Our experimental results suggest a new method to map out a $T$ vs $\nu$ phase diagram of the magnetic-field-induced WC precisely., Comment: The formal version is published on Phys. Rev. Lett. 122, 116601 (2019)

New plasmon modes in fractional quantum Hall states are observed, revealing interplays 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.

We review our work on high-frequency conductance in two-dimensional high-mobility electronic systems in wide n-AlGaAs/GaAs/AlGaAs quantum wells. Using simultaneous measurements of the attenuation and velocity of a surface acoustic wave we obtained both real and imaginary components of the complex high-frequency conductance. Based on the experimental results and their analysis we conclude that close to the filling factor ν = 1/5, as well as in the interval 0.18 > ν > 0.125, a Wigner crystal pinned by disorder is formed. Both the melting temperature and the correlation length of the pinning-induced domains in the Wigner crystal were found. In close vicinities of ν = 1 and 2, transitions from single-electron localization to a Wigner crystal were observed.

Stripe-like and bubble-like patterns spontaneously form in numerous physical, chemical, and biological systems when competing long-range and short-range interactions banish uniformity. Stripe-like and the related nematic morphology are also under intense scrutiny in various strongly correlated electron systems. In contrast, the electronic bubble morphology is rare. Some of the most intriguing electron bubbles develop in the two-dimensional electron gas subjected to a perpendicular magnetic field. However, in contrast to bubbles forming in classical systems such as the Turing activator-inhibitor reaction or Langmuir films, bubbles in electron gases owe their existence to elementary quantum mechanics: they are stabilized as wavefunctions of individual electrons overlap. Here we report a rich pattern of multi-electron bubble phases in a high Landau level and we conclude that this richness is due to the nodal structure of the orbital component of the electronic wavefunction.

Using acoustic method we study dependences of transverse AC conductance, $\sigma (\omega)$, on magnetic field, temperature and the amplitude of AC electric field in a wide (75 nm) quantum well (QW) structure focusing on the vicinity of the filling factor $\nu =1/2$. Measurements are performed in the frequency domain 30-307 MHz and in the temperature domain 20-500 mK. Usually, in wide QW structures closely to $\nu =1/2$ the fractional quantum Hall effect (FQHE) regime is realized at some parameters of the sample. However, in our structure, at $\nu =1/2$ it is a compressible state corresponding to gas of composite fermions which is observed. This is confirmed by apparent frequency independence and weakly decreasing temperature dependence of $\mathrm{Re}\, \sigma(\omega)$. Comparing the dependences of this quantity on temperature and power of the acoustic wave we conclude that the observed nonlinear behavior of the conductance is compatible with heating of the composite fermions by the acoustic wave. For comparison, we also study the vicinity of $\nu = 3/2$ where the FQHE regime is clearly observed., Comment: 6 pages, 6 figures

We report on quantum Hall stripes (QHSs) formed in higher Landau levels of GaAs/AlGaAs quantum wells with high carrier density ($n_e > 4 \times 10^{11}$ cm$^{-2}$) which is expected to favor QHS orientation along unconventional $\left < 1\bar{1}0 \right >$ crystal axis and along the in-plane magnetic field $B_{||}$. Surprisingly, we find that at $B_{||} = 0$ QHSs in our samples are aligned along $\left < 110 \right >$ direction and can be reoriented only perpendicular to $B_{||}$. These findings suggest that high density alone is not a decisive factor for either abnormal native QHS orientation or alignment with respect to $B_{||}$, while quantum confinement of the 2DEG likely plays an important role., 4 pages

We report on the generation of frequency combs from the recently-discovered phenomenon of high-order sideband generation (HSG). A near-band gap continuous-wave (cw) laser with frequency $f_\text{NIR}$ was transmitted through an epitaxial layer containing GaAs/AlGaAs quantum wells that were driven by quasi-cw in-plane electric fields $F_\text{THz}$ between 4 and 50 kV/cm oscillating at frequencies $f_\text{THz}$ between 240 and 640 GHz. Frequency combs with teeth at $f_\text{sideband}=f_\text{NIR}+nf_\text{THz}$ ($n$ even) were produced, with maximum reported $n>120$, corresponding to a maximum comb span $>80$ THz. Comb spectra with the identical product $f_\text{THz}\times F_\text{THz}$ were found to have similar spans and shapes in most cases, as expected from the picture of HSG as a scattering-limited electron-hole recollision phenomenon. The HSG combs were used to measure the frequency and linewidth of our THz source as a demonstration of potential applications.

When two 2D electron gas layers, each at Landau level filling factor $\nu=1/2$, are close together a condensate of interlayer excitons emerges at low temperature. Although the excitonic phase is qualitatively well understood, the incoherent phase just above the critical layer separation is not. Using a combination of interlayer tunneling spectroscopy and conventional transport, we explore the incoherent phase in samples both near the phase boundary and further from it. In the more closely spaced bilayers we find the electronic spectral functions narrower and the Fermi energy of the $\nu = 1/2$ composite fermion metal smaller than in the more widely separated bilayers. We attribute these effects to a softening of the intralayer Coulomb interaction due to interlayer screening., Comment: 5 pages, 3 postscript figures. Final published version