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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Lithography-Defined Semiconductor Moirés with Anomalous In-Gap Quantum Hall States

Quantum materials and phenomena have attracted great interest for their potential applications in next-generation microelectronics and quantum-information technologies. In one especially interesting class of quantum materials, moiré superlattices (MSLs) formed by twisted bilayers of 2D materials, a wide range of novel phenomena are observed. However, there exist daunting challenges such as reproducibility and scalability of utilizing 2D MSLs for microelectronics and quantum technologies due to their exfoliate-tear-stack method. Here, we propose lithography-defined semiconductor MSLs, in which three fundamental parameters electron−electron interaction, spin−orbit coupling, and band topology are designable. We experimentally investigate quantum-transport properties in a moiré specimen made in an InAs quantum well. Strong anomalous in-gap states are observed within the same integer quantum Hall state. Our work opens up new horizons for studying 2D quantum-materials phenomena in semiconductors featuring superior industry-level quality and state-of-the-art technologies, and they may potentially enable new quantum-information and microelectronics technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Spontaneous Localization at a Potential Saddle Point from Edge State Reconstruction in a Quantum Hall Point Contact

Quantum point contacts (QPCs) are an essential component in mesoscopic devices. Here, in this work, we study the transmission of quantum Hall edge modes through a gate-defined QPC in monolayer graphene. We observe resonant tunneling peaks and a nonlinear conductance pattern characteristic of Coulomb-blockaded localized states. The in-plane electric polarizability reveals the states are localized at a classically unstable electrostatic saddle point. We explain this unexpected finding within a self-consistent Thomas-Fermi model, finding that localization of a zero-dimensional state at the saddle point is favored whenever the applied confinement potential is sufficiently soft compared to the Coulomb energy. Our results provide a direct demonstration of Coulomb-driven reconstruction at the boundary of a quantum Hall system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Localizing individual exciton on a quantum Hall antidot

Excitons are bond states of electron-hole pairs formed through Coulomb interaction. While excitonic phases have been widely studied in semiconductors and quantum Hall double-layers, prior works largely focus on bulk systems with large number of excitons, limiting their applications in quantum devices. Here, employing the approach of quantum Hall antidot with two spatially separated edge channels, we demonstrate a type of quantum Hall quasiparticle exciton which represents a quantum-coherent bound state of an electron and a hole situated on their corresponding edges coupled through intralayer tunneling and Coulomb interaction. This approach allows localization and electrical tuning of individual quantum Hall excitons. Quantum-coherent dynamics of exciton are observed in the gate-dependence of antidot conductance peaks near the electron-hole resonance, which signifies a quantum superposition of vacuum- and electron-hole pairing states. Modeling the electron-hole pair as a coupled two-level system, semi-quantitative understanding of experimental observations is achieved. This work opens avenues for creating quantum systems of multiple quantum Hall quasiparticles.

36 MATERIALS SCIENCE↗
DOE OSTI2025

High spatial resolution charge sensing of quantum Hall states

Charge distribution offers a unique fingerprint of important properties of electronic systems, including dielectric response, charge ordering, and charge fractionalization. Here, we develop an architecture for charge sensing in two-dimensional electronic systems in a strong magnetic field. We probe local change of the chemical potential in a proximitized detector layer using scanning tunneling microscopy, allowing us to infer the chemical potential and the charge profile in the sample. Our technique has both high energy (<0.3 meV) and spatial (<10 nm) resolution exceeding that of previous studies by an order of magnitude. We apply our technique to study the chemical potential of quantum Hall liquids in monolayer graphene under high magnetic fields and their responses to charge impurities. The chemical potential measurement provides a local probe of the thermodynamic gap of quantum Hall ferromagnets and fractional quantum Hall states. The screening charge profile reveals spatially oscillatory response of the quantum Hall liquids to charge impurities and is consistent with the composite Fermi liquid picture close to the half-filling. Our technique also paves the way to map moiré potentials, probe Wigner crystals, and investigate fractional charges in quantum Hall and Chern insulators.

charge sensing↗
DOE OSTI2025

Visualizing interaction-driven restructuring of quantum Hall edge states

Many topological phases host gapless boundary modes that can be dramatically modified by electronic interactions. Even for the long-studied edge modes of quantum Hall phases, forming at the boundaries of two-dimensional (2D) electron systems, the nature of such interaction-induced changes has been elusive. Despite advances made using local probes, key experimental challenges persist: the lack of direct information about the internal structure of edge states on microscopic scales, and complications from edge disorder. Here, we use scanning tunneling microscopy (STM) to image pristine electrostatically defined quantum Hall edge states in graphene with high spatial resolution and demonstrate how correlations dictate the structures of edge channels on both magnetic and atomic length scales. For integer quantum Hall states in the zeroth Landau level, we show that interactions renormalize the edge velocity, dictate the spatial profile for copropagating modes, and induce unexpected edge valley polarization that differ from those of the bulk. While some of our findings can be understood by mean-field theory, others show breakdown of this picture, highlighting the roles of edge fluctuations and inter-channel couplings. We also extend our measurements to spatially resolve the edge state of fractional quantum Hall phases and detect spectroscopic signatures of interactions in this chiral Luttinger liquid. Furthermore, our study establishes STM as a promising tool for exploring edge physics of the rapidly expanding 2D topological phases, including newly realized fractional Chern insulators.

Electronic properties and materials↗
DOE OSTI2024

Density Dependence of the Phases of the v = 1 Integer Quantum Hall Plateau in Low Disorder Electron Gases

Recent magnetotransport measurements in low-disorder electron systems confined to GaAs/AlGaAs samples reveal that the v = 1 integer quantum Hall plateau is broken into three distinct regions. These three regions are associated with two phases with different types of bulk localization: the Anderson insulator is due to random quasiparticle localization, and the integer quantum Hall Wigner solid is due to pinning of a stiff quasiparticle lattice. Universal properties of the v = 1 plateau are highlighted: the structure of the stability diagram, the nonmonotonic dependence of the activation energy on the filling factor, and the alignment of features of the activation energy with features of the stability regions of the different phases are found to be similar in three samples spanning a wide range of electron densities. Quantitative differences between the samples are also discussed, such as the dependence of the onset temperature and the activation energy of the integer quantum Hall Wigner solid on the electron density. The findings provide insights into the localization behavior along the v = 1 integer quantum Hall plateau in the low disorder regime.

Anderson insulator↗
DOE OSTI2026

Ordering the topological order in the fractional quantum Hall effect

Here, we discuss the possible topological order/topological quantum field theory of different quantum Hall systems. Given the value of the Hall conductivity, we constrain the global symmetry of the low-energy theory and its anomaly. Specifically, the one-form global symmetry and its anomaly are presented as the organizing principle of these systems. This information is powerful enough to lead to a unique minimal topological order (or a small number of minimal topological orders). Almost all of the known experimentally discovered topological orders are these minimal theories. Since this work is interdisciplinary, we made a special effort to relate to researchers with different backgrounds by providing translations between different perspectives.

Anyons↗
DOE OSTI2025

Photocurrent Nanoscopy of Quantum Hall Bulk

Understanding nanoscale electronic and thermal transport of two-dimensional (2D) electron systems in the quantum Hall regime, particularly in the bulk insulating state, poses considerable challenges. One of the primary difficulties arises from the presence of chiral edge channels, whose transport behavior obscures the investigation of the insulating bulk. Using near-field optical and photocurrent nanoscopy, we probe real-space variations of the optical and thermal dynamics of graphene in the quantum Hall regime without relying on complex sample or electrode geometries. Near the charge-neutrality point, we detect strong optical and photothermal signals from resonant inter-Landau-level (LL) magnetoexciton excitations between the zeroth and ± 1 st LLs, which gradually weaken with increasing doping due to Pauli blocking. Interestingly, at higher doping levels and full-integer LL fillings, photothermal signals reappear across the entire sample over an approximately 10 − μ m scale, indicating unexpectedly long cooling lengths and nonlocal photothermal heating through the insulating bulk. This observation suggests that thermal conductivity persists for the localized states even as electronic transport is suppressed—a clear violation of the Wiedemann-Franz law. Our experiments provide novel insights into nanoscale thermal and electronic transport in incompressible 2D gases, highlighting the roles of magnetoexcitons and chiral edge states in the thermo-optoelectric dynamics of the Dirac quantum Hall state. Published by the American Physical Society 2025

36 MATERIALS SCIENCE↗
DOE OSTI2025

Designing an exciton-condensate Josephson junction in quantum Hall heterostructures

The exciton condensate, a counterpart of superconductors realized in two-dimensional quantum Hall bilayer systems, has yet to demonstrate definitive experimental evidence of phase coherence such as the Josephson effect. This work introduces a gate-defined Josephson junction designed to exhibit the in-plane Josephson effect in van der Waals heterostructures. Unlike superconducting S-I-S junctions, the proposed device leverages a nearly layer-polarized gated region to mediate Josephson coupling via layer pseudospin variation. This coupling mechanism is tunable through gate voltages and magnetic fields, offering a high degree of experimental control. We demonstrate the feasibility of the design using realistic parameters, paving the way for direct observation of excitonic phase coherence in clean quantum Hall systems.

Wang, Tianle↗
DOE OSTI2025

High-resolution tunnelling spectroscopy of fractional quantum Hall states

Strong interactions between electrons in two-dimensional systems in the presence of a high magnetic field give rise to fractional quantum Hall states that host quasiparticles with a fractional charge and fractional exchange statistics. Here, in this work, we demonstrate high-resolution scanning tunnelling microscopy and spectroscopy of fractional quantum Hall states in ultra-clean Bernal-stacked bilayer graphene devices. Spectroscopy measurements show sharp excitations that have been predicted to emerge when electrons fractionalize into bound states of quasiparticles. We found energy gaps for candidate non-abelian fractional states that are larger by a factor of five than those in other related systems, for example, semiconductor heterostructures, and this suggests that bilayer graphene is an ideal platform for manipulating these quasiparticles and for creating topological quantum bits. We also found previously unobserved fractional states in our very clean graphene samples.

quantum Hall↗
DOE OSTI2026

Microwave Imaging of Edge Conductivity in Graphene at Charge Neutrality and Quantum Hall States

Here, we report local conductivity imaging of edge states in monolayer graphene by millikelvin microwave impedance microscopy. At the charge-neutrality point, as the magnetic field increases, the local conductivity at the edge drops to zero more slowly than in the bulk. This behavior is consistent with the calculated spatial profile of the charge gap in the canted antiferromagnetic phase. For comparison, we also perform microwave imaging of integer quantum Hall states away from neutrality, which host dissipationless chiral edge channels. The evolution of the edge signal as a function of the bulk gap is fundamentally different between the Landau level filling factor 𝜈 = 0 and |𝜈| ≥ 1 integer quantum Hall states, which can be qualitatively explained by numerical simulations and theoretical analysis. Our results provide a comprehensive microscopic picture of the edge and bulk states as the Fermi level moves across the unique Landau-level spectrum of graphene.

Hall effect↗
DOE OSTI2024

Splitting of the Girvin-MacDonald-Platzman Density Wave and the Nature of Chiral Gravitons in the Fractional Quantum Hall Effect

A fundamental manifestation of the nontrivial correlations of an incompressible fractional quantum Hall (FQH) state is that an electron added to it disintegrates into more elementary particles, namely fractionally-charged composite fermions (CFs). We show here that the Girvin-MacDonald-Platzman (GMP) density-wave excitation of the 𝜈=𝑛/(2⁢𝑝⁢𝑛±1) FQH states also splits into more elementary single CF excitons. In particular, the GMP graviton, which refers to the recently observed spin-2 neutral excitation in the vanishing wave vector limit [Liang et al., Nature 628, 78 (2024)], remains undivided for 𝜈 =𝑛/(2⁢𝑛 ±1) but splits into two gravitons at 𝜈 =𝑛/(4⁢𝑛 ±1) with 𝑛 >1. Here, a detailed experimental confirmation of the many observable consequences of the splitting of the GMP mode should provide a unique window into the correlations underlying the FQH effect.

Composite fermions↗
DOE OSTI2025

Unlocking New Regimes in Fractional Quantum Hall Effect with Quaternions

We demonstrate that formulating the composite-fermion theory of the fractional quantum Hall (FQH) effect in terms of quaternions greatly expands its reach and opens the door into many interesting issues that were previously not amenable to quantitative theoretical investigation. As an illustration, we explore the possibility of a nematic or a charge-density wave instability of the composite-fermion Fermi sea at half-filled Landau level and of the nearby FQH states by looking for a gap closing instability of the neutral magneto-roton excitation. As a result, our quaternion formulation of the FQH effect has been inspired by mathematical developments in the theoretical analyses of gravitational wave modes and cosmic microwave background radiation, where an important role is played by spin-weighted spherical harmonics that are nothing but monopole harmonics appearing in the spherical geometry for the FQH effect.

Composite fermions↗
DOE OSTI2026

Competition between excitonic insulators and quantum Hall states in correlated electron–hole bilayers

Excitonic insulators represent a unique quantum phase of matter that enables the study of exotic quantum bosonic states. Strongly coupled electron–hole bilayers, which host stable dipolar exciton fluids with an exciton density that can be adjusted electrostatically, offer an ideal platform to investigate correlated excitonic insulators. On the basis of electron–hole bilayers made of MoSe2/hexagonal boron nitride/WSe2 heterostructures, here we study the behaviour of excitonic insulators in a perpendicular magnetic field. We report the observation of excitonic quantum oscillations in both Coulomb drag signals and electrical resistance at low to medium magnetic fields. Under a strong magnetic field, we identify multiple quantum phase transitions between the excitonic insulator phase and the bilayer quantum Hall insulator phase. These findings underscore the interplay between the electron–hole interactions and Landau-level quantization, and enable further exploration of quantum phenomena in composite bosonic insulators.

Qi, Ruishi↗
DOE OSTI2026

Slow Quasiparticle Dynamics and Anyonic Statistics in a Fractional Quantum Hall Fabry-Pérot Interferometer

Anyons are two-dimensional particles with fractional exchange statistics that emerge as elementary excitations of fractional quantum Hall phases. Experimentally, their exchange statistics can be measured in the edge-state Fabry-Pérot interferometer, wherein the presence of 𝑁 𝑞⁢𝑝 localized anyons contributes a phase 𝑁 𝑞⁢𝑝⁢ 𝜃 𝑎 to the interference pattern where 𝜃 𝑎 is twice the exchange phase. Here we report the observation of large, hysteretic phase jumps in a monolayer graphene Fabry-Pérot interferometer at 𝜈 = 1/3. When the filling factor is increased from 𝜈 < 1/3 toward the center of the plateau, we observe phase slips with magnitude Δ⁢𝜃 ≈ 2⁢𝜋/3, consistent with the addition of individual quasiparticles to the interferometer bulk. These phase slips occur as instantaneous jumps in the interference signal, with intervals between the jumps indicating quasiparticle equilibration times exceeding 20 min. We use this long timescale to investigate the effect of changes in interferometer area 𝐴 𝐼 and 𝑁 𝑞⁢𝑝 independently at fixed magnetic field, revealing a striking memory effect in the phase slip magnitude. In particular, as the 𝜈 =1/3 plateau is approached from higher filling, we observed phase slips with Δ⁢𝜃 significantly larger than 2⁢𝜋/3 over the same range of gate voltage where quantized jumps are seen for increasing 𝜈. We discuss this asymmetry in terms of bulk-edge coupling of quasiparticles localized near the edge or in the bulk, and argue that this effect can be qualitatively reconciled with theoretical expectations for strongly interacting quasiparticles in the presence of weak disorder and strongly nonequilibrium charge dynamics. Besides providing a replication of interferometric measurements sensitive to 𝜃 𝑎 , our results highlight the key role played by charge dynamics on signatures of the anyon phase, and demonstrate that fractional quasiparticles can be indefinitely localized in nonequilibrium configurations.

anyons↗
DOE OSTI2025

Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene

A two-dimensional electron system exposed to a strong magnetic field produces a plethora of strongly interacting fractional quantum Hall (FQH) states, the complex topological orders of which are revealed through exotic emergent particles, such as composite fermions, and fractionally charged Abelian and non-Abelian anyons. Much insight has been gained by the study of multicomponent FQH states, where spin and pseudospin indices of the electron contribute additional correlation. Traditional multicomponent FQH states develop in situations where the components share the same orbital states and the resulting interactions are pseudospin independent; this homo-orbital nature is also crucial to their theoretical understanding. Here, we study “hetero-orbital” two-component FQH states, in which the orbital index is part of the pseudospin, rendering the multicomponent interactions strongly SU(2) anisotropic in the pseudospin space. Such states, obtained in bilayer graphene at the isospin transition between 𝑁 = 0 and 𝑁 = 1 electron Landau levels, are markedly different from previous homo-orbital two-component FQH states. In particular, we observe strikingly different behaviors for the parallel-vortex and reverse-vortex attachment composite fermion states, and an anomalously strong two-component 2/5 state over a wide range of magnetic field before it abruptly disappears at a high field. Our findings, combined with detailed theoretical calculations, reveal the surprising robustness of the hetero-orbital FQH effects, significantly enriching our understanding of FQH physics in this novel regime.

Bilayer graphene↗
DOE OSTI2026

Excitation and tunneling spectra of a fractional quantum Hall system in the thin-cylinder limit

Here, the excitations of fractional quantum Hall effect (FQHE) states have been largely inaccessible to experimental probes until recently. New electron scanning tunneling microscopy (STM) results from Hu et al. [Nat. Phys. 21, 716 (2025)] show promise in detecting and identifying these excited states via the local density of states (LDOS) spectrum. On a torus, there exists a mapping from the lowest Landau level states to a 1D lattice with a Hamiltonian that features dipole moment conservation. In this work, we apply perturbation theory starting from the thin-cylinder limit (𝐿 𝑥 → ∞, 𝐿 𝑦 < 𝑙 𝐵 for torus dimensions 𝐿 𝑥 and 𝐿 𝑦 and magnetic length 𝑙 𝐵 ) to obtain an analytical approach to the low-lying neutral and charged excitations of the 𝜈 = 1/3 FQHE state. Notably, in the thin cylinder, we can systematically enumerate all the low-lying excitations by the patterns of “dipoles” formed by the electron occupation pattern on the 1D lattice. We find that the thin-cylinder limit predicts a significant dispersion of the low-lying neutral excitations but sharpness of the LDOS spectra, which measure charged excitations. We also discuss connections between our work and several different approaches to the FQHE STM spectra, including those using the composite fermion theory. Numerical exact diagonalization beyond the thin-cylinder limit suggests that the energies of charged excitations remain largely confined to a narrow range of energies, which in experiments might appear as a single peak.

Adhidewata, Jyesta M. [University of California, B↗