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Topology is essential for achieving unchanged (or protected) quantum properties in the presence of perturbations. A challenge facing the application is the variable protection levels displayed in real systems associated with the reconstructive behaviors of the dissipationless modes. Despite various insights on potential causes of backscattering, the edge-state-based approach is incomplete because the bulk states also contribute indispensably. This study investigates sample-scale reconstruction where dissipationless modes are global objects instead of being restricted to the sample edge. An integer quantum Hall effect hosted in a Corbino geometry is adopted and brought to the verge of a breakdown. Two independent and simultaneous detections are performed to capture transport responses in both longitudinal and transverse directions. The real-time correspondence between orthogonal results confirms two facts. 1. Dissipationless 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 reconstructed dissipationless current paths bridging opposite edge contacts. 2. Topological protection is subject to an interplay of disorder, electron-electron interaction, and topology. The proposed reconstruction mechanism qualitatively explains the robustness variations, beneficial for protection optimization. Understanding the mechanisms influencing the robustness of topologically protected states is of fundamental relevance. This experimental work demonstrates, through the observation of real-time longitudinal and transverse responses, the importance of transverse reconstruction of protected modes which is influenced by electron-electron interaction in addition to disorder. [ABSTRACT FROM AUTHOR]

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 ν = 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. Huang et al. study fractional quantum Hall (fQH) states in high-quality GaAs/AlGaAs samples. They report evidence for a fQH state at filling factor ν = 9/11, which they associate with the formation of six-flux composite fermions. [ABSTRACT FROM AUTHOR]

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. The fractional quantum Hall state at the filling factor 5/2 has been intensively studied due to its predicted non-Abelian statistics. Petrescu et al. measure the composite fermion effective mass of this state and find that it is several times larger than that in the half-filled lowest Landau level. [ABSTRACT FROM AUTHOR]

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 (≳ 20 × 106 cm2/ Vs) and with distinct electron density of 1.7 and 3.6 × 1011 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 decrease in resistance is observed with 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. Metallic resistance of two-dimensional electron gases normally increases with temperature increasing. Here, the authors find a resistance decrease with increasing temperature at very low temperatures in two-dimensional electron metal described by Fermi liquid theory. [ABSTRACT FROM AUTHOR]

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 crystals1 (now known as Bloch wavefunctions), rapid scattering processes have so far prevented their direct experimental reconstruction. In high-order sideband generation2–9, 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.Bloch wavefunctions of two types of hole in gallium arsenide are reconstructed by measuring the polarization of light emitted by collisions of electrons and holes accelerated by a terahertz laser. [ABSTRACT FROM AUTHOR]

Topological physics relies on the structure of the eigenstates of the Hamiltonians. The geometry of the eigenstates is encoded in the quantum geometric tensor1—comprising the Berry curvature2 (crucial for topological matter)3 and the quantum metric4, which defines the distance between the eigenstates. Knowledge of the quantum metric is essential for understanding many phenomena, such as superfluidity in flat bands5, orbital magnetic susceptibility6,7, the exciton Lamb shift8 and the non-adiabatic anomalous Hall effect6,9. However, the quantum geometry of energy bands has not been measured. Here we report the direct measurement of both the Berry curvature and the quantum metric in a two-dimensional continuous medium—a high-finesse planar microcavity10—together with the related anomalous Hall drift. The microcavity hosts strongly coupled exciton–photon modes (exciton polaritons) that are subject to photonic spin–orbit coupling11 from which Dirac cones emerge12, and to exciton Zeeman splitting, breaking time-reversal symmetry. The monopolar and half-skyrmion pseudospin textures are measured using polarization-resolved photoluminescence. The associated quantum geometry of the bands is extracted, enabling prediction of the anomalous Hall drift, which we measure independently using high-resolution spatially resolved epifluorescence. Our results unveil the intrinsic chirality of photonic modes, the cornerstone of topological photonics13–15. These results also experimentally validate the semiclassical description of wavepacket motion in geometrically non-trivial bands9,16. The use of exciton polaritons (interacting photons) opens up possibilities for future studies of quantum fluid physics in topological systems. Direct measurement of the Berry curvature and the quantum metric of photonic modes in a high-finesse planar microcavity is achieved, enabling quantitative prediction of the independently measured anomalous Hall drift. [ABSTRACT FROM AUTHOR]

This document is a correction notice for an article titled "Large composite fermion effective mass at filling factor 5/2" published in Nature Communications. The correction addresses an error in Figure 4, where the legend referenced the wrong reference. The error has been corrected in both the PDF and HTML versions of the article. Additionally, there was an error in the Supplementary Information, which has been updated to include the correct reference. The document also provides a link to the online version of the supplementary material. The authors of the article are M. Petrescu, Z. Berkson-Korenberg, Sujatha Vijayakrishnan, K. W. West, L. N. Pfeiffer, and G. Gervais. [Extracted from the article]

In spite of its ubiquity in strongly correlated systems, the competition of paired and nematic ground states remains poorly understood. Recently such a competition was reported in the two-dimensional electron gas at filling factor ν = 5/2. At this filling factor a pressure-induced quantum phase transition was observed from the paired fractional quantum Hall state to the quantum Hall nematic. Here we show that the pressure-induced paired-to-nematic transition also develops at ν = 7/2, demonstrating therefore this transition in both spin branches of the second orbital Landau level. However, we find that pressure is not the only parameter controlling this transition. Indeed, ground states consistent with those observed under pressure also develop in a sample measured at ambient pressure, but in which the electron–electron interaction was tuned close to its value at the quantum critical point. Our experiments suggest that electron–electron interactions play a critical role in driving the paired-to-nematic transition. [ABSTRACT FROM AUTHOR]

Coulomb drag is a process whereby the repulsive interactions between electrons in spatially separated conductors enable a current flowing in one of the conductors to induce a voltage drop in the other. If the second conductor is part of a closed circuit, a net current will flow in that circuit. The drag current is typically much smaller than the drive current owing to the heavy screening of the Coulomb interaction. There are, however, rare situations in which strong electronic correlations exist between the two conductors. For example, double quantum well systems can support exciton condensates, which consist of electrons in one well tightly bound to holes in the other. 'Perfect' drag is therefore expected; a steady transport current of electrons driven through one quantum well should be accompanied by an equal current of holes in the other. Here we demonstrate this effect, taking care to ensure that the electron-hole pairs dominate the transport and that tunnelling of charge between the quantum wells, which can readily compromise drag measurements, is negligible. We note that, from an electrical engineering perspective, perfect Coulomb drag is analogous to an electrical transformer that functions at zero frequency. [ABSTRACT FROM AUTHOR]

At high magnetic fields, where the Fermi level lies in the N=0 lowest Landau level (LL), a clean two-dimensional electron system (2DES) shows numerous incompressible liquid phases which exhibit the fractional quantum Hall effect (FQHE; ref. ). These liquid phases do not break rotational symmetry, exhibiting resistivities which are isotropic in the plane. In contrast, at lower fields, when the Fermi level lies in the N?2 third and several higher LLs, the 2DES exhibits a distinctly different class of collective states. In particular, near half-filling of these high LLs the 2DES exhibits a strongly anisotropic longitudinal resistance at low temperatures. These 'stripe' phases, which do not exhibit the quantized Hall effect, resemble nematic liquid crystals, possessing broken rotational symmetry and orientational order. Here we report a surprising new observation: an electronic configuration in the N=1 LL, the resistivity tensor of which simultaneously exhibits a robust fractionally quantized Hall plateau and a strongly anisotropic longitudinal resistance resembling that of the stripe phases. [ABSTRACT FROM AUTHOR]

Understanding the flow of spins in magnetic layered structures has resulted in an increase in data storage density in hard drives over the past decade of more than two orders of magnitude. Following this remarkable success, the field of ‘spintronics’ or spin-based electronics is moving beyond effects based on local spin polarization and is turning towards spin–orbit interaction (SOI) effects, which hold promise for the production, detection and manipulation of spin currents, allowing coherent transmission of information within a device. Although SOI-induced spin transport effects have been observed in two- and three-dimensional samples, these have been subtle and elusive, often detected only indirectly in electrical transport or else with more sophisticated techniques. Here we present the first observation of a predicted ‘spin–orbit gap’ in a one-dimensional sample, where counter-propagating spins, constituting a spin current, are accompanied by a clear signal in the easily measured linear conductance of the system. We first introduce the class of phenomena we dub ‘the one-dimensional spin–orbit gap’ using a simple example adapted from ref. 10, then describe our experiment in detail and finally present a more elaborate model that captures most of the features seen in our data. [ABSTRACT FROM AUTHOR]

The two-dimensional electron system is a powerful laboratory for investigating the physics of interacting particles. Application of a large magnetic field produces massively degenerate quantum levels known as Landau levels; within a Landau level the kinetic energy of the electrons is suppressed, and electron–electron interactions set the only energy scale. Coulomb interactions break the degeneracy of the Landau levels and can cause the electrons to order into complex ground states. Here we observe, in the high energy single particle spectrum of this system, salient and unexpected structure that extends across a wide range of Landau level filling fractions. The structure appears only when the two-dimensional electron system is cooled to very low temperatures, indicating that it arises from delicate ground state correlations. We characterize this structure by its evolution with changing electron density and applied magnetic field, and present two possible models for understanding these observations. Some of the energies of the features agree qualitatively with what might be expected for composite fermions, which have proven effective for interpreting other experiments in this regime. At the same time, a simple model with electrons localized on ordered lattice sites also generates structure similar to that observed in the experiment. Neither of these models alone is sufficient to explain the observations across the entire range of densities measured. The discovery of this unexpected prominent structure in the single particle spectrum of an otherwise thoroughly studied system suggests that there exist core features of the two-dimensional electron system that have yet to be understood. [ABSTRACT FROM AUTHOR]

When a strong magnetic field is applied perpendicularly (along z) to a sheet confining electrons to two dimensions (x–y), highly correlated states emerge as a result of the interplay between electron–electron interactions, confinement and disorder. These so-called fractional quantum Hall liquids form a series of states that ultimately give way to a periodic electron solid that crystallizes at high magnetic fields. This quantum phase of electrons has been identified previously as a disorder-pinned two-dimensional Wigner crystal with broken translational symmetry in the x–y plane. Here, we report our discovery of a new insulating quantum phase of electrons when, in addition to a perpendicular field, a very high magnetic field is applied in a geometry parallel (y direction) to the two-dimensional electron sheet. Our data point towards this new quantum phase being an electron solid in a ‘quasi-three-dimensional’ configuration induced by orbital coupling with the parallel field. [ABSTRACT FROM AUTHOR]

Semiconductor devices continue to press into the nanoscale regime, and new applications have been proposed for which a single dopant atom acts as the functional part of the device. Moreover, because shallow donors and acceptors are analogous to hydrogen atoms, experiments on small numbers of dopants have the potential to be a testing ground for fundamental questions of atomic and molecular physics. Although dopant properties are well understood with respect to the bulk, the study of configurations of dopants in small numbers is an emerging field. Here we present local capacitance measurements of electrons entering silicon donors in a gallium arsenide heterostructure. To the best of our knowledge, this study is the first example of single-electron capacitance spectroscopy carried out directly with a scanning probe tip. The precise position with respect to tip voltage of the observed single-electron peaks varies with the location of the probe, reflecting a random distribution of silicon within the donor plane. In addition, three broad capacitance peaks are observed independent of the probe location, indicating clusters of electrons entering the system at approximately the same voltages. These broad peaks are consistent with the addition energy spectrum of donor molecules, effectively formed by nearest-neighbour pairs of silicon donors. [ABSTRACT FROM AUTHOR]

The magnetoresistance oscillations that occur in a two-dimensional electron system exposed to strong microwave radiation when the microwave frequency ω coincides with the nth subharmonic of the cyclotron frequency ω c have been investigated for n = 2, 3, and 4. It is shown that these subharmonic features can be explained within a nonequilibrium energy distribution function picture without invoking multiphoton absorption processes. The existence of a frequency threshold above which such oscillations disappear lends further support to this explanation. [ABSTRACT FROM AUTHOR]

GaAs-based two-dimensional electron gases (2DEGs) show a wealth of remarkable electronic states, and serve as the basis for fast transistors, research on electrons in nanostructures and prototypes of quantum-computing schemes. All of these uses depend on the extremely low levels of disorder in GaAs 2DEGs, with low-temperature mean free paths ranging from micrometres to hundreds of micrometres. Here we study how disorder affects the spatial structure of electron transport by imaging electron flow in three different GaAs/AlGaAs 2DEGs, whose mobilities range over an order of magnitude. As expected, electrons flow along narrow branches that we find remain straight over a distance roughly proportional to the mean free path. We also observe two unanticipated phenomena in high-mobility samples. In our highest-mobility sample we observe an almost complete absence of sharp impurity or defect scattering, indicated by the complete suppression of quantum coherent interference fringes. Also, branched flow through the chaotic potential of a high-mobility sample remains stable to significant changes to the initial conditions of injected electrons. [ABSTRACT FROM AUTHOR]

Spectroscopic methods involving the sudden injection or ejection of electrons in materials are a powerful probe of electronic structure and interactions. These techniques, such as photoemission and tunnelling, yield measurements of the ‘single-particle’ density of states spectrum of a system. This density of states is proportional to the probability of successfully injecting or ejecting an electron in these experiments. It is equal to the number of electronic states in the system able to accept an injected electron as a function of its energy, and is among the most fundamental and directly calculable quantities in theories of highly interacting systems. However, the two-dimensional electron system (2DES), host to remarkable correlated electron states such as the fractional quantum Hall effect, has proved difficult to probe spectroscopically. Here we present an improved version of time-domain capacitance spectroscopy that allows us to measure the single-particle density of states of a 2DES with unprecedented fidelity and resolution. Using the method, we perform measurements of a cold 2DES, providing direct measurements of interesting correlated electronic effects at energies that are difficult to reach with other techniques; these effects include the single-particle exchange-enhanced spin gap, single-particle lifetimes in the quantum Hall system, and exchange splitting of Landau levels not at the Fermi surface. [ABSTRACT FROM AUTHOR]

The melting temperature Tm of a solid is generally determined by its solid–liquid transition on being heated at a fixed pressure, usually ambient pressure. It is also determined indirectly by the density n by means of the equation of state. This remains true even for solid helium, in which quantum effects often lead to unusual properties. Here, we present experimental evidence to show that for a two-dimensional (2D) solid formed by electrons in a semiconductor sample under a strong perpendicular magnetic field (B), Tm is not controlled by n, but effectively by the quantum correlation between the electrons through the Landau level filling factor ν=nh/eB (where h is the Planck constant and e is the electronic charge). Such melting behaviour, different from that of all other known solids (including a classical 2D electron solid at zero magnetic field), suggests the quantum nature of the magnetic-field-induced electron solid. Moreover, Tm increases with the strength of the sample-dependent disorder that tends to pin the electron solid in place. [ABSTRACT FROM AUTHOR]

The conductivity of an Al0.24Ga0.76As/GaAs quantum well was studied as a function of the surface charge generated by electron bombardment of the sample in the absence of an externally applied surface electric field. Under a suitable rate of electron irradiation, it was possible to completely shut off the conductive channel, implying a surface density $n=2.5 \times 10^{11}\,\mbox{el/cm}^2 $. Light illumination quenches the increase of the resistivity, apparently due to photoemission from the metastable surface states. Upon turning off the electron bombardment the surface charge on adsorbed layers of xenon and water at 8 K decays in room temperature darkness with a lifetime τ= 0.30 ±0.02 s. The average charging efficiency, is μ0 ≃0.001. Surface charging is shown to be an effective method for contactless gating of field effect devices. [ABSTRACT FROM AUTHOR]

At present, wavelength-division-multiplexed fibre lines routinely operate at 10 Gbit s−1 per channel. The transition from static-path networks to true all-optical networks encompassing many nodes, in which channels are added/dropped and efficiently reassigned, will require improved tools for all-optical wavelength shifting. Specifically, one must be able to shift the carrier wavelength (frequency) of an optical data signal over tens of nanometres (a THz range) without the bottleneck of electrical conversion. Popular approaches to this problem make use of the nonlinear interaction between two wavelengths within a semiconductor optical amplifier whereas more novel methods invoke terahertz-frequency electro–optic modulation and polaritons. Here we outline the principles and demonstrate the use of optically excited plasmons as a tunable frequency source that can be mixed with a laser frequency through Raman scattering. The scheme is all-optical and enables dynamical control of the output carrier wavelength simply by varying the power of a control laser. [ABSTRACT FROM AUTHOR]

Presents a study about the electrical resistance in a single-mode ballistic quantum wire. Research methodology; Results and discussion; Conclusions.

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 h e 2 ∕ 3 2 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. [ABSTRACT FROM AUTHOR]

One of the most intriguing and fundamental properties of topological systems is the correspondence between the conducting edge states and the gapped bulk spectrum. Here, we use a GaAs cleaved edge quantum wire to perform momentum-resolved spectroscopy of the quantum Hall edge states in a tunnel-coupled 2D electron gas. This reveals the momentum and position of the edge states with unprecedented precision and shows the evolution from very low magnetic fields all the way to high fields where depopulation occurs. We present consistent analytical and numerical models, inferring the edge states from the well-known bulk spectrum, finding excellent agreement with the experiment—thus providing direct evidence for the bulk to edge correspondence. In addition, we observe various features beyond the single-particle picture, such as Fermi level pinning, exchange-enhanced spin splitting and signatures of edge-state reconstruction. [ABSTRACT FROM AUTHOR]