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Semiconducting transitional metal dichalcogenides (TMDCs) moir\'e superlattice provides an exciting platform for manipulating excitons. The in-situ control of moir\'e potential confined exciton would usher in unprecedented functions of excitonic devices but remains challenging. Meanwhile, as a dipolar composite boson, interlayer exciton in the type-II aligned TMDC moir\'e superlattice strongly interacts with fermionic charge carriers. Here, we demonstrate active manipulation of the exciton diffusivity by tuning their interplay with correlated carriers in moir\'e potentials. At fractional fillings where carriers are known to form generalized Wigner crystals, we observed suppressed diffusivity of exciton. In contrast, in Fermi liquid states where carriers dynamically populate all moir\'e traps, the repulsive carrier-exciton interaction can effectively reduce the moir\'e potential confinement seen by the exciton, leading to enhanced diffusivity with the increase of the carrier density. Notably, the exciton diffusivity is enhanced by orders of magnitude near the Mott insulator state, and the enhancement is much more pronounced for the 0-degree than the 60-degree aligned WS2/WSe2 heterobilayer due to the more localized nature of interlayer excitons. Our study inspires further engineering and controlling exotic excitonic states in TMDC moir\'e superlattices for fascinating quantum phenomena and novel excitonic devices.

Moir\'e superlattices of semiconducting transition metal dichalcogenides (TMDCs) enable unprecedented spatial control of electron wavefunctions in an artificial lattice with periodicities more than ten times larger than that of atomic crystals, leading to emerging quantum states with fascinating electronic and optical properties. The breaking of translational symmetry further introduces a new degree of freedom inside each moir\'e unit cell: high symmetry points of energy minima called moir\'e sites, behaving as spatially separated quantum dots. The superposition of a quasiparticle wavefunction between different moir\'e sites will enable a new platform for quantum information processing but is hindered by the suppressed electron tunneling between moir\'e sites. Here we demonstrate the superposition between two moir\'e sites by constructing an angle-aligned trilayer WSe2/monolayer WS2 moir\'e heterojunction. The two moir\'e sites with energy minimum allow the formation of two different interlayer excitons, with the hole residing in either moir\'e site of the first WSe2 layer interfacing the WS2 layer and the electron in the third WSe2 layer. An external electric field can drive the hybridization of either of the interlayer excitons with the intralayer excitons in the third WSe2 layer, realizing the continuous tuning of interlayer exciton hopping between two moir\'e sites. Therefore, a superposition of the two interlayer excitons localized at different moir\'e sites can be realized, which can be resolved in the electric-field-dependent optical reflectance spectra, distinctly different from that of the natural trilayer WSe2 in which the moir\'e modulation is absent. Our study illustrates a strategy of harnessing the new moir\'e site degree of freedom for quantum information science, a new direction of twistronics.

Strongly enhanced electron-electron interaction in semiconducting moir\'e superlattices formed by transition metal dichalcogenides (TMDCs) heterobilayers has led to a plethora of intriguing fermionic correlated states. Meanwhile, interlayer excitons in a type-II aligned TMDC heterobilayer moir\'e superlattice, with electrons and holes separated in different layers, inherit this enhanced interaction and strongly interact with each other, promising for realizing tunable correlated bosonic quasiparticles with valley degree of freedom. We employ photoluminescence spectroscopy to investigate the strong repulsion between interlayer excitons and correlated electrons in a WS2/WSe2 moir\'e superlattice and combine with theoretical calculations to reveal the spatial extent of interlayer excitons and the band hierarchy of correlated states. We further find that an excitonic Mott insulator state emerges when one interlayer exciton occupies one moir\'e cell, evidenced by emerging photoluminescence peaks under increased optical excitation power. Double occupancy of excitons in one unit cell requires overcoming the energy cost of exciton-exciton repulsion of about 30-40 meV, depending on the stacking configuration of the WS2/WSe2 heterobilayer. Further, the valley polarization of the excitonic Mott insulator state is enhanced by nearly one order of magnitude. Our study demonstrates the WS2/WSe2 moir\'e superlattice as a promising platform for engineering and exploring new correlated states of fermion, bosons, and a mixture of both.

Moir\'e superlattices of transitional metal dichalcogenides exhibit strong electron-electron interaction that has led to experimental observations of Mott insulators and generalized Wigner crystals. In this letter, we report direct measurements of the thermodynamic gaps of these correlated insulating states in a dual-gate WS2/WSe2 moir\'e bilayer. We employ the microwave impedance microscopy to probe the electronic features in both the graphene top gate and the moir\'e bilayer, from which we extract the doping dependence of the chemical potential of the moir\'e bilayer and the energy gaps for various correlated insulating states utilizing the Landau quantization of graphene. These gaps are relatively insensitive to the application of an external electric field to the WS2/WSe2 moir\'e bilayer.

Transition metal dichalcogenide (TMDC) moir\'e superlattices, owing to the moir\'e flatbands and strong correlation, can host periodic electron crystals and fascinating correlated physics. The TMDC heterojunctions in the type-II alignment also enable long-lived interlayer excitons that are promising for correlated bosonic states, while the interaction is dictated by the asymmetry of the heterojunction. Here we demonstrate a new excitonic state, quadrupolar exciton, in a symmetric WSe2-WS2-WSe2 trilayer moir\'e superlattice. The quadrupolar excitons exhibit a quadratic dependence on the electric field, distinctively different from the linear Stark shift of the dipolar excitons in heterobilayers. This quadrupolar exciton stems from the hybridization of WSe2 valence moir\'e flatbands. The same mechanism also gives rise to an interlayer Mott insulator state, in which the two WSe2 layers share one hole laterally confined in one moir\'e unit cell. In contrast, the hole occupation probability in each layer can be continuously tuned via an out-of-plane electric field, reaching 100% in the top or bottom WSe2 under a large electric field, accompanying the transition from quadrupolar excitons to dipolar excitons. Our work demonstrates a trilayer moir\'e system as a new exciting playground for realizing novel correlated states and engineering quantum phase transitions.

Multiple magnetic skyrmion phases add an additional degree of freedom for skyrmion based ultrahigh-density spin memory devices. Extending the field to two-dimensional van der Waals magnets is a rewarding challenge, where the realizable degree of freedoms (e.g. thickness, twisting angle and electrical gating) and high skyrmion density result in intriguing new properties and enhanced functionality. We report a van der Waals interface, formed by two 2D ferromagnets Cr2Ge2Te6 and Fe3GeTe2 with a Curie temperature of ~65 K and ~205 K, respectively, hosting two groups of magnetic skyrmions. Two sets of topological Hall effect are observed below 60 K when Cr2Ge2Te6 is magnetically ordered. These two groups of skyrmions are directly imaged using magnetic force microscopy. Interestingly, the magnetic skyrmions persist in the heterostructure in the remanent state with zero applied magnetic field. Our results are promising for the realization of skyrmionic devices based on van der Waals heterostructures hosting multiple skyrmion phases., Comment: 4 figure for the main text

A single monolayer of the layered semimetal WTe2 behaves as a two-dimensional topological insulator, with helical conducting edge modes surrounding a bulk state that becomes insulating at low temperatures. Here we present evidence that the bulk state has a very unusual nature, containing electrons and holes bound by Coulomb attraction (excitons) that spontaneously form in thermal equilibrium. On cooling from room temperature to 100 K the conductivity develops a V-shaped dependence on electrostatic doping, while the chemical potential develops a ~43 meV step at the neutral point. These features are much sharper than is possible in an independent-electron picture, but they can be largely accounted for by positing that some of the electrons and holes are paired in equilibrium. Our calculations from first principles show that the exciton binding energy is larger than 100 meV and the radius as small as 4 nm, explaining their formation at high temperature and doping levels. Below 100 K more strongly insulating behavior is seen, suggesting that a charge-ordered state forms. The observed absence of charge density waves in this state appears surprising within an excitonic insulator picture, but we show that it can be explained by the symmetries of the exciton wave function. Monolayer WTe2 therefore presents an exceptional combination of topological properties and strong correlations over a wide temperature range., Comment: Initial submission. Includes supplementary information. Revised version to appear in Nature Physics

The interplay between band topology and magnetism can give rise to exotic states of matter. For example, magnetically doped topological insulators can realize a Chern insulator that exhibits quantized Hall resistance at zero magnetic field. While prior works have focused on ferromagnetic systems, little is known about band topology and its manipulation in antiferromagnets. Here, we report that MnBi$_2$Te$_4$ is a rare platform for realizing a canted-antiferromagnetic (cAFM) Chern insulator with electrical control. We show that the Chern insulator state with Chern number $C = 1$ appears as soon as the AFM to canted-AFM phase transition happens. The Chern insulator state is further confirmed by observing the unusual transition of the $C = 1$ state in the cAFM phase to the $C = 2$ orbital quantum Hall states in the magnetic field induced ferromagnetic phase. Near the cAFM-AFM phase boundary, we show that the Chern number can be toggled on and off by applying an electric field alone. We attribute this switching effect to the electrical field tuning of the exchange gap alignment between the top and bottom surfaces. Our work paves the way for future studies on topological cAFM spintronics and facilitates the development of proof-of-concept Chern insulator devices., Comment: 13 pages, 4 figures, and 5 supplementary figures. Comments are welcome

Moir\'e superlattices (MSL) formed in angle-aligned bilayers of van der Waals materials have become a promising platform to realize novel two-dimensional electronic states. Angle-aligned trilayer structures can form two sets of MSLs which could potentially interfere with each other. In this work, we directly image the moir\'e patterns in both monolayer graphene aligned on hBN and twisted bilayer graphene aligned on hBN, using combined scanning microwave impedance microscopy and conductive atomic force microscopy. Correlation of the two techniques reveals the contrast mechanism for the achieved ultrahigh spatial resolution (<2 nm). We observe two sets of MSLs with different periodicities in the trilayer stack. The smaller MSL breaks the 6-fold rotational symmetry and exhibits abrupt discontinuities at the boundaries of the larger MSL. Using a rigid atomic-stacking model, we demonstrate that the hBN layer considerably modifies the MSL of twisted bilayer graphene. We further analyze its effect on the reciprocal space spectrum of the dual-moir\'e system.

Moir\'e superlattices are excellent platforms to realize strongly correlated quantum phenomena, such as Mott insulation and superconductivity. In particular, recent research has revealed stripe phases and generalized Wigner crystals at fractional fillings of moir\'e superlattices. But these experiments have not focused on the influence of electronic crystallization on the excitonic and valleytronic properties of the superlattices. Here we report excitonic and valleytronic signatures of correlated states at fractional fillings in a WSe$_2$/WS$_2$ moir\'e superlattice. We observe reflection spectral modulation of three intralayer moir\'e excitons at filling factors $\nu$ = 1/3 and 2/3. We also observe luminescence spectral modulation of interlayer trions at around a dozen fractional filling factors, including $\nu$ = -3/2, 1/4, 1/3, 2/5, 2/3, 6/7, 5/3. In addition, the valley polarization of interlayer trions is noticeably suppressed at some fractional fillings. These results demonstrate a new regime of light-matter interactions, in which electron crystallization significantly modulates the absorption, emission, and valley dynamics of the excitonic states in a moir\'e superlattice.

The interplay between band topology and magnetic order plays a key role in quantum states of matter. MnBi2Te4, a van der Waals magnet, has recently emerged as an exciting platform for exploring Chern insulator physics. Its layered antiferromagnetic order was predicted to enable even-odd layer-number dependent topological states, supported by promising edge transport measurements. Furthermore, it becomes a Chern insulator when all spins are aligned by an applied magnetic field. However, the evolution of the bulk electronic structure as the magnetic state is continuously tuned and its dependence on layer number remains unexplored. Here, employing multimodal probes, we establish one-to-one correspondence between bulk electronic structure, magnetic state, topological order, and layer thickness in atomically thin MnBi2Te4 devices. As the magnetic state is tuned through the canted magnetic phase, we observe a band crossing, i.e., the closing and reopening of the bulk bandgap, corresponding to the concurrent topological phase transition. Surprisingly, we find that the even- and odd-layer number devices exhibit a similar topological phase transition coupled to magnetic states, distinct from recent theoretical and experimental reports. Our findings shed new light on the interplay between band topology and magnetic order in this newly discovered topological magnet and validate the band crossing with concurrent measurements of topological invariant in a continuously tuned topological phase transition.

Evidence for the quantum spin Hall (QSH) effect has been reported in several experimental systems in the form of approximately quantized edge conductance. However, the most fundamental feature of the QSH effect, spin-momentum locking in the edge channels, has never been demonstrated experimentally. Here, we report clear evidence for spin-momentum locking in the edge channels of monolayer WTe2, thought to be a two-dimensional topological insulator (2D TI). We observe that the edge conductance is controlled by the component of an applied magnetic field perpendicular to a particular axis, which we identify as the spin axis. The axis is the same for all edges, situated in the mirror plane perpendicular to the tungsten chains at 40$\pm$2{\deg} to the layer normal, implying that the spin-orbit coupling is inherited from the bulk band structure. We show that this finding is consistent with theory if the band-edge orbitals are taken to have like parity. We conclude that this parity assignment is correct and that both edge states and bulk bands in monolayer WTe2 share the same simple spin structure. Combined with other known features of the edge states this establishes spin-momentum locking, and therefore that monolayer WTe2 is truly a natural 2D TI.

Moir\'e superlattices of van der Waals materials, such as twisted graphene and transitional metal dichalcogenides, have recently emerged as a fascinating platform to study strongly correlated states in two dimensions, thanks to the strong electron interaction in the moir\'e minibands. In most systems, the correlated states appear when the moir\'e lattice is filled by integer number of electrons per moir\'e unit cell. Recently, correlated states at fractional fillings of 1/3 and 2/3 holes per moir\'e unit cell has been reported in the WS2/WSe2 heterobilayer, hinting the long range nature of the electron interaction. In this work, employing a scanning microwave impedance microscopy technique that is sensitive to local electrical properties, we observe a series of correlated insulating states at fractional fillings of the moir\'e minibands on both electron- and hole-doped sides in angle-aligned WS2/WSe2 hetero-bilayers, with certain states persisting at temperatures up to 120 K. Monte Carlo simulations reveal that these insulating states correspond to ordering of electrons in the moir\'e lattice with a periodicity much larger than the moir\'e unit cell, indicating a surprisingly strong and long-range interaction beyond the nearest neighbors. Our findings usher in unprecedented opportunities in the study of strongly correlated states in two dimensions.

The magnetic properties in two-dimensional van der Waals materials depend sensitively on structure. CrI3, as an example, has been recently demonstrated to exhibit distinct magnetic properties depending on the layer thickness and stacking order. Bulk CrI3 is ferromagnetic (FM) with a Curie temperature of 61 K and a rhombohedral layer stacking, while few-layer CrI3 has a layered antiferromagnetic (AFM) phase with a lower ordering temperature of 45 K and a monoclinic stacking. In this work, we use cryogenic magnetic force microscopy to investigate CrI3 flakes in the intermediate thickness range (25 - 200 nm) and find that the two types of magnetic orders hence the stacking orders can coexist in the same flake, with a layer of ~13 nm at each surface being in the layered AFM phase similar to few-layer CrI3 and the rest in the bulk FM phase. The switching of the bulk moment proceeds through a remnant state with nearly compensated magnetic moment along the c-axis, indicating formation of c-axis domains allowed by a weak interlayer coupling strength in the rhombohedral phase. Our results provide a comprehensive picture on the magnetism in CrI3 and point to the possibility of engineering magnetic heterostructures within the same material.

Two-dimensional ferromagnet Cr2Ge2Te6 (CGT) is so resistive below its Curie temperature that probing its magnetism by electrical transport becomes extremely difficult. By forming heterostructures with Pt, however, we observe clear anomalous Hall effect (AHE) in 5 nm thick Pt deposited on thin (< 50 nm) exfoliated flakes of CGT. The AHE hysteresis loops persist to ~ 60 K, which matches well to the Curie temperature of CGT obtained from the bulk magnetization measurements. The slanted AHE loops with a narrow opening indicate magnetic domain formation, which is confirmed by low-temperature magnetic force microscopy (MFM) imaging. These results clearly demonstrate that CGT imprints its magnetization in the AHE signal of the Pt layer. Density functional theory calculations of CGT/Pt heterostructures suggest that the induced ferromagnetism in Pt may be primarily responsible for the observed AHE. Our results establish a powerful way of investigating magnetism in 2D insulating ferromagnets which can potentially work for monolayer devices.

A two-dimensional (2D) topological insulator (TI) exhibits the quantum spin Hall (QSH) effect, in which topologically protected spin-polarized conducting channels exist at the sample edges. Experimental signatures of the QSH effect have recently been reported for the first time in an atomically thin material, monolayer WTe2. Electrical transport measurements on exfoliated samples and scanning tunneling spectroscopy on epitaxially grown monolayer islands signal the existence of edge modes with conductance approaching the quantized value. Here, we directly image the local conductivity of monolayer WTe2 devices using microwave impedance microscopy, establishing beyond doubt that conduction is indeed strongly localized to the physical edges at temperatures up to 77 K and above. The edge conductivity shows no gap as a function of gate voltage, ruling out trivial conduction due to band bending or in-gap states, and is suppressed by magnetic field as expected. Interestingly, we observe additional conducting lines and rings within most samples which can be explained by edge states following boundaries between topologically trivial and non-trivial regions. These observations will be critical for interpreting and improving the properties of devices incorporating WTe2 or other air-sensitive 2D materials. At the same time, they reveal the robustness of the QSH channels and the potential to engineer and pattern them by chemical or mechanical means in the monolayer material platform., Comment: 9 pages, 4 figures

Surface Acoustic Wave (SAW) resonances were imaged within a closed domain in the ferroelectric LiTaO$_3$ via scanning Microwave Impedance Microscopy (MIM). The MIM probe is used for both SAW generation and measurement, allowing contact-less measurement within a mesoscopic structure. Measurements taken over a range of microwave frequencies are consistent with a constant acoustic velocity, demonstrating the acoustic nature of the measurement., Comment: 5 pages, 3 figures

We report simultaneous transport and scanning microwave impedance microscopy to examine the correlation between transport quantization and filling of the bulk Landau levels in the quantum Hall regime in gated graphene devices. Surprisingly, a comparison of these measurements reveals that quantized transport typically occurs below the complete filling of bulk Landau levels, when the bulk is still conductive. This result points to a revised understanding of transport quantization when carriers are accumulated by gating. We discuss the implications on transport study of the quantum Hall effect in graphene and related topological states in other two-dimensional electron systems., Comment: 4 figures

Quantum systems in confined geometries are host to novel physical phenomena. Examples include quantum Hall systems in semiconductors and Dirac electrons in graphene. Interest in such systems has also been intensified by the recent discovery of a large enhancement in photoluminescence quantum efficiency and a potential route to valleytronics in atomically thin layers of transition metal dichalcogenides, MX2 (M = Mo, W; X = S, Se, Te), which are closely related to the indirect to direct bandgap transition in monolayers. Here, we report the first direct observation of the transition from indirect to direct bandgap in monolayer samples by using angle resolved photoemission spectroscopy on high-quality thin films of MoSe2 with variable thickness, grown by molecular beam epitaxy. The band structure measured experimentally indicates a stronger tendency of monolayer MoSe2 towards a direct bandgap, as well as a larger gap size, than theoretically predicted. Moreover, our finding of a significant spin-splitting of 180 meV at the valence band maximum of a monolayer MoSe2 film could expand its possible application to spintronic devices., Comment: 8 pages, 3 figures. Nature Nanotechnology (2013)

The realization of quantum spin Hall (QSH) effect in HgTe quantum wells (QWs) is considered a milestone in the discovery of topological insulators. The QSH edge states are predicted to allow current to flow at the edges of an insulating bulk, as demonstrated in various experiments. A key prediction of QSH theory that remains to be experimentally verified is the breakdown of the edge conduction under broken time reversal symmetry (TRS). Here we first establish a rigorous framework for understanding the magnetic field dependence of electrostatically gated QSH devices. We then report unexpected edge conduction under broken TRS, using a unique cryogenic microwave impedance microscopy (MIM), on a 7.5 nm HgTe QW device with an inverted band structure. At zero magnetic field and low carrier densities, clear edge conduction is observed in the local conductivity profile of this device but not in the 5.5 nm control device whose band structure is trivial. Surprisingly, the edge conduction in the 7.5 nm device persists up to 9 T with little effect from the magnetic field. This indicates physics beyond simple QSH models, possibly associated with material- specific properties, other symmetry protection and/or electron-electron interactions., Comment: 18 pages, 3 figures, accepted to Nature Communication

We demonstrate a simple network-analyzer technique to make quantitative measurements of the bias dependence of spin torque in a magnetic tunnel junction. We apply a microwave current to exert an oscillating spin torque near the ferromagnetic resonance frequency of the tunnel junction's free layer. This produces an oscillating resistance that, together with an applied direct current, generates a microwave signal that we measure with the network analyzer. An analysis of the resonant response yields the strength and direction of the spin torque at non-zero bias. We compare to measurements of the spin torque vector by time-domain spin-torque ferromagnetic resonance., Comment: 13 pages, 3 figures

A pure spin current generated within a nonlocal spin valve can exert a spin transfer torque on a nanomagnet. This nonlocal torque enables new design schemes for magnetic memory devices that do not require the application of large voltages across tunnel barriers that can suffer electrical breakdown. Here we report a quantitative measurement of this nonlocal spin torque using spin-torque-driven ferromagnetic resonance. Our measurement agrees well with the prediction of an effective circuit model for spin transport. Based on this model, we suggest strategies for optimizing the strength of nonlocal torque., Comment: 21 pages, 3 figures. Supplement included

Several experimental techniques have been introduced in recent years in attempts to measure spin transfer torque in magnetic tunnel junctions (MTJs). The dependence of spin torque on bias is important for understanding fundamental spin physics in magnetic devices and for applications. However, previous techniques have provided only indirect measures of the torque and their results to date for the bias dependence are qualitatively and quantitatively inconsistent. Here we demonstrate that spin torque in MTJs can be measured directly by using time-domain techniques to detect resonant magnetic precession in response to an oscillating spin torque. The technique is accurate in the high-bias regime relevant for applications, and because it detects directly small-angle linear-response magnetic dynamics caused by spin torque it is relatively immune to artifacts affecting competing techniques. At high bias we find that the spin torque vector differs markedly from the simple lowest-order Taylor series approximations commonly assumed., Comment: 29 pages, 5 figures including supplementary material