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When interactions overcome disorder, integer quantum Hall plateaus support topological phases with different bulk insulators. In the center of the $\nu=1$ plateau the bulk is an Anderson-type insulator, while in the flanks of the plateau the bulk is the integer quantum Hall Wigner solid. We find that the activation energy along the $\nu=1$ plateau exhibits a very dramatic non-monotonic dependence on the magnetic field, a dependence that is strongly correlated with the stability regions of the two phases. Furthermore, the activation energy has an unexpected minimum at the boundary between the Anderson insulator and the Wigner solid. Our findings constrain the theory of the integer quantum Hall Wigner solid, determine its thermodynamic properties, and reveal novel behavior at the boundary between the Anderson insulator and the Wigner solid.

The emergence of spatial coherence in a confined two-dimensional Bose gas of exciton-polaritons with tuneable interactions offers a unique opportunity to explore the role of interactions in a phase transition in a driven-dissipative quantum system, where both the phase transition and thermalisation are mediated by interactions. We investigate, experimentally and numerically, the phase correlations and steady-state properties of the gas over a wide range of interaction strengths by varying the photonic/excitonic fraction of the polaritons and their density. We find that the first order spatial coherence function exhibits algebraic decay consistent with the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. Surprisingly, the exponent of the algebraic decay is inversely proportional to the coherent density of polaritons, in analogy to equilibrium superfluids above the BKT transition, but with a different proportionality constant. Our work paves the way for future investigations of the phenomenon of phase transitions and superfluidity in a driven-dissipative setting, Comment: 11 pages, 6 figures

The concept of fluidic viscosity is ubiquitous in our everyday life and for it to arise the fluidic medium must necessarily form a continuum where macroscopic properties can emerge. While a powerful concept for tangible liquids, hydrodynamic manifestation of collective flow in electronic systems such as two-dimensional electron gases (2DEGs) has only been shown recently to occur in graphene and GaAs/AlGaAs. Here, we present nonlocal electronic transport measurements in concentric annular rings formed in high-mobility GaAs/AlGaAs 2DEGs and the resulting data strongly suggest that viscous hydrodynamic flow can occur far away from the source-drain current region. Our conclusion of viscous electronic transport is further corroborated by simulations of the Navier-Stokes equations that are found to be in agreement with our measurements below 1K temperature. Most importantly, our work emphasizes the key role played by viscosity via electron-electron (e-e) interaction when hydrodynamic transport is restricted radially, and for which a priori should not have played a major role.

Low-disorder two-dimensional electron systems in the presence of a strong, perpendicular magnetic field terminate at very small Landau level filling factors in a Wigner crystal (WC), where the electrons form an ordered array to minimize the Coulomb repulsion. The nature of this exotic, many-body, quantum phase is yet to be fully understood and experimentally revealed. Here we probe one of WC's most fundamental parameters, namely the energy gap that determines its low-temperature conductivity, in record-mobility, ultra-high-purity, two-dimensional electrons confined to GaAs quantum wells. The WC domains in these samples contain $\simeq$ 1000 electrons. The measured gaps are a factor of three larger than previously reported for lower quality samples, and agree remarkably well with values predicted for the lowest-energy, intrinsic, hyper-corelated bubble defects in a WC made of flux-electron composite fermions, rather than bare electrons. The agreement is particularly noteworthy, given that the calculations are done for disorder-free composite fermion WCs, and there are no adjustable parameters. The results reflect the exceptionally high quality of the samples, and suggest that composite fermion WCs are indeed more stable compared to their electron counterparts.

A two dimensional system with extra degrees of freedom, such as spin and valley, is of great interest in the study of quantum phase transitions. The critical condition when a transition between different multicomponent fractional quantum Hall states appears is one of the very few junctions for many body problems between theoretical calculations and experiments. In this work, we present that uniaxial strain induces pseudospin transitions of composite fermions in a two-dimensional hole gas. Determined from transport behavior, strain along <111> effectively changes pseudospin energy levels. We deduce that diagonal strain dominates these variations. Our experiment provides a wedge for manipulating two dimensional interacting systems mechanically., Comment: 12 pages with 4 figures and 9 pages with 4 figures

AB oscillation in weak magnetic field (B<1.5kG) is observed in QPC due to interference between electrons propagating along different QPC channels. We also investigate photo-induced magnetoresistance oscillation in open-regime split-gate QPC under MW irradiation. It is attributed to EMPs interfering in the QPC region. The influence of MW power, frequency and split gate voltage is discussed thoroughly. We unify the result of photoconductance at B=0 with EMP theories.

We measure the resistance oscillation of quantum point contact (QPC) under microwave (MW) radiation. What is different from the common resistance oscillation induced by edge magnetoplasmon (EMP) is that at lower magnetic field ({\omega}>{\omega}_c), photoconductance is positive (negative) with weak (strong) MW radiation. This transport phenomenon is proved to be related to superballistic flow of electrons through QPC. The distinction between the regions {\omega}>{\omega}_c and {\omega}<{\omega}_c is attributed to different absorption rate of MW radiation. Violent absorption occurs when cyclotron orbits or current domains are destroyed in QPC region.

Topology provides an essential concept for achieving unchanged (or protected) quantum properties in the presence of perturbations. A challenge facing realistic applications is that the level of protection displayed in real systems is subject to substantial variations. Some key differences stem from mechanisms influencing the reconstruction behaviors of extended dissipationless modes. Despite various insightful results on potential causes of backscattering, the edge-state-based approach is limited because the bulk states, as shown by breakdown tests, contribute indispensably. This study investigates the influence of bulk reconstruction where dissipationless modes are global objects instead of being restricted to the sample edge. An integer quantum Hall effect (IQHE) hosted in a Corbino sample geometry is adopted and brought continuously to the verge of a breakdown. A detection technique is developed to include two independent setups capable of simultaneously capturing the onset of dissipation in both longitudinal and transverse directions. The real-time correspondence between orthogonal results confirms two facts. 1. Dissipationless charge modes undergo frequent reconstruction in response to electrochemical potential changes, causing dissipationless current paths to expand transversely into the bulk while preserving chirality. A breakdown only occurs when a backscattering emerges between reconfigured dissipationless current paths bridging opposite edge contacts. 2. Impurity screening is vital in enhancing protection, and topological protection is subject to an intriguing interplay of disorder, electron-electron interaction, and topology. The proposed reconstruction mechanism qualitatively explains the robustness variations, beneficial for developing means for optimization.

The composite fermion theory opened a new chapter in understanding many-body correlations through the formation of emergent particles. The formation of two-flux and four-flux composite fermions is well established. While there are limited data linked to the formation of six-flux composite fermions, topological protection associated with them is conspicuously lacking. Here we report evidence for the formation of a quantized and gapped fractional quantum Hall state at the filling factor $\nu=9/11$, which we associate with the formation of six-flux composite fermions. Our result provides evidence for the most intricate composite fermion with six fluxes and expands the already diverse family of highly correlated topological phases with a new member that cannot be characterized by correlations present in other known members. Our observations pave the way towards the study of higher order correlations in the fractional quantum Hall regime.

In low-disorder, two-dimensional electron systems (2DESs), the fractional quantum Hall states at very small Landau level fillings ($\nu$) terminate in a Wigner solid (WS) phase, where electrons arrange themselves in a periodic array. The WS is typically pinned by the residual disorder sites and manifests an insulating behavior, with non-linear current-voltage (\textit{I-V}) and noise characteristics. We report here, measurements on an ultra-low-disorder, dilute 2DES, confined to a GaAs quantum well. In the $\nu < 1/5$ range, superimposed on a highly-insulating longitudinal resistance, the 2DES exhibits a developing fractional quantum Hall state at $\nu=1/7$, attesting to its exceptional high quality, and dominance of electron-electron interaction in the low filling regime. In the nearby insulating phases, we observe remarkable non-linear \textit{I-V} and noise characteristics as a function of increasing current, with current thresholds delineating three distinct phases of the WS: a pinned phase (P1) with very small noise, a second phase (P2) in which $dV/dI$ fluctuates between positive and negative values and is accompanied by very high noise, and a third phase (P3) where $dV/dI$ is nearly constant and small, and noise is about an order of magnitude lower than in P2. In the depinned (P2 and P3) phases, the noise spectrum also reveals well-defined peaks at frequencies that vary linearly with the applied current, suggestive of washboard frequencies. We discuss the data in light of a recent theory that proposes different dynamic phases for a driven WS.

The 5/2 fractional quantum Hall effect in the second Landau level of extremely clean two-dimensional electron gases has attracted much attention due to its topological order predicted to host quasiparticles that obey non-Abelian quantum statistics and could serve as a basis for fault-tolerant quantum computations. While previous works have establish the Fermi liquid (FL) nature of its putative composite fermion (CF) normal phase, little is known regarding its thermodynamics properties and as a result its effective mass is entirely unknown. Here, we report on time-resolved specific heat measurements at filling factor 5/2, and we examine the ratio of specific heat to temperature as a function of temperature. Combining these specific heat data with existing longitudinal thermopower data measuring the entropy in the clean limit we find that, unless a phase transition/crossover gives rise to large specific heat anomaly, both datasets point towards a large effective mass in the FL phase of CFs at 5/2. We estimate the effective-to-bare mass ratio m*/me to be ranging from ~2 to 4, which is two to three times larger than previously measured values in the first Landau level.

Disorder and electron-electron interaction play essential roles in the physics of electron systems in condensed matter. In two-dimensional, quantum Hall systems, extensive studies of disorder-induced localization have led to the emergence of a scaling picture with a single extended state, characterized by a power-law divergence of the localization length in the zero-temperature limit. Experimentally, scaling has been investigated via measuring the temperature dependence of plateau-to-plateau transitions between the integer quantum Hall states (IQHSs), yielding a critical exponent $\kappa\simeq 0.42$. Here we report scaling measurements in the fractional quantum Hall state (FQHS) regime where interaction plays a dominant role. Our study is partly motivated by recent calculations, based on the composite fermion theory, that suggest identical critical exponents in both IQHS and FQHS cases to the extent that the interaction between composite fermions is negligible. The samples used in our experiments are two-dimensional electron systems confined to GaAs quantum wells of exceptionally high quality. We find that $\kappa$ varies for transitions between different FQHSs observed on the flanks of Landau level filling factor $\nu=1/2$, and has a value close to that reported for the IQHS transitions only for a limited number of transitions between high-order FQHSs with intermediate strength. We discuss possible origins of the non-universal $\kappa$ observed in our experiments.

Real-time probing of electrons can uncover intricate relaxation mechanisms and many-body interactions hidden in strongly correlated materials. While experimenters have used ultrafast optical pump-probe methods in bulk materials, laser heating and insensitivity below the surface prevent their application to encapsulated low-dimensional electron systems at millikelvin temperatures, home to numerous intriguing electronic phases. Here, we introduce time, momentum, and energy resolved pump-probe tunneling spectroscopy (Tr-MERTS). The method allows the injection of electrons at particular energies and observation of their subsequent decay in energy-momentum space. Using Tr-MERTS, we visualize electronic decay processes in Landau levels with lifetimes up to tens of microseconds. Although most observed features agree with simple energy-relaxation, we discover an unexpected splitting in the nonequilibrium energy spectrum in the vicinity of a ferromagnetic state. An exact diagonalization study of the system suggests that the splitting arises from a maximally spin-polarized higher energy state, distinct from a conventional equilibrium skyrmion. Furthermore, we observe time-dependent relaxation of the splitting, which we attribute to single-flipped spins forming topological spin textures. These results establish Tr-MERTS as a powerful tool for studying the dynamics and properties of a two-dimensional electronic system beyond equilibrium.

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 $\nu=3/2$. 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 wavefunction 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., Comment: 7+15 pages, 4+6 figures

Fractional quantum Hall states (FQHSs) at even-denominator Landau level filling factors ($\nu$) are of prime interest as they are predicted to host exotic, topological states of matter. We report here the observation of a FQHS at $\nu=1/2$ in a two-dimensional electron system of exceptionally high quality, confined to a wide AlAs quantum well, where the electrons can occupy multiple conduction-band valleys with an anisotropic effective mass. The anisotropy and multi-valley degree of freedom offer an unprecedented tunability of the $\nu=1/2$ FQHS as we can control both the valley occupancy via the application of in-plane strain, and the ratio between the strengths of the short- and long-range Coulomb interaction by tilting the sample in the magnetic field to change the electron charge distribution. Thanks to this tunability, we observe phase transitions from a compressible Fermi liquid to an incompressible FQHS and then to an insulating phase as a function of tilt angle. We find that this evolution and the energy gap of the $\nu=1/2$ FQHS depend strongly on valley occupancy.

We report low-temperature electronic transport measurements performed in two multi-terminal Corbino samples formed in GaAs/Al-GaAs two-dimensional electron gases (2DEG) with both ultra-high electron mobility ($\gtrsim 20\times 10^6$ $cm^2/Vs)$ and with distinct electron density of $1.7$ and $3.6\times 10^{11}~cm^{-2}$. In both Corbino samples, a non-monotonic behavior is observed in the temperature dependence of the resistance below 1~$K$. Surprisingly, a sharp {\it decrease} in resistance is observed with {\it increasing} temperature in the sample with lower electron density, whereas an opposite behavior is observed in the sample with higher density. To investigate further, transport measurements were performed in large van der Pauw samples having identical heterostructures, and as expected they exhibit resistivity that is monotonic with temperature. Finally, we discuss the results in terms of various lengthscales leading to ballistic and hydrodynamic electronic transport, as well as a possible Gurzhi effect.

Persistent circulation is a canonical effect of superfluidity. In previous experiments, quantized circulation has been observed in polariton condensates, usually far from equilibrium, but persistent current in the absence of any stirring has not been seen. We report here the direct observation of persistent circulation of a polariton condensate with no driving force and with no observable change in time. We can cause the condensate to circulate in either direction on demand using a short laser pulse, after which the condensate continues to circulate for dozens to hundreds of rotations around a ring trap without any further stimulation. Our theoretical model successfully shows how the pulse, despite not carrying any angular momentum, causes the circulation.

We focused on the transverse AC magneto-conductance of a high mobility $p$-GaAs/AlGaAs quantum well ($p=1.2\times 10^{11}$~cm$^{-2}$) in the vicinity of two values of the Landau level filling factor $\nu$: $\nu =1$ (integer quantum Hall effect) and $\nu =1/3$ (fractional quantum Hall effect). The complex transverse AC conductance, $\sigma_{xx}^{AC} (\omega)$, was found from simultaneous measurements of attenuation and velocity of surface acoustic waves (SAWs) propagating along the interface between a piezoelectric crystal and the two-dimensional hole system under investigation. We analyzed both the real and imaginary parts of the hole conductance and compared the similarities and differences between the results for filling factor 1 and filling factor 1/3. Both to the left and to the right of these values maxima of a specific shape, "wings", arose in the $\sigma (\nu)$ dependences at those two $\nu$. Analysis of the results of our acoustic measurements at different temperatures and surface acoustic wave frequencies allowed us to attribute these wings to the formation of collective localized states, namely the domains of a pinned Wigner crystal, i.e., a Wigner solid. While the Wigner solid has been observed in 2D hole systems previously, we were able to detect 20 it at the highest hole density and, therefore, the lowest hole-hole interaction reported., Comment: 9 pages, 6 figures

Strong interactions and topology drive a wide variety of correlated ground states. Some of the most interesting of these ground states, such as fractional quantum Hall states and fractional Chern insulators, have fractionally charged quasiparticles. Correlations in these phases are captured by the binding of electrons and vortices into emergent particles called composite fermions. Composite fermion quasiparticles are randomly localized at high levels of disorder and may exhibit charge order when there is not too much disorder in the system. However, more complex correlations were predicted when composite fermion quasiparticles cluster into a bubble, then these bubbles order on a lattice. Such a highly correlated ground state was termed the bubble phase of composite fermions. Here we report the observation of this bubble phase of composite fermions, evidenced by the reentrance of the fractional quantum Hall effect. We associate this reentrance with a bubble phase with two composite fermion quasiparticles per bubble. Our results demonstrate the existence of a new class of strongly correlated topological phases driven by clustering and charge ordering of emergent quasiparticles.

Electrons' multiple quantum degrees of freedom can lead to rich physics, including a competition between various exotic ground states, as well as novel applications such as spintronics and valleytronics. Here we report magneto-transport experiments demonstrating how the valley degree of freedom impacts the fractional quantum states (FQHSs), and the related magnetic-flux-electron composite fermions (CFs), at very high magnetic fields in the extreme quantum limit when only the lowest Landau level is occupied. Unlike in other multivalley two-dimensional electron systems such as Si or monolayer graphene and transition-metal dichalcogenides, in our AlAs sample we can continuously tune the valley polarization via the application of in-situ strain. We find that the FQHSs remain exceptionally strong even as they make valley polarization transitions, revealing a surprisingly robust ferromagnetism of the FQHSs and the underlying CFs. Our observation implies that the CFs are strongly interacting in our system. We are also able to obtain a phase diagram for the FQHS and CF valley polarization in the extreme quantum limit as we monitor transitions of the FHQSs with different valley polarizations.

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 $\nu=1$. As we tune the field position of the crossing from one side of $\nu=1$ to the other by changing the hole density, the energy gap for the quantum Hall state at $\nu=1$ 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., Comment: 7+2 pages, 4+4 figures

Fractional quantum Hall states (FQHSs) exemplify exotic phases of low-disorder two-dimensional (2D) electron systems when electron-electron interaction dominates over the thermal and kinetic energies. Particularly intriguing among the FQHSs are those observed at even-denominator Landau level filling factors, as their quasi-particles are generally believed to obey non-Abelian statistics and be of potential use in topological quantum computing. Such states, however, are very rare and fragile, and are typically observed in the excited Landau level of 2D electron systems with the lowest amount of disorder. Here we report the observation of a new and unexpected even-denominator FQHS at filling factor {\nu} = 3/4 in a GaAs 2D hole system with an exceptionally high quality (mobility). Our magneto-transport measurements reveal a strong minimum in the longitudinal resistance at {\nu} = 3/4, accompanied by a developing Hall plateau centered at (h/e2)/(3/4). This even-denominator FQHS is very unusual as it is observed in the lowest Landau level and in a 2D hole system. While its origin is unclear, it is likely a non-Abelian state, emerging from the residual interaction between composite fermions., Comment: 6+6 pages, 3+3 figures; featured in Physics; featured as Editor's suggestion

Composite fermions (CFs), exotic quasi-particles formed by pairing an electron and an even number of magnetic flux quanta emerge at high magnetic fields in an interacting electron system, and can explain phenomena such as the fractional quantum Hall state (FQHS) and other many-body phases. CFs possess an effective mass ($m_{CF}$) whose magnitude is inversely related to the most fundamental property of a FQHS, namely its energy gap. We present here experimental measurements of $m_{CF}$ in ultra-high quality two-dimensional electron systems confined to GaAs quantum wells of varying thickness. An advantage of measuring $m_{CF}$ over gap measurements is that mass values are insensitive to disorder and are therefore ideal for comparison with theoretical calculations, especially for high-order FQHS. Our data reveal that $m_{CF}$ increases with increasing well width, reflecting a decrease in the energy gap as the electron layer becomes thicker and the in-plane Coulomb energy softens. Comparing our measured masses with available theoretical results, we find significant quantitative discrepancies, highlighting that more rigorous and accurate calculations are needed to explain the experimental data.

Quantum information can be coded by the topologically protected edges of fractional quantum Hall (FQH) states. Investigation on FQH edges in the hope of searching and utilizing non-Abelian statistics has been a focused challenge for years. Manipulating the edges, e.g. to bring edges close to each other or to separate edges spatially, is a common and essential step for such studies. The FQH edge structures in a confined region are typically presupposed to be the same as that in the open region in analysis of experimental results, but whether they remain unchanged with extra confinement is obscure. In this work, we present a series of unexpected plateaus in a confined single-layer two-dimensional electron gas (2DEG), which are quantized at anomalous fractions such as 9/4, 17/11, 16/13 and the reported 3/2. We explain all the plateaus by assuming surprisingly larger filling factors in the confined region. Our findings enrich the understanding of edge states in the confined region and in the applications of gate manipulation, which is crucial for the experiments with quantum point contact and interferometer., Comment: 6 pages, 4 figures

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.

For several decades now, ultra-high-mobility GaAs two-dimensional electron systems (2DESs) have served as the hallmark platform for various branches of research in condensed matter physics. Fundamental to this long-standing history of success for GaAs 2DESs was continuous sample quality improvement, which enabled scattering-free transport over macroscopic length scales as well as the emergence of a diverse range of exotic many-body phenomena. While the recent breakthrough in the quality of GaAs 2DESs grown by molecular beam epitaxy is highly commendable in this context, it is also important and timely to establish an up-to-date understanding of what obstructs us from pushing the mobility limit even further. Here, we present mobility data taken at a temperature of 0.3 K for a wide variety of state-of-the-art GaAs 2DESs, exhibiting a maximum, world-record mobility of $\mu\simeq57\times10^6$ cm$^2$/Vs at a 2DES density of $n=1.55\times10^{11}$ /cm$^2$. We also provide comprehensive analyses of the collective scattering mechanisms that can explain the results. Furthermore, based on our study, we discuss potential scenarios where GaAs 2DES mobility values exceeding $100\times10^6$ cm$^2$/Vs could be achieved., Comment: 11 pages, 4 figures

Viscous fluid in an ultrahigh-mobility two-dimensional electron gas (2DEG) in GaAs/AlGaAs quantum wells is systematically studied through measurements of negative magnetoresistance (NMR) and photoresistance under microwave radiation, and the data are analyzed according to recent theoretical work by e.g., Alekseev, Physical Review Letters 117,166601 (2016). Size-dependent and temperature dependent NMR are found to conform to the theoretical predictions. In particular, transport of 2DEG with relatively weak Coulomb interaction (interparticle interaction parameter r_s<1) manifests a crossover between viscous liquid and viscous gas. The size dependence of microwave induced resistance oscillations and that of the '2nd harmonic' peak indicate that 2DEG in a moderate magnetic field should be regarded as viscous fluid as well. Our results suggest that the hydrodynamic effects must be considered in order to understand semiclassical electronic transport in a clean 2DEG.

The ground state of two-dimensional electron systems (2DESs) at low Landau level filling factors ($\nu\lesssim1/6$) has long been a topic of interest and controversy in condensed matter. Following the recent breakthrough in the quality of ultra-high-mobility GaAs 2DESs, we revisit this problem experimentally and investigate the impact of reduced disorder. In a GaAs 2DES sample with density $n=6.1\times10^{10}$ /cm$^2$ and mobility $\mu=25\times10^6$ cm$^2$/Vs, we find a deep minimum in the longitudinal magnetoresistance ($R_{xx}$) at $\nu=1/7$ when $T\simeq104$ mK. There is also a clear sign of a developing minimum in the $R_{xx}$ at $\nu=2/13$. While insulating phases are still predominant when $\nu\lesssim1/6$, these minima strongly suggest the existence of fractional quantum Hall states at filling factors that comply with the Jain sequence $\nu=p/(2mp\pm1)$ even in the very low Landau level filling limit. The magnetic field dependent activation energies deduced from the relation $R_{xx}\propto e^{E_A/2kT}$ corroborate this view, and imply the presence of pinned Wigner solid states when $\nu\neq p/(2mp\pm1)$. Similar results are seen in another sample with a lower density, further generalizing our observations., Comment: 6 pages, 4 figures

The complex band structure, large spin-orbit induced band splitting, and heavy effective mass of two-dimensional (2D) hole systems hosted in GaAs quantum wells render them rich platforms to study many-body physics and ballistic transport phenomena. Here we report ultra-high-quality (001) GaAs 2D hole systems, fabricated using molecular beam epitaxy and modulation doping, with mobility values as high as $5.8\times10^6$ cm$^2$/Vs at a hole density of $p=1.3\times10^{11}$ /cm$^2$, implying a mean-free path of $\simeq27$ $\mu$m. In the low-temperature magnetoresistance trace of this sample, we observe high-order fractional quantum Hall states up to the Landau level filling $\nu=12/25$ near $\nu=1/2$. Furthermore, we see a deep minimum develop at $\nu=1/5$ in the magnetoresistance of a sample with a much lower hole density of $p=4.0\times10^{10}$ /cm$^2$ where we measure a mobility of $3.6\times10^6$ cm$^2$/Vs. These improvements in sample quality were achieved by reduction of residual impurities both in the GaAs channel and the AlGaAs barrier material, as well as optimization in design of the sample structure., Comment: 9 pages, 4 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 <$2 T conductance oscillations undergo beating induced by a spin-orbit interaction. Analysis of the beating character made it possible to separate the conductance contributions from the two heavy holes subbands split by the spin-orbit interaction. For each of the subbands the values of the effective masses and quantum relaxation times have been determined, and then the energy of the spin-orbit interaction was obtained. The quantum well profile, as well as the small magnitude of the spin-orbit interaction, allowed us to conclude that the spin-orbit splitting is governed by the Dresselhaus mechanism., Comment: 6 pages, 7 figures

We report complex magnetotransport patterns of the $\nu=1$ 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 $\nu=1$ 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 $\nu$-$T$ phase space.

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 $4\leq\nu\leq5$.

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)

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., Comment: 5 pages, 4 figures

The fractional quantum Hall effect (FQHE) stands as a quintessential manifestation of an interacting two-dimensional electron system. One of FQHE'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 quantitative comparison between the measured energy gaps and the available theoretical calculations that take into account the role of finite layer thickness and Landau level mixing. Our systematic experimental study of the FQHE energy gaps uses very high-quality two-dimensional electron systems confined to GaAs quantum wells with varying well widths. All the measured energy gaps fall bellow 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 the measured energy gaps to be in reasonable quantitative agreement with calculations, although some discrepancies remain.

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.

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., Comment: Total: 27 pages, 12 figures. Main text 13 pages, 4 figures

Topological insulators are a class of electronic materials exhibiting robust edge states immune to perturbations and disorder. This concept has been successfully adapted in photonics, where topologically nontrivial waveguides and topological lasers were developed. However, the exploration of topological properties in a given photonic system is limited to a fabricated sample, without the flexibility to reconfigure the structure in-situ. Here, we demonstrate an all-optical realization of the orbital Su-Schrieffer-Heeger (SSH) model in a microcavity exciton-polariton system, whereby a cavity photon is hybridized with an exciton in a GaAs quantum well. We induce a zigzag potential for exciton polaritons all-optically, by shaping the nonresonant laser excitation, and measure directly the eigenspectrum and topological edge states of a polariton lattice in a nonlinear regime of bosonic condensation. Furthermore, taking advantage of the tunability of the optically induced lattice we modify the intersite tunneling to realize a topological phase transition to a trivial state. Our results open the way to study topological phase transitions on-demand in fully reconfigurable hybrid photonic systems that do not require sophisticated sample engineering., Comment: 7 pages, 4 figures

Collective (elementary) excitations of quantum bosonic condensates, including condensates of exciton polaritons in semiconductor microcavities, are a sensitive probe of interparticle interactions. In anisotropic microcavities with momentum-dependent TE-TM splitting of the optical modes, the excitations dispersions are predicted to be strongly anisotropic, which is a consequence of the synthetic magnetic gauge field of the cavity, as well as the interplay between different interaction strengths for polaritons in the singlet and triplet spin configurations. Here, by directly measuring the dispersion of the collective excitations in a high-density optically trapped exciton-polariton condensate, we observe excellent agreement with the theoretical predictions for spinor polariton excitations. We extract the inter- and intra-spin polariton interaction constants and map out the characteristic spin textures in an interacting spinor condensate of exciton polaritons.

Memory or transistor devices based on 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 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 one by a small reduction in density, simply tuned by a gate bias, in a two-dimensional electron system. This phenomenon 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, two-fold 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.

We have observed the effect of pseudo magnetic field originating from the polaritonic analog of spin-orbit coupling (TE$-$TM splitting) on a polariton condensate in a ring-shaped microcavity. The effect gives rise to a stable four-leaf pattern around the ring as seen from the linear polarization measurements of the condensate photoluminescence. This pattern is found to originate from the interplay of the cavity potential, energy relaxation, and TE-TM splitting in the ring. Our observations are compared to the dissipative one-dimensional spinor Gross-Pitaevskii equation with the TE-TM splitting energy which shows good qualitative agreement., Comment: 13 pages, 7 figures, preprint version, minor edit v2

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 $r_s$, 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 $r_s$ surpasses 35, and then a phase with strongly non-linear current-voltage characteristics, suggestive of a pinned Wigner solid, when $r_s$ exceeds $\simeq 38$. However, our sample makes a transition to an insulating state at $r_s\simeq 27$, 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.

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.

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)

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 energy. We report here the observation of an abrupt, interaction-driven transition to full magnetization, highly reminiscent of Bloch ferromagnetism that has eluded experiments for the last ninety years. Our platform is the exotic two-dimensional Fermi sea of composite fermions at half-filling of the lowest Landau level. Via quantitative measurements of the Fermi wavevector, which provides a direct measure of the spin polarization, we observe a sudden transition from a partially-spin-polarized to a fully-spin-polarized ground state as we lower the composite fermions' density. Our detailed theoretical calculations provide a semi-quantitative account of this phenomenon.

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., Comment: 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

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)