Observation of fractionally quantized anomalous Hall effect.

The integer quantum anomalous Hall (QAH) effect is a lattice analogue of the quantum Hall effect at zero magnetic field1-3. This phenomenon occurs in systems with topologically non-trivial bands and spontaneous time-reversal symmetry breaking. Discovery of its fractional counterpart in the presence of strong electron correlations, that is, the fractional QAH effect4-7, would open a new chapter in condensed matter physics. Here we report the direct observation of both integer and fractional QAH effects in electrical measurements on twisted bilayer MoTe2. At zero magnetic field, near filling factor ν = -1 (one hole per moiré unit cell), we see an integer QAH plateau in the Hall resistance Rxy quantized to h/e2 ± 0.1%, whereas the longitudinal resistance Rxx vanishes. Remarkably, at ν = -2/3 and -3/5, we see plateau features in Rxy at [Formula: see text] and [Formula: see text], respectively, whereas Rxx remains small. All features shift linearly versus applied magnetic field with slopes matching the corresponding Chern numbers -1, -2/3 and -3/5, precisely as expected for integer and fractional QAH states. Additionally, at zero magnetic field, Rxy is approximately 2h/e2 near half-filling (ν = -1/2) and varies linearly as ν is tuned. This behaviour resembles that of the composite Fermi liquid in the half-filled lowest Landau level of a two-dimensional electron gas at high magnetic field8-14. Direct observation of the fractional QAH and associated effects enables research in charge fractionalization and anyonic statistics at zero magnetic field.

Visualizing electrostatic gating effects in two-dimensional heterostructures.

The ability to directly monitor the states of electrons in modern field-effect devices-for example, imaging local changes in the electrical potential, Fermi level and band structure as a gate voltage is applied-could transform our understanding of the physics and function of a device. Here we show that micrometre-scale, angle-resolved photoemission spectroscopy1-3 (microARPES) applied to two-dimensional van der Waals heterostructures4 affords this ability. In two-terminal graphene devices, we observe a shift of the Fermi level across the Dirac point, with no detectable change in the dispersion, as a gate voltage is applied. In two-dimensional semiconductor devices, we see the conduction-band edge appear as electrons accumulate, thereby firmly establishing the energy and momentum of the edge. In the case of monolayer tungsten diselenide, we observe that the bandgap is renormalized downwards by several hundreds of millielectronvolts-approaching the exciton energy-as the electrostatic doping increases. Both optical spectroscopy and microARPES can be carried out on a single device, allowing definitive studies of the relationship between gate-controlled electronic and optical properties. The technique provides a powerful way to study not only fundamental semiconductor physics, but also intriguing phenomena such as topological transitions5 and many-body spectral reconstructions under electrical control.

Conduction Band Replicas in a 2D Moiré Semiconductor Heterobilayer.

Stacking monolayer semiconductors creates moiré patterns, leading to correlated and topological electronic phenomena, but measurements of the electronic structure underpinning these phenomena are scarce. Here, we investigate the properties of the conduction band in moiré heterobilayers of WS2/WSe2 using submicrometer angle-resolved photoemission spectroscopy with electrostatic gating. We find that at all twist angles the conduction band edge is the K-point valley of the WS2, with a band gap of 1.58 ± 0.03 eV. From the resolved conduction band dispersion, we deduce an effective mass of 0.15 ± 0.02 me. Additionally, we observe replicas of the conduction band displaced by reciprocal lattice vectors of the moiré superlattice. We argue that the replicas result from the moiré potential modifying the conduction band states rather than final-state diffraction. Interestingly, the replicas display an intensity pattern with reduced 3-fold symmetry, which we show implicates the pseudo vector potential associated with in-plane strain in moiré band formation.

Towards two-dimensional van der Waals ferroelectrics.

The discovery of ferroelectricity in two-dimensional (2D) van der Waals (vdW) materials has brought important functionalities to the 2D materials family, and may trigger a revolution in next-generation nanoelectronics and spintronics. In this Perspective, we briefly review recent progress in the field of 2D vdW ferroelectrics, focusing on the mechanisms that drive spontaneous polarization in 2D systems, unique properties brought about by the reduced lattice dimensionality and promising applications of 2D vdW ferroelectrics. We finish with an outlook for challenges that need to be addressed and our view on possible future research directions.

Ferroelectric switching of a two-dimensional metal.

A ferroelectric is a material with a polar structure whose polarity can be reversed (switched) by applying an electric field1,2. In metals, itinerant electrons screen electrostatic forces between ions, which explains in part why polar metals are very rare3-7. Screening also excludes external electric fields, apparently ruling out the possibility of ferroelectric switching. However, in principle, a thin enough polar metal could be sufficiently penetrated by an electric field to have its polarity switched. Here we show that the topological semimetal WTe2 provides an embodiment of this principle. Although monolayer WTe2 is centro-symmetric and thus non-polar, the stacked bulk structure is polar. We find that two- or three-layer WTe2 exhibits spontaneous out-of-plane electric polarization that can be switched using gate electrodes. We directly detect and quantify the polarization using graphene as an electric-field sensor8. Moreover, the polarization states can be differentiated by conductivity and the carrier density can be varied to modify the properties. The temperature at which polarization vanishes is above 350 kelvin, and even when WTe2 is sandwiched between graphene layers it retains its switching capability at room temperature, demonstrating a robustness suitable for applications in combination with other two-dimensional materials9-12.

Symmetry-Broken Chern Insulators in Twisted Double Bilayer Graphene.

Twisted double bilayer graphene (tDBG) has emerged as a rich platform for studying strongly correlated and topological states, as its flat bands can be continuously tuned by both a perpendicular displacement field and a twist angle. Here, we construct a phase diagram representing the correlated and topological states as a function of these parameters, based on measurements of over a dozen tDBG devices encompassing two distinct stacking configurations. We find a hierarchy of symmetry-broken states that emerge sequentially as the twist angle approaches an apparent optimal value of θ ≈ 1.34°. Nearby this angle, we discover a symmetry-broken Chern insulator (SBCI) state associated with a band filling of 7/2 as well as an incipient SBCI state associated with 11/3 filling. We further observe an anomalous Hall effect at zero field in all samples supporting SBCI states, indicating spontaneous time-reversal symmetry breaking and possible moiré unit cell enlargement at zero magnetic field.

Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit.

Since the discovery of graphene, the family of two-dimensional materials has grown, displaying a broad range of electronic properties. Recent additions include semiconductors with spin-valley coupling, Ising superconductors that can be tuned into a quantum metal, possible Mott insulators with tunable charge-density waves, and topological semimetals with edge transport. However, no two-dimensional crystal with intrinsic magnetism has yet been discovered; such a crystal would be useful in many technologies from sensing to data storage. Theoretically, magnetic order is prohibited in the two-dimensional isotropic Heisenberg model at finite temperatures by the Mermin-Wagner theorem. Magnetic anisotropy removes this restriction, however, and enables, for instance, the occurrence of two-dimensional Ising ferromagnetism. Here we use magneto-optical Kerr effect microscopy to demonstrate that monolayer chromium triiodide (CrI3) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temperature of 45 kelvin is only slightly lower than that of the bulk crystal, 61 kelvin, which is consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phase, highlighting thickness-dependent physical properties typical of van der Waals crystals. Remarkably, bilayer CrI3 displays suppressed magnetization with a metamagnetic effect, whereas in trilayer CrI3 the interlayer ferromagnetism observed in the bulk crystal is restored. This work creates opportunities for studying magnetism by harnessing the unusual features of atomically thin materials, such as electrical control for realizing magnetoelectronics, and van der Waals engineering to produce interface phenomena.

Gate-Tunable Proximity Effects in Graphene on Layered Magnetic Insulators.

The extreme versatility of van der Waals materials originates from their ability to exhibit new electronic properties when assembled in close proximity to dissimilar crystals. For example, although graphene is inherently nonmagnetic, recent work has reported a magnetic proximity effect in graphene interfaced with magnetic substrates, potentially enabling a pathway toward achieving a high-temperature quantum anomalous Hall effect. Here, we investigate heterostructures of graphene and chromium trihalide magnetic insulators (CrI3, CrBr3, and CrCl3). Surprisingly, we are unable to detect a magnetic exchange field in the graphene but instead discover proximity effects featuring unprecedented gate tunability. The graphene becomes highly hole-doped due to charge transfer from the neighboring magnetic insulator and further exhibits a variety of atypical gate-dependent transport features. The charge transfer can additionally be altered upon switching the magnetic states of the nearest CrI3 layers. Our results provide a roadmap for exploiting proximity effects arising in graphene coupled to magnetic insulators.

Field-Dependent Band Structure Measurements in Two-Dimensional Heterostructures.

In electronic and optoelectronic devices made from van der Waals heterostructures, electric fields can induce substantial band structure changes which are crucial to device operation but cannot usually be directly measured. Here, we use spatially resolved angle-resolved photoemission spectroscopy to monitor changes in band alignment of the component layers, corresponding to band structure changes of the composite heterostructure system, that are produced by electrostatic gating. Our devices comprise graphene on a monolayer semiconductor, WSe2 or MoSe2, atop a boron nitride dielectric and a graphite gate. Applying a gate voltage creates an electric field that shifts the semiconductor bands relative to those in the graphene by up to 0.2 eV. The results can be understood in simple terms by assuming that the materials do not hybridize.

Magnetic proximity and nonreciprocal current switching in a monolayer WTe2 helical edge.

The integration of diverse electronic phenomena, such as magnetism and nontrivial topology, into a single system is normally studied either by seeking materials that contain both ingredients, or by layered growth of contrasting materials1-9. The ability to simply stack very different two-dimensional van der Waals materials in intimate contact permits a different approach10,11. Here we use this approach to couple the helical edges states in a two-dimensional topological insulator, monolayer WTe2 (refs. 12-16), to a two-dimensional layered antiferromagnet, CrI3 (ref. 17). We find that the edge conductance is sensitive to the magnetization state of the CrI3, and the coupling can be understood in terms of an exchange field from the nearest and next-nearest CrI3 layers that produces a gap in the helical edge. We also find that the nonlinear edge conductance depends on the magnetization of the nearest CrI3 layer relative to the current direction. At low temperatures this produces an extraordinarily large nonreciprocal current that is switched by changing the antiferromagnetic state of the CrI3.

Monolayer Semiconductor Auger Detector.

Auger recombination in semiconductors is a many-body phenomenon in which the recombination of electrons and holes is accompanied by excitation of other charge carriers. The excess energy of the excited carriers is normally rapidly converted to heat, making Auger processes difficult to probe directly. Here, we employ a technique in which the Auger-excited carriers are detected by their ability to tunnel out of the semiconductor through a thin barrier, generating a current. We use vertical van der Waals heterostructures with monolayer WSe2 as the semiconductor, with hexagonal boron nitride as the tunnel barrier, and a graphite collector electrode. The Auger processes combined with resonant absorption produce characteristic negative photoconductance. We detect holes Auger-excited by both neutral and charged excitons and find that the Auger scattering is surprisingly strong under weak excitation. Our work expands the range of techniques available for probing relaxation processes in 2D materials.

Switching 2D magnetic states via pressure tuning of layer stacking.

The physical properties of two-dimensional van der Waals crystals can be sensitive to interlayer coupling. For two-dimensional magnets1-3, theory suggests that interlayer exchange coupling is strongly dependent on layer separation while the stacking arrangement can even change the sign of the interlayer magnetic exchange, thus drastically modifying the ground state4-10. Here, we demonstrate pressure tuning of magnetic order in the two-dimensional magnet CrI3. We probe the magnetic states using tunnelling8,11-13 and scanning magnetic circular dichroism microscopy measurements2. We find that interlayer magnetic coupling can be more than doubled by hydrostatic pressure. In bilayer CrI3, pressure induces a transition from layered antiferromagnetic to ferromagnetic phase. In trilayer CrI3, pressure can create coexisting domains of three phases, one ferromagnetic and two antiferromagnetic. The observed changes in magnetic order can be explained by changes in the stacking arrangement. Such coupling between stacking order and magnetism provides ample opportunities for designer magnetic phases and functionalities.

Atomically Thin CrCl3: An In-Plane Layered Antiferromagnetic Insulator.

The recent discovery of magnetism in atomically thin layers of van der Waals (vdW) crystals has created new opportunities for exploring magnetic phenomena in the two-dimensional (2D) limit. In most 2D magnets studied to date, the c-axis is an easy axis, so that at zero applied field the polarization of each layer is perpendicular to the plane. Here, we demonstrate that atomically thin CrCl3 is a layered antiferromagnetic insulator with an easy-plane normal to the c-axis, that is, the polarization is in the plane of each layer and has no preferred direction within it. Ligand-field photoluminescence at 870 nm is observed down to the monolayer limit, demonstrating its insulating properties. We investigate the in-plane magnetic order using tunneling magnetoresistance in graphene/CrCl3/graphene tunnel junctions, establishing that the interlayer coupling is antiferromagnetic down to the bilayer. From the temperature dependence of the magnetoresistance, we obtain an effective magnetic phase diagram for the bilayer. Our result shows that CrCl3 should be useful for studying the physics of 2D phase transitions and for making new kinds of vdW spintronic devices.

Voltage Control of a van der Waals Spin-Filter Magnetic Tunnel Junction.

Atomically thin chromium triiodide (CrI3) has recently been identified as a layered antiferromagnetic insulator, in which adjacent ferromagnetic monolayers are antiferromagnetically coupled. This unusual magnetic structure naturally comprises a series of antialigned spin filters, which can be utilized to make spin-filter magnetic tunnel junctions with very large tunneling magnetoresistance (TMR). Here we report voltage control of TMR formed by four-layer CrI3 sandwiched by monolayer graphene contacts in a dual-gated structure. By varying the gate voltages at fixed magnetic field, the device can be switched reversibly between bistable magnetic states with the same net magnetization but drastically different resistance (by a factor of 10 or more). In addition, without switching the state, the TMR can be continuously modulated between 17,000% and 57,000%, due to the combination of spin-dependent tunnel barrier with changing carrier distributions in the graphene contacts. Our work demonstrates new kinds of magnetically moderated transistor action and opens up possibilities for voltage-controlled van der Waals spintronic devices.

Two-dimensional itinerant ferromagnetism in atomically thin Fe3GeTe2.

Discoveries of intrinsic two-dimensional (2D) ferromagnetism in van der Waals (vdW) crystals provide an interesting arena for studying fundamental 2D magnetism and devices that employ localized spins1-4. However, an exfoliable vdW material that exhibits intrinsic 2D itinerant magnetism remains elusive. Here we demonstrate that Fe3GeTe2 (FGT), an exfoliable vdW magnet, exhibits robust 2D ferromagnetism with strong perpendicular anisotropy when thinned down to a monolayer. Layer-number-dependent studies reveal a crossover from 3D to 2D Ising ferromagnetism for thicknesses less than 4 nm (five layers), accompanied by a fast drop of the Curie temperature (TC) from 207 K to 130 K in the monolayer. For FGT flakes thicker than ~15 nm, a distinct magnetic behaviour emerges in an intermediate temperature range, which we show is due to the formation of labyrinthine domain patterns. Our work introduces an atomically thin ferromagnetic metal that could be useful for the study of controllable 2D itinerant ferromagnetism and for engineering spintronic vdW heterostructures5.

Measurement of a solid-state triple point at the metal-insulator transition in VO2.

First-order phase transitions in solids are notoriously challenging to study. The combination of change in unit cell shape, long range of elastic distortion and flow of latent heat leads to large energy barriers resulting in domain structure, hysteresis and cracking. The situation is worse near a triple point, where more than two phases are involved. The well-known metal-insulator transition in vanadium dioxide, a popular candidate for ultrafast optical and electrical switching applications, is a case in point. Even though VO2 is one of the simplest strongly correlated materials, experimental difficulties posed by the first-order nature of the metal-insulator transition as well as the involvement of at least two competing insulating phases have led to persistent controversy about its nature. Here we show that studying single-crystal VO2 nanobeams in a purpose-built nanomechanical strain apparatus allows investigation of this prototypical phase transition with unprecedented control and precision. Our results include the striking finding that the triple point of the metallic phase and two insulating phases is at the transition temperature, Ttr = Tc, which we determine to be 65.0 ± 0.1 °C. The findings have profound implications for the mechanism of the metal-insulator transition in VO2, but they also demonstrate the importance of this approach for mastering phase transitions in many other strongly correlated materials, such as manganites and iron-based superconductors.

Interlayer Exciton Optoelectronics in a 2D Heterostructure p-n Junction.

Semiconductor heterostructures are backbones for solid-state-based optoelectronic devices. Recent advances in assembly techniques for van der Waals heterostructures have enabled the band engineering of semiconductor heterojunctions for atomically thin optoelectronic devices. In two-dimensional heterostructures with type II band alignment, interlayer excitons, where Coulomb bound electrons and holes are confined to opposite layers, have shown promising properties for novel excitonic devices, including a large binding energy, micron-scale in-plane drift-diffusion, and a long population and valley polarization lifetime. Here, we demonstrate interlayer exciton optoelectronics based on electrostatically defined lateral p-n junctions in a MoSe2-WSe2 heterobilayer. Applying a forward bias enables the first observation of electroluminescence from interlayer excitons. At zero bias, the p-n junction functions as a highly sensitive photodetector, where the wavelength-dependent photocurrent measurement allows the direct observation of resonant optical excitation of the interlayer exciton. The resulting photocurrent amplitude from the interlayer exciton is about 200 times smaller than the resonant excitation of intralayer exciton. This implies that the interlayer exciton oscillator strength is 2 orders of magnitude smaller than that of the intralayer exciton due to the spatial separation of electron and hole to the opposite layers. These results lay the foundation for exploiting the interlayer exciton in future 2D heterostructure optoelectronic devices.

Ultrafast Nanoimaging of the Photoinduced Phase Transition Dynamics in VO2.

Many phase transitions in correlated matter exhibit spatial inhomogeneities with expected yet unexplored effects on the associated ultrafast dynamics. Here we demonstrate the combination of ultrafast nondegenerate pump-probe spectroscopy with far from equilibrium excitation, and scattering scanning near-field optical microscopy (s-SNOM) for ultrafast nanoimaging. In a femtosecond near-field near-IR (NIR) pump and mid-IR (MIR) probe study, we investigate the photoinduced insulator-to-metal (IMT) transition in nominally homogeneous VO2 microcrystals. With pump fluences as high as 5 mJ/cm(2), we can reach three distinct excitation regimes. We observe a spatial heterogeneity on ∼50-100 nm length scales in the fluence-dependent IMT dynamics ranging from <100 fs to ∼1 ps. These results suggest a high sensitivity of the IMT with respect to small local variations in strain, doping, or defects that are difficult to discern microscopically. We provide a perspective with the distinct requirements and considerations of ultrafast spatiotemporal nanoimaging of phase transitions in quantum materials.

Visualization of one-dimensional diffusion and spontaneous segregation of hydrogen in single crystals of VO2.

Hydrogen intercalation in solids is common, complicated, and very difficult to monitor. In a new approach to the problem, we have studied the profile of hydrogen diffusion in single-crystal nanobeams and plates of VO2, exploiting the fact that hydrogen doping in this material leads to visible darkening near room temperature connected with the metal-insulator transition at 65 °C. We observe hydrogen diffusion along the rutile c-axis but not perpendicular to it, making this a highly one-dimensional diffusion system. We obtain an activated diffusion coefficient, [Formula: see text] applicable in metallic phase. In addition, we observe dramatic supercooling of the hydrogen-induced metallic phase and spontaneous segregation of the hydrogen into stripes implying that the diffusion process is highly nonlinear, even in the absence of defects. Similar complications may occur in hydrogen motion in other materials but are not revealed by conventional measurement techniques.

Lateral heterojunctions within monolayer MoSe2-WSe2 semiconductors.

Heterojunctions between three-dimensional (3D) semiconductors with different bandgaps are the basis of modern light-emitting diodes, diode lasers and high-speed transistors. Creating analogous heterojunctions between different 2D semiconductors would enable band engineering within the 2D plane and open up new realms in materials science, device physics and engineering. Here we demonstrate that seamless high-quality in-plane heterojunctions can be grown between the 2D monolayer semiconductors MoSe2 and WSe2. The junctions, grown by lateral heteroepitaxy using physical vapour transport, are visible in an optical microscope and show enhanced photoluminescence. Atomically resolved transmission electron microscopy reveals that their structure is an undistorted honeycomb lattice in which substitution of one transition metal by another occurs across the interface. The growth of such lateral junctions will allow new device functionalities, such as in-plane transistors and diodes, to be integrated within a single atomically thin layer.