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All sourcesNASA NTRSDOE OSTI
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 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 OSTI2024

Even–Odd Layer-Dependent Exchange Bias Effect in MnBi 2 Te 4 Chern Insulator Devices

Magnetic topological materials with coexisting magnetism and nontrivial band structures exhibit many novel quantum phenomena, including the quantum anomalous Hall effect, the axion insulator state, and the Weyl semimetal phase. As a stoichiometric layered antiferromagnetic topological insulator, thin films of MnBi 2 Te 4 show fascinating even–odd layer-dependent physics. Here, in this work, we fabricate a series of thin-flake MnBi 2 Te 4 devices using stencil masks and observe the Chern insulator state at high magnetic fields. Upon magnetic field training, a large exchange bias effect is observed in odd but not in even septuple layer (SL) devices. Through theoretical calculations, we attribute the even–odd layer-dependent exchange bias effect to the contrasting surface and bulk magnetic properties of MnBi 2 Te 4 devices. Our findings reveal the microscopic magnetic configuration of MnBi 2 Te 4 thin flakes and highlight the challenges in replicating the zero magnetic field quantum anomalous Hall effect in odd SL MnBi 2 Te 4 devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Chern Insulators at Integer and Fractional Filling in Moiré Pentalayer Graphene

The advent of moiré platforms for engineered quantum matter has led to discoveries of integer and fractional quantum anomalous Hall effects, with predictions for correlation-driven topological states based on electron crystallization. Here, we report an array of trivial and topological insulators formed in a moiré lattice of rhomobohedral pentalayer graphene (R5G). At a doping of one electron per moiré unit cell ( ν = 1 ), we see a correlated insulator with a Chern number that can be tuned between C = 0 and + 1 by an electric displacement field. This is accompanied by a series of additional Chern insulators with C = + 1 originating from fractional fillings of the moiré lattice— ν = 1 / 4 , 1 / 3 , and 2 / 3 —associated with the formation of moiré-driven topological electronic crystals. At ν = 2 / 3 the system exhibits an integer quantum anomalous Hall effect at zero magnetic field, but further develops hints of an incipient C = 2 / 3 fractional Chern insulator in a modest field. Our results establish moiré R5G as a fertile platform for studying the competition and potential intertwining of integer and fractional Chern insulators. Published by the American Physical Society 2025

Waters, Dacen (ORCID:0000000335880039)↗
DOE OSTI2026

Intrinsic even-odd thickness-driven anomalous Hall effect in epitaxial MnBi2⁢Te4 thin films

We demonstrate precise control of magnetism in MnBi2⁢Te4 thin films through careful synthesis by molecular beam epitaxy, achieving minimal defects and accurate layer thickness control. By optimizing Mn-Bi-Te ratios and growth temperatures, we minimize detrimental self-doping effects and accurately target integer-layer films. X-ray diffraction and reflectivity provide quantitative measures of film quality and thickness. When these macroscale probes of structure and thickness are integrated with magnetotransport measurements, a striking even-odd layer dependence of the anomalous Hall effect is revealed. Odd-layer films exhibit a large hysteresis up to the Néel temperature (∼25K), consistent with noncompensated antiferromagnetism, while even-layer films show minimal response, as expected for an antiferromagnet. The sign of the anomalous Hall effect exhibits a sign reversal for intrinsic magnetism versus magnetism associated with defects. This work identifies critical factors for inducing pure, noncompensated ferromagnetism and reveals the characteristics of the intrinsic anomalous Hall effect in MnBi2⁢Te4, which together is a step toward realizing the zero-field quantum anomalous Hall effect in topological materials.

Mallick, Deb [ORNL] (ORCID:000900005806411X)↗
DOE OSTI2026

Spin Texture Control and Magnetic Gap Engineering in a Ferromagnetic Insulator–Topological Insulator Sandwiched Heterostructure

Quantum materials that combine magnetism with topological order are emerging as key platforms for next-generation spintronics and low-energy electronics. They enable the realization of emergent quantum phenomena, such as the quantum anomalous Hall effect and axion insulator states. The ferromagnetic insulator (FMI)/topological insulator (TI)/FMI sandwich structure of a single-septuple layer (1SL) MnBi 2 Te 4 /four-quintuple layer (4QL) Bi 2 Te 3 /1SL MnBi 2 Te 4 holds great potential to achieve such desirable quantum phenomena at an elevated temperature, owing to its large Dirac point band gap and high Curie temperature. Here, for this work, spin- and angle-resolved photoemission spectroscopy (spin-ARPES) is employed to directly verify that the band gap arises from broken time-reversal symmetry via proximity-driven magnetization. This study demonstrates direct control of the spin state via external magnetic fields and unambiguously confirms the exchange interaction as the gap-opening mechanism. The robust magnetic gap and controllable spin texture make this heterostructure a suitable candidate for spintronic applications and magnetic topological quantum phases.

exchange gap↗
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

Moiré-driven topological electronic crystals in twisted graphene

In a dilute two-dimensional electron gas, Coulomb interactions can stabilize the formation of a Wigner crystal. Although Wigner crystals are topologically trivial, it has been predicted that electrons in a partially filled band can break continuous translational symmetry and time-reversal symmetry spontaneously, resulting in a type of topological electron crystal known as an anomalous Hall crystal. Here we report signatures of a generalized version of the anomalous Hall crystal in twisted bilayer–trilayer graphene, whose formation is driven by the moiré potential. The crystal forms at a band filling of one electron per four moiré unit cells (ν = 1/4) and quadruples the unit-cell area, coinciding with an integer quantum anomalous Hall effect. The Chern number of the state is exceptionally tunable, and it can be switched reversibly between +1 and −1 by electric and magnetic fields. Several other topological electronic crystals arise in a modest magnetic field, originating from ν = 1/3, 1/2, 2/3 and 3/2. As a result, the quantum geometry of the interaction-modified bands is likely to be very different from that of the original parent band, which enables possible future discoveries of correlation-driven topological phenomena.

Electronic properties and materials↗
DOE OSTI2024

Atomic-Scale Characterization of Dilute Dopants in Topological Insulators via STEM–EDS Using Registration and Cell Averaging Techniques

Magnetic dopants in three-dimensional topological insulators (TIs) offer a promising avenue for realizing the quantum anomalous Hall effect (QAHE) without the necessity for an external magnetic field. Understanding the relationship between site occupancy of magnetic dopant elements and their effect on macroscopic property is crucial for controlling the QAHE. By combining atomic-scale energy-dispersive X-ray spectroscopy (EDS) maps obtained by aberration-corrected scanning transmission electron microscopy (AC-STEM) and novel data processing methodologies, including semi-automatic lattice averaging and frame registration, we have determined the substitutional sites of Mn atoms within the 1.2% Mn-doped Sb 2 Te 3 crystal. More importantly, the methodology developed in this study extends beyond Mn-doped Sb 2 Te 3 to other quantum materials, traditional semiconductors, and even electron irradiation sensitive materials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Nanoscale Control of Intrinsic Magnetic Topological Insulator MnBi 2 Te 4 Using Molecular Beam Epitaxy: Implications for Defect Control

Intrinsic magnetic topological insulators have emerged as a promising platform to study the interplay between the topological surface states and ferromagnetism. This unique interplay can give rise to a variety of exotic quantum phenomena, including the quantum anomalous Hall effect and axion insulating states. Here, in this study, utilizing molecular beam epitaxy (MBE), we present a comprehensive study of the growth of MnBi 2 Te 4 thin films on Si (111), epitaxial graphene, and highly ordered pyrolytic graphite substrates. By combining a suite of in situ characterization techniques, we obtain critical insights into the nanoscale control of MnBi 2 Te 4 epitaxial growth. First, we extract the free energy landscape for the epitaxial relationship as a function of the in-plane angular distribution. Then, by employing an optimized layer-by-layer growth, we determine the chemical potential and Dirac point of the thin film at different thicknesses and how this quantity is manifested by the dopant compensation from different antisite defects. Overall, these results establish a foundation for understanding the growth kinetics of MnBi 2 Te 4 and pave the way for future applications of MBE-grown thin films in emerging topological quantum materials.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Visualizing electronic structure of twisted bilayer MoTe 2 in devices

The pursuit of emergent quantum phenomena lies at the forefront of modern condensed matter physics. A recent breakthrough in this arena is the discovery of the fractional quantum anomalous Hall effect (FQAHE) in twisted bilayer MoTe₂ (tbMoTe₂), marking a paradigm shift and establishing a versatile platform for exploring the intricate interplay among topology, magnetism, and electron correlations. While significant progress has been made through both optical and electrical transport measurements, direct experimental insights into the electronic structure – crucial for understanding and modeling this system – have remained elusive. Here, using spatially and angle-resolved photoemission spectroscopy (μ-ARPES), we directly map the electronic band structure of tbMoTe₂. We identify the valence band maximum, whose partial filling underlies the FQAHE, at the K points, situated approximately 150 meV above the Γ valley. By fine-tuning the doping level via in-situ alkali metal deposition, we also resolve the conduction band minimum at the K point, providing direct evidence that tbMoTe₂ exhibits a direct band gap – distinct from all previously known moiré bilayer transition metal dichalcogenide systems. These results offer critical insights for theoretical modeling and advance our understanding of fractionalized excitations and correlated topological phases in this emergent quantum material.

Chen, Cheng [Univ. of Oxford (United Kingdom)]↗
DOE OSTI2025

Spectroscopic evidence of intra-unit-cell charge redistribution in a charge-neutral magnetic topological insulator

The magnetic topological insulator MnBi 6 Te 10 has emerged as a promising candidate for realizing the quantum anomalous Hall effect (QAHE), owing to its ability to retain ferromagnetism through precise control of anti-site defects. The next important task for realizing the QAHE is to tune the chemical potential into the energy gap formed by the broken time-reversal symmetry. Here we reveal an intra-unit-cell charge redistribution even when the overall doping suggests a near-charge-neutral condition. By performing time- and angle-resolved photoemission spectroscopy (trARPES) on the optimally 18% Sb-doped MnBi 6 Te 10 , we observe transient surface photovoltage (SPV) effects on both the MnBi 2 Te 4 and single-Bi 2 Te 3 terminations. Furthermore, we observe a time-dependent splitting of the band structure indicating multiple SPV shifts with different magnitudes. This observation suggests that adjacent plateaus with nominally the same terminating layer exhibit a strong intra-unit-cell charge redistribution, resulting in spontaneous electrical polarization. This is consistent with static micro-ARPES measurements revealing significant doping deviations from the charge-neutral configuration. Our findings underscore the challenges of engineering the family of Mn-Bi-Te materials to realize QAHE purely through chemical doping. Achieving the desired topological quantum phase requires both a uniform carrier doping and a ferromagnetic ground state. Furthermore, the light-induced polarization within each unit cell of ferromagnetic Mn(Bi 0.82 Sb 0.18 ) 6 Te 10 may open new possibilities for optoelectronic and spintronics.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2025

Emergence of Moiré Dirac Fermions at the Interface of Topological and 2D Magnetic Insulators

Dirac Fermions on the surface of the topological insulator are spin-momentum locked and topologically protected, making them interesting for spintronics and quantum computing applications. When in proximity to magnetism and superconductivity, these electronic states could result in quantum anomalous Hall effect and Majorana Fermions, respectively. An even more dramatic enrichment of the topological insulators’ physics is expected for moiré superlattices, where, analogously to the twisted graphene layers, electronic correlations could be strongly enhanced, a task previously notoriously difficult to achieve in topological matter. Until now, the experimental confirmation of such moiré properties has remained elusive. Here, we grow the two-dimensional van der Waals magnetic insulators FeX 2 (where X = Cl or Br) on top of the topological insulator Bi 2 Se 3 and establish a moiré superlattice formation at the interface. By means of scanning tunneling microscopy and angle-resolved photoemission spectroscopy, we investigate the electronic properties of the formed moiré superlattice and demonstrate its tunability via the film choice. We reveal replicated Dirac cones and focus on their intersections, which, in the case of FeBr 2 /Bi 2 Se 3 , occur below the Fermi level. We identify the signatures of small gaps at the intersections around the M̅ i points that we attribute to the moiré interaction. These findings point to the specific type of magnetic moiré potential that breaks the time-reversal symmetry at these points but not at the $\barΓ$ point. Our observations provide an intriguing scenario of correlated topological phases induced by moiré superlattice that may result in topological superconductivity, high Chern number phases, and exotic noncollinear magnetic textures.

2D magnets↗
DOE OSTI2025

Intercalation-Engineered Out-of-Plane Polarized van der Waals Ferromagnetic Superlattice with Room-Temperature Néel-Type Skyrmions

Superlattices (SLs) based on two-dimensional (2D) van der Waals (vdW) materials, abbreviated as 2D-SLs, have garnered significant attention due to their customizable properties. 2D-SLs can be engineered by mechanical stacking or chemical intercalation to achieve diverse forms of symmetry breaking, resulting in exotic phenomena like the quantum anomalous Hall effect and topological magnetism. Hitherto, broken symmetries in 2D-SLs have been widely produced within lateral planes or three dimensions. However, symmetry breaking along the vertical direction, specifically as an out-of-plane one-dimensional (1D) polarized superlattice, has not yet been achieved. Here, in this paper, we report a so far unseen out-of-plane 1D polarized vdW ferromagnetic superlattice achieved through an approach of two-step intercalation and de-embedding of chromium (Cr)-based 2D vdW magnets. The off-centering polarization of both intrinsic and intercalated Cr atoms in this (1 × 1 × 2) superstructure breaks the mirror symmetry vertically, yielding a Dzyaloshinskii–Moriya interaction (DMI). This results in high-density Néel-type magnetic skyrmions over a broad temperature range. Notably, sub-100 nm Néel-type skyrmions at room temperature (RT) can be achieved by tuning the Cr intercalation ratio, marking the first binary compound RT Néel-type skyrmionic vdW magnet. Our work expands the 2D-SL family with a class of out-of-plane 1D polarized ferromagnetic superlattice with tunable topological magnetism.

1D polarized superlattice↗
DOE OSTI2024

Distinguishing surface and bulk electromagnetism via their dynamics in an intrinsic magnetic topological insulator

The indirect exchange interaction between local magnetic moments via surface electrons has been long predicted to bolster the surface ferromagnetism in magnetic topological insulators (MTIs), which facilitates the quantum anomalous Hall effect. This unconventional effect is critical to determining the operating temperatures of future topotronic devices. However, the experimental confirmation of this mechanism remains elusive, especially in intrinsic MTIs. Here, we combine time-resolved photoemission spectroscopy with time-resolved magneto-optical Kerr effect measurements to elucidate the unique electromagnetism at the surface of an intrinsic MTI MnBi 2 Te 4 . Theoretical modeling based on 2D Ruderman-Kittel-Kasuya-Yosida interactions captures the initial quenching of a surface-rooted exchange gap within a factor of two but overestimates the bulk demagnetization by one order of magnitude. This mechanism directly explains the sizable gap in the quasi-2D electronic state and the nonzero residual magnetization in even-layer MnBi 2 Te 4 . Furthermore, it leads to efficient light-induced demagnetization comparable to state-of-the-art magnetophotonic crystals, promising an effective manipulation of magnetism and topological orders for future topotronics.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Epitaxial 2D Magnet and Topological Insulator Heterostructures

I will discuss our latest advances on the epitaxial growth of 2D van der Waals (vdW) magnets and their integration with topological insulators (TI). This work is motivated by the realization of topological phases such as the quantum anomalous Hall effect and highly efficient spin-orbit torque produced by TIs. Our initial studies of MnSe2 growth on Bi2Se3 showed a tendency for the interdiffusion of Mn into the Bi2Se3. This ultimately led to the synthesis of MnBi2Se4 (MBS), a new magnetic TI. Interestingly, the vdW phase is not the thermodynamically stable phase and bulk crystals do not exist, so the epitaxial stabilization of MBS creates the opportunity to explore the magnetic and topological properties of this material. We find that MBS is a layered antiferromagnet, similar to MnBi2Te4, but a difference is that the magnetic moments lie in the plane of the film. Angle resolved photoemission experiments show the presence of a topological surface state with Dirac dispersion. For bilayers of 2D magnets and TIs, we have developed FGT films on Bi2Te3. We first optimized FGT by studying its growth on Ge(111) substrates, where we find that kinetic considerations play a major role. Using cross-sectional scanning transmission electron microscopy and scanning tunneling microscopy, we optimize the FGT films to have atomically smooth surfaces and abrupt interfaces with the Ge(111). Subsequently, we have developed the growth of FGT on Bi2Te3 for the integration of 2D magnets with Tis. Interestingly, we observe room temperature ferromagnetism in FGT/Bi2Te3 heterostructures by varying the growth conditions.

Kawakami, Roland↗