Search NASA⌕ Search

SEARCH · Search NASA

Results for “quantum Hall effect”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
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↗
NASA NTRS1989

Effective-field-theory model for the fractional quantum Hall effect

Starting directly from the microscopic Hamiltonian, a field-theory model is derived for the fractional quantum Hall effect. By considering an approximate coarse-grained version of the same model, a Landau-Ginzburg theory similar to that of Girvin (1986) is constructed. The partition function of the model exhibits cusps as a function of density. It is shown that the collective density fluctuations are massive.

Zhang, S. C.↗
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 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 OSTI2024

Noncommutative gauge symmetry in the fractional quantum Hall effect

Abstract We show that a system of particles on the lowest Landau level can be coupled to a probe U(1) gauge field$$ \mathcal{A} $$ A μ in such a way that the theory is invariant under a noncommutative U(1) gauge symmetry. While the temporal component$$ \mathcal{A} $$ A 0 of the probe field is coupled to the projected density operator, the spatial components$$ \mathcal{A} $$ A i are best interpreted as quantum displacements, which distort the interaction potential between the particles. We develop a Seiberg-Witten-type map from the noncommutative U(1) gauge symmetry to a simpler version, which we call “baby noncommutative” gauge symmetry, where the Moyal brackets are replaced by the Poisson brackets. The latter symmetry group is isomorphic to the group of volume preserving diffeomorphisms. By using this map, we resolve the apparent contradiction between the noncommutative gauge symmetry, on the one hand, and the particle-hole symmetry of the half-filled Landau level and the presence of the mixed Chern-Simons terms in the effective Lagrangian of the fractional quantum Hall states, on the other hand. We outline the general procedure which can be used to write down effective field theories which respect the noncommutative U(1) symmetry.

Physics↗
DOE OSTI2024

High-temperature quantum valley Hall effect with quantized resistance and a topological switch

Edge states of a topological insulator can be used to explore fundamental science emerging at the interface of low dimensionality and topology. Achieving a robust conductance quantization, however, has proven challenging for helical edge states. In this work, we show wide resistance plateaus in kink states—a manifestation of the quantum valley Hall effect in Bernal bilayer graphene—quantized to the predicted value at zero magnetic field. The plateau resistance has a very weak temperature dependence up to 50 kelvin and is flat within a dc bias window of tens of millivolts. We demonstrate the electrical operation of a topology-controlled switch with an on/off ratio of 200. These results demonstrate the robustness and tunability of the kink states and its promise in constructing electron quantum optics devices.

Science & Technology - Other Topics↗
DOE OSTI2025

Fractional Quantum Anomalous Hall Effect

The realization of the fractional quantum anomalous Hall effect (FQAHE) in a zero-field fractional Chern insulator is a new advancement in condensed matter physics, resulting from the interplay among strong correlations, topology, and spontaneous time-reversal symmetry breaking in lattice systems. In this review, we highlight the experimental and theoretical progress toward achieving FQAHE in two material platforms: twisted bilayer MoTe 2 and rhombohedral-stacked multilayer graphene. These systems host narrow topological bands with nontrivial Chern numbers, enabling interaction-driven fractionalized states analogous to the fractional quantum Hall effect, but without external magnetic fields. We discuss how spontaneous ferromagnetism, moiré lattice reconstruction, and band topological effects underpin the emergence of FQAHE in twisted MoTe 2 . We describe experimental discoveries of zero-field fractional Chern insulators in both transport and optical experiments, as well as signatures of composite Fermi liquids and higher-energy Chern band, which may shed light on engineering nonabelian states. In rhombohedral graphene/hexagonal boron nitride moiré superlattices, we review the recent observations of fractionally quantized Hall resistance, connections between FQAHE and extended quantum anomalous Hall phases, and the coexistence of superconductivity and FQAHE. Furthermore, these discoveries not only deepen our understanding of strongly correlated topological matter but also open new frontiers for exploring nonabelian anyons, fault-tolerant quantum computation, and topological opto-spintronics free of magnetic fields.

bilayer↗
DOE OSTI2024

Recent progress of MnBi 2 Te 4 epitaxial thin films as a platform for realising the quantum anomalous Hall effect

Since the first realisation of the quantum anomalous Hall effect (QAHE) in a dilute magnetic-doped topological insulator thin film in 2013, the quantisation temperature has been limited to less than 1 K due to magnetic disorder in dilute magnetic systems. With magnetic moments ordered into the crystal lattice, the intrinsic magnetic topological insulator MnBi 2 Te 4 has the potential to eliminate or significantly reduce magnetic disorder and improve the quantisation temperature. Surprisingly, to date, the QAHE has yet to be observed in molecular beam epitaxy (MBE)-grown MnBi 2 Te 4 thin films at zero magnetic field, and what leads to the difficulty in quantisation is still an active research area. Although bulk MnBi 2 Te 4 and exfoliated flakes have been well studied, revealing both the QAHE and axion insulator phases, experimental progress on MBE thin films has been slower. Furthermore, understanding how the breakdown of the QAHE occurs in MnBi 2 Te 4 thin films and finding solutions that will enable mass-produced millimetre-size QAHE devices operating at elevated temperatures are required. In this mini-review, we will summarise recent studies on the electronic and magnetic properties of MBE MnBi 2 Te 4 thin films and discuss mechanisms that could explain the failure of the QAHE from the aspects of defects, electronic structure, magnetic order, and consequences of their delicate interplay. Finally, we propose several strategies for realising the QAHE at elevated temperatures in MnBi 2 Te 4 thin films.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Quantum criticality in coupled hybrid metal-semiconductor islands

We show that the combined effects of a dynamical Coulomb blockade and integer quantum Hall effect in a coupled hybrid metal-semiconductor setup provide a pathway for realizing resonant tunneling in Luttinger liquids. This hybrid setup can be brought to the quantum critical regime by varying gate voltages and contact resistances. We explore the nature of quantum criticality, Kondo effect, charge fractionalization, and transport in such a hybrid setup, and verify their robust non-Fermi-liquid behaviors. In conclusion, our work opens a promising route for quantum simulating exotic zero-temperature quantum critical phenomena associated with Luttinger-liquid physics in a nanoengineered electronic circuit with well-defined quantum Hall channels.

Coulomb blockade↗
DOE OSTI2024

Local probe of bulk and edge states in a fractional Chern insulator

The fractional quantum Hall effect is a key example of topological quantum many-body phenomena, arising from the interplay between strong electron correlation, topological order and time-reversal symmetry breaking. Recently, a lattice analogue of the fractional quantum Hall effect at zero magnetic field has been observed, confirming the existence of a zero-field fractional Chern insulator (FCI). Despite this, the bulk–edge correspondence—a hallmark of a FCI featuring an insulating bulk with conductive edges—has not been directly observed. In fact, this correspondence has not been visualized in any system for fractional states owing to experimental challenges. Here we report the imaging of FCI edge states in twisted MoTe 2 (t-MoTe 2 ) using microwave impedance microscopy. By tuning the carrier density, we observe the system evolving between metallic and FCI states, the latter of which exhibits insulating bulk and conductive edges, as expected from the bulk–boundary correspondence. Further analysis suggests the composite nature of the FCI edge states. We also observe the evolution of edge states across the topological phase transition as a function of interlayer electric field and reveal exciting prospects of neighbouring domains with different fractional orders. Furthermore, these findings pave the way for research into topologically protected one-dimensional interfaces between various anyonic states at zero magnetic field, such as gapped one-dimensional symmetry-protected phases with non-zero topological entanglement entropy, Halperin–Laughlin interfaces and the creation of non-abelian anyons.

Imaging techniques↗
DOE OSTI2025

Quantum Nonlinear Acoustic Hall Effect and Inverse Acoustic Faraday Effect in Dirac Insulators

Here, we propose to realize the quantum nonlinear Hall effect and the inverse Faraday effect through the acoustic wave in a time-reversal invariant but inversion broken Dirac insulator. We focus on the acoustic frequency much lower than the Dirac gap such that the interband transition is suppressed and these effects arise solely from the intrinsic valley-contrasting band topology. The corresponding acoustoelectric conductivity and magnetoacoustic susceptibility are both proportional to the quantized valley Chern number and independent of the quasiparticle lifetime. The linear and nonlinear components of the longitudinal and transverse topological currents can be tuned by adjusting the polarization and propagation directions of the surface acoustic wave. The static magnetization generated by a circularly polarized acoustic wave scales linearly with the acoustic frequency as well as the strain-induced charge density. Our results unveil a quantized nonlinear topological acoustoelectric response of gapped Dirac materials, like hexagonal boron nitride and transition-metal dichalcogenide, paving the way toward room-temperature acoustoelectric devices due to their large band gaps.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Interplay of superconducting, metallic, and crystalline states of composite fermions at 𝜈 = $\frac{1}{6}$ in wide quantum wells

Evidence for developing fractional quantum Hall effect (FQHE) at filling fraction 𝜈 = 1/6 and 1/8 was recently reported in wide GaAs quantum wells [Wang et al., Phys. Rev. Lett. 134, 046502 (2025)]. In this article, we theoretically investigate the nature of the state at 𝜈 = 1/6 as a function of the quantum well width and the density by considering composite-fermion (CF) crystals, CF Fermi sea, and various kinds of paired CF states. The 𝑓-wave paired state has the lowest energy among the paired CF states. However, for parameters of interest, the energies of the CF crystal, the CF Fermi liquid, and the 𝑓-wave paired CF state are too close to distinguish. We, therefore, predict that 𝑖𝑓 the FQHE at 𝜈 = 1/6 is experimentally confirmed, this state would be an 𝑓-wave paired state of CFs, which can be verified by measurement of its thermal Hall conductance. Exact diagonalization studies on clean systems with up to eight electrons show that the ground states at 𝜈 = 𝑛/(6⁢𝑛 ± 1) are incompressible for all widths and densities we have considered, and are well described by the corresponding Laughlin and Jain states. We propose a phase diagram for large quantum well widths and densities in which at zero disorder, incompressible FQHE states are stabilized at 𝜈 = 𝑛/(6⁢𝑛 ± 1) and 𝜈 = 1/6, but in between these fillings the CF crystal is stabilized. We also present a qualitative discussion on the effects of disorder and propose a schematic phase diagram based on it. With disorder, which creates a spatial variation in the filling factor, two regimes are identified: (i) for small disorder, when the incompressible states percolate at the special fillings, FQHE with quantized Hall plateaus and vanishing longitudinal resistance should occur; and (ii) for larger disorder, when the CF crystal percolates, the longitudinal resistance rises with decreasing temperature but the domains of FQHE liquid produce minima at the special filling factors. Here, experiments are consistent with the latter scenario. We also mention a possible connection of the phase diagram presented here to a puzzling behavior observed for the fractional quantum anomalous Hall effect in pentalayer graphene.

Composite fermions↗
DOE OSTI2025

Conductivity space isotherm behavior in quantum anomalous Hall devices

The quantum Hall effect (QHE) has enhanced accessibility to measure and disseminate electrical units, owed in part to the recently redefined International System of Units in 2019. Graphene remains one of the preferred options to realize the ohm despite the limitations of high magnetic fields to produce a robust QHE. Topological insulators, on the other hand, show promise in providing quantized resistance via the quantum anomalous Hall effect, a phenomenon that removes the need for magnetic fields during operation. To optimize future devices for metrological applications, it is important to gain a better understanding of magnetically doped topological insulators like Cr-doped bismuth antimony telluride. The application of differential conductivity space analyses offers a more sensitive way to analyze the data and distinguish between 2D and 3D transport behaviors. This is particularly important in thin films, where the transition between 2D and 3D behavior can be subtle. The ability to confidently determine the dimensionality of the transport is crucial for selecting appropriate theoretical models for future device optimization. Furthermore, this work identifies variable range hopping as the dominant transport mechanism in the 2D regime using a rigorous statistical analysis (via the Bayes factor). These elements assist in the understanding of microscopic processes that govern charge transport in these materials.

Tran, N. T. M. [National Inst. of Standards and Te↗
DOE OSTI2026

Nanoscale Imaging of Magnetotransport around a Circular 𝑝−𝑛 Junction in Graphene

Magnetoresistance studies of 2D systems are often shaped by the motion of electrons that occupy spatially confined wave functions, such as topological edge modes and disorder-induced bound states. Directly probing how such states form and behave in situ , under applied currents, provides a clear way of connecting microscopic physics to the macroscopic transport response. Here, in this Letter, scanning tunneling potentiometry is used to probe the local, current-induced electrochemical potential of carriers in graphene near circular 𝑝−𝑛 junctions in an out-of-plane magnetic field ranging from 0 to 1.4 T. These measurements provide detailed information about the motion of carriers at the nanometer scale, revealing how it evolves with increasing field. The electrochemical potential displays distinct patterns, such as dipoles, spirals, and concentric disks in weak, moderate, and high fields, respectively. The size and orientation of these patterns can be used to understand how local carrier dynamics change in different transport regimes as well as to directly extract physical parameters such as the electron mean free path and cyclotron diameter.

36 MATERIALS SCIENCE↗
NASA NTRS1990

AlSb/InAs/AlSb quantum wells

Researchers studied the InAs/AlSb system recently, obtaining 12nm wide quantum wells with room temperature mobilities up to 28,000 cm(exp 2)/V center dot S and low-temperature mobilities up to 325,000 cm(exp 2)/V center dot S, both at high electron sheet concentrations in the 10(exp 12)/cm(exp 2) range (corresponding to volume concentrations in the 10(exp 18)/cm(exp 2) range). These wells were not intentionally doped; the combination of high carrier concentrations and high mobilities suggest that the electrons are due to not-intentional modulation doping by an unknown donor in the AlSb barriers, presumably a stoichiometric defect, like an antisite donor. Inasmuch as not intentionally doped bulk AlSb is semi-insulating, the donor must be a deep one, being ionized only by draining into the even deeper InAs quantum well. The excellent transport properties are confirmed by other observations, like excellent quantum Hall effect data, and the successful use of the quantum wells as superconductive weak links between Nb electrodes, with unprecendentedly high critical current densities. The system is promising for future field effect transistors (FETs), but many processing problems must first be solved. Although the researchers have achieved FETs, the results so far have not been competitive with GaAs FETs.

Kroemer, Herbert↗
DOE OSTI2026

Orbital Inverse Faraday and Cotton-Mouton Effects in Hall Fluids

We report two light-induced orbital magnetization effects in quantum Hall (QH) fluids, stemming from their transverse response. The first is a purely transverse contribution to the inverse Faraday effect (IFE), where circularly polarized light induces a dc magnetization by stirring the charged fluid. This contribution dominates the IFE in the QH regime. The second is the orbital inverse Cotton-Mouton effect (ICME), in which linearly polarized light generates a dc magnetization. Since the applied field in the ICME does not break time-reversal symmetry, the induced magnetization directly probes the chiral orbital response of the fluid at the driving frequency. We estimate that the resulting magnetization lies in the range of 0.5–10 Bohr magnetons per charge carrier in materials such as graphene and transition-metal dichalcogenides (TMDs) in the QH regime. Finally, we show that the induced magnetization is accompanied by a local correction to the static particle density, enabling optical quantum printing of density profiles into the QH fluid.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗