Kin Fai Mak

The spin Hall effect (SHE), in which an electrical current generates a transverse spin current, plays an important role in spintronics for the generation and manipulation of spin-polarized electrons. The phenomenon originates from spin–orbit coupling. In general, stronger spin–orbit coupling favours larger SHEs but shorter spin relaxation times and diffusion lengths. However, correlated magnetic materials often do not support large SHEs. Achieving large SHEs, long-range spin transport and magnetism simultaneously in a single material is attractive for spintronics applications but has remained a challenge. Here we demonstrate a giant intrinsic SHE coexisting with ferromagnetism in AB-stacked MoTe2/WSe2 moiré bilayers by direct magneto-optical imaging. Under moderate electrical currents with density <1 A m−1, we observe spin accumulation on transverse sample edges that nearly saturates the spin density …

Quantum spin Hall (QSH) insulators are a topologically protected phase of matter in two dimensions that can support non-dissipative spin transport. A hallmark of the phase is a pair of helical edge states surrounding an insulating bulk. A higher (even) number of helical edge state pairs is usually not possible in real materials because spin mixing would gap out the edge states. Multiple pairs of helical edge states have been proposed in materials with spin conservation symmetry and high spin Chern bands, but remained experimentally elusive. Here, we demonstrate a QSH phase with one and two pairs of helical edge states in twisted bilayer WSe2 at moir\'e hole filling factor {\nu}= 2 and 4, respectively. We observe nearly quantized conductance or resistance plateaus of h/({\nu}e^2 ) at {\nu} = 2 and 4 while the bulk is insulating. The conductance is nearly independent of out-of-plane magnetic field and decreases under an in-plane magnetic field. We also observe nonlocal transport, which is sensitive only to the in-plane magnetic field. The results agree with quantum transport of helical edge states protected by Ising spin conservation symmetry and open a promising platform for low-power spintronics.

The chemical potential (μ) of an electron system is a fundamental property of a solid. A precise measurement of μ plays a crucial role in understanding the electron interaction and quantum states of matter. However, thermodynamics measurements in micro- and nanoscale samples are challenging because of the small sample volume and large background signals. Here we report an optical readout technique for μ of an arbitrary two-dimensional material. A monolayer semiconductor sensor is capacitively coupled to the sample. The sensor optical response determines a bias that fixes its chemical potential to the band edge and directly reads the μ value of the sample. We demonstrate the technique in AB-stacked MoTe2/WSe2 moiré bilayers. We obtain the μ value with a d.c. sensitivity of about 20 µeV Hz–1/2 and the compressibility and interlayer electric polarization using a.c. readout. The results reveal a …

Moiré materials provide fertile ground for the correlated and topological quantum phenomena. Among them, the quantum anomalous Hall (QAH) effect, in which the Hall resistance is quantized even under zero magnetic field, is a direct manifestation of the intrinsic topological properties of a material and an appealing attribute for low-power electronics applications. The QAH effect has been observed in both graphene and transition metal dichalcogenide (TMD) moiré materials. It is thought to arise from the interaction-driven valley polarization of the narrow moiré bands. Here, we show that the newly discovered QAH state in AB-stacked MoTe 2/W S e 2 moiré bilayers is not valley polarized but valley coherent. The layer-and helicity-resolved optical spectroscopy measurement reveals that the QAH ground state possesses spontaneous spin (valley) polarization aligned (antialigned) in two TMD layers. In addition …

Quantum spin Hall (QSH) insulators are two-dimensional electronic materials that have a bulk band gap similar to an ordinary insulator but have topologically protected pairs of edge modes of opposite chiralities 1, 2, 3, 4, 5, 6. So far, experimental studies have found only integer QSH insulators with counter-propagating up-spins and down-spins at each edge leading to a quantized conductance G 0= e 2/h (with e and h denoting the electron charge and Planck’s constant, respectively) 7, 8, 9, 10, 11, 12, 13, 14. Here we report transport evidence of a fractional QSH insulator in 2.1 twisted bilayer MoTe 2, which supports spin-S z conservation and flat spin-contrasting Chern bands 15, 16. At filling factor ν= 3 of the moiré valence bands, each edge contributes a conductance with zero anomalous Hall conductivity. The state is probably a time-reversal pair of the even-denominator 3/2-fractional Chern insulators …

The Chern insulator displays a quantized Hall effect without Landau levels. Theoretically, this state can be realized by engineering complex next-nearest-neighbour hopping in a honeycomb lattice—the so-called Haldane model. Despite its profound effect on the field of topological physics and recent implementation in cold-atom experiments, the Haldane model has not yet been realized in solid-state materials. Here we report the experimental realization of a Haldane Chern insulator in AB-stacked MoTe2/WSe2 moiré bilayers, which form a honeycomb moiré lattice with two sublattices residing in different layers. We show that the moiré bilayer filled with two holes per unit cell is a quantum spin Hall insulator with a tunable charge gap. Under a small out-of-plane magnetic field, it becomes a Chern insulator with a finite Chern number because the Zeeman field splits the quantum spin Hall insulator into two halves with …

Two-dimensional moiré materials are formed by overlaying two layered crystals with small differences in orientation or/and lattice constant, where their direct coupling generates moiré potentials. Moiré materials have emerged as a platform for the discovery of new physics and device concepts, but while moiré materials are highly tunable, once formed, moiré lattices cannot be easily altered. Here we demonstrate the electrostatic imprinting of moiré lattices onto a target monolayer semiconductor. The moiré potential—created by a lattice of electrons that is supported by a Mott insulator state in a remote MoSe2/WS2 moiré bilayer—imprints a moiré potential that generates flat bands and correlated insulating states in the target monolayer and can be turned on/off by gate tuning the doping density of the moiré bilayer. Additionally, we studied the interplay between the electrostatic and structural relaxation contributions to …

The electron’s kinetic energy plays a pivotal role in magnetism. While virtual electron hopping promotes antiferromagnetism in an insulator, real hopping processes usually favour ferromagnetism. However, in kinetically frustrated systems such as hole-doped triangular lattice Mott insulators, real hopping has instead been shown to favour antiferromagnetism. Kinetic frustration has also been predicted to induce a new quasiparticle, a bound state of the doped hole and a spin flip called a spin polaron, at intermediate magnetic fields, which could form an unusual metallic state. Here we report the direct observation of spin polarons in triangular lattice MoTe2/WSe2 moiré bilayers. A spin polaron phase emerges at a lattice filling factor just below 1 and is separated from the fully spin-polarized phase by a metamagnetic transition. We determine that the spin polaron is a spin-3/2 particle and that its binding energy is …

Strongly correlated bosons in a lattice are a platform that can realize rich bosonic states of matter and quantum phase transitions. While strongly correlated bosons in a lattice have been studied in cold-atom experiments, –, their realization in a solid-state system has remained challenging. Here we trap interlayer excitons–bosons composed of bound electron–hole pairs, in a lattice provided by an angle-aligned WS2/bilayer WSe2/WS2 multilayer. The heterostructure supports Coulomb-coupled triangular moiré lattices of nearly identical period at the top and bottom interfaces. We observe correlated insulating states when the combined electron filling factor of the two lattices, with arbitrary partitions, equals and . These states can be interpreted as exciton density waves in a Bose–Fermi mixture of excitons and holes,. Because of the strong repulsive interactions between the constituents, the holes form robust …

Moiré materials with superlattice periodicity many times the atomic length scale have shown strong electronic correlations and band topology with unprecedented tunability. Non-volatile control of the moiré potentials could allow on-demand switching of superlattice effects but has remained challenging to achieve. Here we demonstrate the switching of the correlated and moiré band insulating states, and the associated nonlinear anomalous Hall effect, by the ferroelectric effect. This is achieved in a ferroelectric WTe2 bilayer of the Td structure with a centred-rectangular moiré superlattice induced by interfacing with a WSe2 monolayer of the H structure. The results can be understood in terms of polarization-dependent charge transfer between two WTe2 monolayers, in which the interfacial layer has a much stronger moiré potential depth; ferroelectric switching thus turns on and off the moiré insulating states. Our study …

Surface acoustic waves (SAWs) provide a contactless method for measuring wave-vector-dependent conductivity. This technique has been used to discover emergent length scales in the fractional quantum Hall regime of traditional, semiconductor-based heterostructures. SAWs would appear to be an ideal match for van der Waals heterostructures, but the right combination of substrate and experimental geometry to allow access to the quantum transport regime has not yet been found. We demonstrate that SAW resonant cavities fabricated on LiNbO 3 substrates can be used to access the quantum Hall regime of high-mobility, hexagonal boron nitride encapsulated, graphene heterostructures. Our work establishes SAW resonant cavities as a viable platform for performing contactless conductivity measurements in the quantum transport regime of van der Waals materials.

Trions are a three-particle bound state of electrons and holes. Experimental realization of a trion liquid in the degenerate quantum limit would open a wide range of phenomena in quantum many-body physics. However, trions have been observed only as optically excited states in doped semiconductors to date. Here we report the emergence of a degenerate trion liquid in a Bose-Fermi mixture of holes and excitons in Coulomb-coupled MoSe2/WSe2 monolayers. By electrically tuning the hole density in WSe2 to be two times the electron density in MoSe2, we generate equilibrium interlayer trions with binding energy about 1 meV at temperatures two orders of magnitude below the Fermi temperature. We further demonstrate a density-tuned phase transition to an electron-hole plasma, spin-singlet correlations for the constituent holes and Zeeman-field-induced dissociation of trions. The results pave the way for exploration of the correlated phases of composite particles in solids.

In spin torque magnetic memories, electrically actuated spin currents are used to switch a magnetic bit. Typically, these require a multilayer geometry including both a free ferromagnetic layer and a second layer providing spin injection. For example, spin may be injected by a non-magnetic layer exhibiting a large spin Hall effect, a phenomenon known as spin–orbit torque. Here we demonstrate a spin–orbit torque magnetic bit in a single two-dimensional system with intrinsic magnetism and strong Berry curvature. We study AB-stacked MoTe2/WSe2, which hosts a magnetic Chern insulator at a carrier density of one hole per moiré superlattice site. We observe hysteretic switching of the resistivity as a function of applied current. Magnetic imaging reveals that current switches correspond to reversals of individual magnetic domains. The real space pattern of domain reversals aligns with spin accumulation measured …

The interaction of a lattice of localized magnetic moments with a sea of conduction electrons in Kondo lattice models induces rich quantum phases of matter, such as Fermi liquids with heavily renormalized electronic quasiparticles, quantum critical non-Fermi liquid metals and unconventional superconductors, among others. The recent demonstration of moir\'e Kondo lattices has opened the door to investigate the Kondo problem with continuously tunable parameters. Although a heavy Fermi liquid phase has been identified in moir\'e Kondo lattices, the magnetic phases and Kondo breakdown transitions remain unexplored. Here we report a density-tuned Kondo destruction in AB-stacked MoTe2/WSe2 moir\'e bilayers by combining magneto transport and optical studies. As the itinerant carrier density decreases, the Kondo temperature decreases. At a critical density, we observe a heavy Fermi liquid to insulator transition, and a nearly concomitant emergence of ferromagnetic order. The observation is consistent with the scenario of a ferromagnetic Anderson insulator and suppression of the Kondo screening effect. Our results pave the path for inducing other exotic quantum phase transitions in moir\'e Kondo lattices.

The Kondo lattice—a matrix of local magnetic moments coupled through spin-exchange interactions to itinerant conduction electrons—is a prototype of strongly correlated quantum matter, , –. Usually, Kondo lattices are realized in intermetallic compounds containing lanthanide or actinide,. The complex electronic structure and limited tunability of both the electron density and exchange interactions in these bulk materials pose considerable challenges to studying Kondo lattice physics. Here we report the realization of a synthetic Kondo lattice in AB-stacked MoTe2/WSe2 moiré bilayers, in which the MoTe2 layer is tuned to a Mott insulating state, supporting a triangular moiré lattice of local moments, and the WSe2 layer is doped with itinerant conduction carriers. We observe heavy fermions with a large Fermi surface below the Kondo temperature. We also observe the destruction of the heavy fermions by an external …

Chern insulators, which are the lattice analogues of the quantum Hall states, can potentially manifest high-temperature topological orders at zero magnetic field to enable next-generation topological quantum devices, –. Until now, integer Chern insulators have been experimentally demonstrated in several systems at zero magnetic field, , , , –, whereas fractional Chern insulators have been reported in only graphene-based systems under a finite magnetic field,. The emergence of semiconductor moiré materials, which support tunable topological flat bands,, provides an opportunity to realize fractional Chern insulators, , –. Here we report thermodynamic evidence of both integer and fractional Chern insulators at zero magnetic field in small-angle twisted bilayer MoTe2 by combining the local electronic compressibility and magneto-optical measurements. At hole filling factor ν = 1 and 2/3, the system is incompressible …

Electrons in two-dimensional semiconductor moiré materials are more delocalized around the lattice sites than those in conventional solids,. The non-local contributions to the magnetic interactions can therefore be as important as the Anderson superexchange, which makes the materials a unique platform to study the effects of competing magnetic interactions,. Here we report evidence of strongly frustrated magnetic interactions in a Wigner–Mott insulator at a two-thirds (2/3) filling of the moiré lattice in angle-aligned WSe2/WS2 bilayers. Magneto-optical measurements show that the net exchange interaction is antiferromagnetic for filling factors below 1 with a strong suppression at a 2/3 filling. The suppression is lifted on screening of the long-range Coulomb interactions and melting of the Wigner–Mott insulators by a nearby metallic gate. The results can be qualitatively captured by a honeycomb-lattice spin model …

Excitonic insulators (EIs), arising in semiconductors when the electron-hole binding energy exceeds the band gap, are a solid-state prototype for bosonic phases of matter. Unlike the charged excitations that are frozen and unable to transport current, the neutral electron-hole pairs (excitons) are free to move in EIs. However, it is intrinsically difficult to demonstrate exciton transport in bulk EI candidates. The recently emerged dipolar EIs based on Coulomb-coupled atomic double layers open the possibility to realize exciton transport across the insulator because separate electrical contacts can be made to the electron and hole layers. Here we show that the strong interlayer excitonic correlation at equal electron and hole densities in the MoSe2/WSe2 double layers separated by a 2-nm barrier gives rise to perfect Coulomb drag. A charge current in one layer induces an equal but opposite drag current in the other. The drag current ratio remains above 0.9 up to about 20 K for low exciton densities. As exciton density increases above the Mott density, the excitons dissociate into the electron-hole plasma abruptly, and only weak Fermi liquid frictional drag is observed. Our experiment moves a step closer to realizing exciton circuitry and superfluidity.

Two-dimensional moiré materials provide a highly controllable solid-state platform for studies of quantum phenomena, –. To date, experimental studies have focused on correlated electronic states, whereas correlated bosonic states in moiré materials have received less attention. Here we report the observation of a correlated dipolar excitonic insulator—a charge-insulating state driven by exciton formation—in a device where a WSe2 monolayer and WSe2/WS2 moiré bilayer are coupled via Coulomb interactions. The system is a Mott insulator when all the holes reside in the moiré layer. Under an out-of-plane electric field, the holes can be continuously transferred to the WSe2 monolayer, but remain strongly bound to the empty moiré sites, effectively forming an interlayer exciton fluid in the moiré lattice. We further observe the emergence of local magnetic moments in the WSe2 monolayer induced by the strong …

Moiré materials with flat electronic bands provide a highly controllable quantum system for studies of strong-correlation physics and topology. In particular, angle-aligned heterobilayers of semiconducting transition metal dichalcogenides with large band offset realize the single-band Hubbard model. Introduction of a new layer degree of freedom is expected to foster richer interactions, enabling Hund’s physics, interlayer exciton condensation and new superconducting pairing mechanisms to name a few. Here we report competing electronic states in twisted AB-homobilayer WSe2, which realizes a bilayer Hubbard model in the weak interlayer hopping limit for holes. By layer-polarizing holes via a perpendicular electric field, we observe a crossover from an excitonic insulator to a charge-transfer insulator at a hole density of ν = 1 (in units of moiré density), a transition from a paramagnetic to an antiferromagnetic …

Moiré superlattices constructed from transition metal dichalcogenides have demonstrated a series of emergent phenomena, including moiré excitons, flat bands, and correlated insulating states. All of these phenomena depend crucially on the presence of strong moiré potentials, yet the properties of these moiré potentials, and the mechanisms by which they can be generated, remain largely open questions. Here, we use angle-resolved photoemission spectroscopy with submicron spatial resolution to investigate an aligned WS2/WSe2 moiré superlattice and graphene/WS2/WSe2 trilayer heterostructure. Our experiments reveal that the hybridization between moiré bands in WS2/WSe2 exhibits an unusually large momentum dependence, with the splitting between moiré bands at the Γ point more than an order of magnitude larger than that at K point. In addition, we discover that the same WS2/WSe2 superlattice can …

Discovering new materials and controlling their properties have been of profound human interest for millennia. Over the past two decades, substantial research efforts have focused on a class of materials known collectively as van der Waals (vdW) materials. The constituent atoms of these materials are strongly bonded within a two-dimensional (2D) plane, with each layer coupled only weakly to its neighbors by a van der Waals adhesion. Thin films of these materials can be isolated down to the atomic monolayer limit, effectively confining charge carriers within the material to two dimensions. This was first demonstrated in 2004 by researchers at the University of Manchester, 1 who used a mechanical exfoliation technique to isolate a single graphene sheet from a bulk graphite crystal. Similar techniques have since been developed to isolate thin films of dozens of other vdW materials. Rapid progress has also been …

Overlaying two atomic layers with a slight lattice mismatch or at a small rotation angle creates a moiré superlattice, which has properties that are markedly modified from (and at times entirely absent in) the ‘parent’ materials. Such moiré materials have progressed the study and engineering of strongly correlated phenomena and topological systems in reduced dimensions. The fundamental understanding of the electronic phases, such as superconductivity, requires a precise control of the challenging fabrication process, involving the rotational alignment of two atomically thin layers with an angular precision below 0.1 degrees. Here we review the essential properties of moiré materials and discuss their fabrication and physics from a reproducibility perspective.

The bandwidth-tuned Wigner-Mott transition is an interaction-driven phase transition from a generalized Wigner crystal to a Fermi liquid. Because the transition is generally accompanied by both magnetic and charge-order instabilities, it remains unclear if a continuous Wigner-Mott transition exists. Here, we demonstrate bandwidth-tuned metal-insulator transitions at fixed fractional fillings of a MoSe2/WS2 moiré superlattice. The bandwidth is controlled by an out-of-plane electric field. The dielectric response is probed optically with the 2s exciton in a remote WSe2 sensor layer. The exciton spectral weight is negligible for the metallic state with a large negative dielectric constant. It continuously vanishes when the transition is approached from the insulating side, corresponding to a diverging dielectric constant or a ‘dielectric catastrophe’ driven by the critical charge dynamics near the transition. Our results support the …

Moiré engineering, – of van der Waals magnetic materials, , , , – can yield new magnetic ground states via competing interactions in moiré superlattices, , –. Theory predicts a suite of interesting phenomena, including multiflavour magnetic states, non-collinear magnetic states, , –, moiré magnon bands and magnon networks in twisted bilayer magnetic crystals, but so far such non-trivial magnetic ground states have not emerged experimentally. Here, by utilizing the stacking-dependent interlayer exchange interactions in two-dimensional magnetic materials, , –, we demonstrate a coexisting ferromagnetic (FM) and antiferromagnetic (AF) ground state in small-twist-angle CrI3 bilayers. The FM–AF state transitions to a collinear FM ground state above a critical twist angle of about 3°. The coexisting FM and AF domains result from a competition between the interlayer AF coupling, which emerges in the monoclinic stacking …

Moiré materials have emerged as a platform for exploring the physics of strong electronic correlations and non-trivial band topology. Here we review the recent progress in semiconductor moiré materials, with a particular focus on transition metal dichalcogenides. Following a brief overview of the general features in this class of materials, we discuss recent theoretical and experimental studies on Hubbard physics, Kane–Mele–Hubbard physics and equilibrium moiré excitons. We also comment on the future opportunities and challenges in the studies of transition metal dichalcogenide and other semiconductor moiré materials.

Moiré heterobilayer transition metal dichalcogenides (TMDs) emerge as an ideal system for simulating the single-band Hubbard model and interesting correlated phases have been observed in these systems. Nevertheless, the moiré bands in heterobilayer TMDs were believed to be topologically trivial. Recently, it was reported that both a quantum valley Hall insulating state at filling ν= 2 (two holes per moiré unit cell) and a valley-polarized quantum anomalous Hall state at filling ν= 1 were observed in A B stacked moiré MoTe 2/WSe 2 heterobilayers. However, how the topologically nontrivial states emerge is not known. In this Letter, we propose that the pseudomagnetic fields induced by lattice relaxation in moiré MoTe 2/WSe 2 heterobilayers could naturally give rise to moiré bands with finite Chern numbers. We show that a time-reversal invariant quantum valley Hall insulator is formed at full filling ν= 2, when two …

Proximity-induced superconductivity in a ferromagnet can induce Cooper pairs with a finite center-of-mass momentum and stabilize Josephson junctions (JJs) with π phase difference in superconductor-ferromagnet-superconductor heterostructures. The emergence of two-dimensional layered superconducting and magnetic materials promises a new platform for realizing π JJs with atomically sharp interfaces. Here we demonstrate a thickness-driven 0-π transition in JJs made of NbSe2 (an Ising superconductor) and Cr2Ge2Te6 (a ferromagnetic semiconductor). By systematically increasing the Cr2Ge2Te6 weak link thickness, we observe a vanishing supercurrent at a critical thickness of ∼8 nm, followed by a re-entrant supercurrent. Near the critical thickness, we further observe unusual supercurrent interference patterns with vanishing critical current around zero in-plane magnetic field. They signify the formation of …

The evolution of a Landau Fermi liquid into a non-magnetic Mott insulator with increasing electronic interactions is one of the most puzzling quantum phase transitions in physics, , , , –. The vicinity of the transition is believed to host exotic states of matter such as quantum spin liquids, , –, exciton condensates and unconventional superconductivity. Semiconductor moiré materials realize a highly controllable Hubbard model simulator on a triangular lattice, , , , , , , , , , , , –, providing a unique opportunity to drive a metal–insulator transition (MIT) via continuous tuning of the electronic interactions. Here, by electrically tuning the effective interaction strength in MoTe2/WSe2 moiré superlattices, we observe a continuous MIT at a fixed filling of one electron per unit cell. The existence of quantum criticality is supported by the scaling collapse of the resistance, a continuously vanishing charge gap as the critical point is …

The strong excitonic effect in monolayer transition metal dichalcogenide (TMD) semiconductors has enabled many fascinating light–matter interaction phenomena. Examples include strongly coupled exciton–polaritons and nearly perfect atomic monolayer mirrors. The strong light–matter interaction also opens the door for dynamical control of mechanical motion through the exciton resonance of monolayer TMDs. Here, we report the observation of exciton-optomechanical coupling in a suspended monolayer MoSe2 mechanical resonator. By moderate optical pumping near the MoSe2 exciton resonance, we have observed optical damping and antidamping of mechanical vibrations as well as the optical spring effect. The exciton-optomechanical coupling strength is also gate-tunable. Our observations can be understood in a model based on photothermal backaction and gate-induced mirror symmetry breaking in the …

Electron correlation and topology are two central threads of modern condensed matter physics. Semiconductor moiré materials provide a highly tuneable platform for studies of electron correlation, , , , , , , , , , –. Correlation-driven phenomena, including the Mott insulator, , –, generalized Wigner crystals,,, stripe phases and continuous Mott transition,, have been demonstrated. However, non-trivial band topology has remained unclear. Here we report the observation of a quantum anomalous Hall effect in AB-stacked MoTe2 /WSe2 moiré heterobilayers. Unlike in the AA-stacked heterobilayers, an out-of-plane electric field not only controls the bandwidth but also the band topology by intertwining moiré bands centred at different layers. At half band filling, corresponding to one particle per moiré unit cell, we observe quantized Hall resistance, h/e2 (with h and e denoting the Planck’s constant and electron charge …

Moiré systems formed by 2D atomic layers have widely tunable electrical and optical properties and host exotic, strongly correlated and topological phenomena, including superconductivity, correlated insulator states and orbital magnetism. In this Viewpoint, researchers studying different aspects of moiré materials discuss the most exciting directions in this rapidly expanding field.

The strong Ising spin–orbit coupling in certain two-dimensional transition metal dichalcogenides can profoundly affect the superconducting state in few-layer samples. For example, in NbSe2, this effect combines with the reduced dimensionality to stabilize the superconducting state against magnetic fields up to ~35 T, and could lead to topological superconductivity. Here we report a two-fold rotational symmetry of the superconducting state in few-layer NbSe2 under in-plane external magnetic fields, in contrast to the three-fold symmetry of the lattice. Both the magnetoresistance and critical field exhibit this two-fold symmetry, and it also manifests deep inside the superconducting state in NbSe2/CrBr3 superconductor-magnet tunnel junctions. In both cases, the anisotropy vanishes in the normal state, demonstrating that it is an intrinsic property of the superconducting phase. We attribute the behaviour to the mixing …

We demonstrate a mechanism for magnetoresistance oscillations in insulating states of two-dimensional (2D) materials arising from the interaction of the 2D layer and proximal graphite gates. We study a series of devices based on different 2D systems, including mono-and bilayer T d− WTe 2, MoTe 2/WSe 2 moiré heterobilayers, and Bernal-stacked bilayer graphene, which all share a similar graphite-gated geometry. We find that the 2D systems, when tuned near an insulating state, generically exhibit magnetoresistance oscillations corresponding to a high-density Fermi surface, in contravention of naïve band theory. Simultaneous measurement of the resistivity of the graphite gates shows that the oscillations of the sample layer are precisely correlated with those of the graphite gates. Further supporting this connection, the oscillations are quenched when the graphite gate is replaced by a low-mobility metal, TaSe 2 …

Excitonic insulators (EIs) arise from the formation of bound electron–hole pairs (excitons), in semiconductors and provide a solid-state platform for quantum many-boson physics, , , , –. Strong exciton–exciton repulsion is expected to stabilize condensed superfluid and crystalline phases by suppressing both density and phase fluctuations, , –. Although spectroscopic signatures of EIs have been reported,, –, conclusive evidence for strongly correlated EI states has remained elusive. Here we demonstrate a strongly correlated two-dimensional (2D) EI ground state formed in transition metal dichalcogenide (TMD) semiconductor double layers. A quasi-equilibrium spatially indirect exciton fluid is created when the bias voltage applied between the two electrically isolated TMD layers is tuned to a range that populates bound electron–hole pairs, but not free electrons or holes, –. Capacitance measurements show that the …

Superconductivity and magnetism are generally incompatible because of the opposing requirement on electron spin alignment. When combined, they produce a multitude of fascinating phenomena, including unconventional superconductivity and topological superconductivity. The emergence of two-dimensional (2D)layered superconducting and magnetic materials that can form nanoscale junctions with atomically sharp interfaces presents an ideal laboratory to explore new phenomena from coexisting superconductivity and magnetic ordering. Here we report tunneling spectroscopy under an in-plane magnetic field of superconductor-ferromagnet-superconductor (S/F/S) tunnel junctions that are made of 2D Ising superconductor NbSe2 and ferromagnetic insulator CrBr3. We observe nearly 100% tunneling anisotropic magnetoresistance (AMR), that is, difference in tunnel resistance upon changing magnetization direction from out-of-plane to inplane. The giant tunneling AMR is induced by superconductivity, particularly, a result of interfacial magnetic exchange coupling and spin-dependent quasiparticle scattering. We also observe an intriguing magnetic hysteresis effect in superconducting gap energy and quasiparticle scattering rate with a critical temperature that is 2 K below the superconducting transition temperature. Our study paves the path for exploring superconducting spintronic and unconventional superconductivity in van der Waals heterostructures.

Stripe phases, in which the rotational symmetry of charge density is spontaneously broken, occur in many strongly correlated systems with competing interactions, , , , , , , , , –. However, identifying and studying such stripe phases remains challenging. Here we uncover stripe phases in WSe2/WS2 moiré superlattices by combining optical anisotropy and electronic compressibility measurements. We find strong electronic anisotropy over a large doping range peaked at 1/2 filling of the moiré superlattice. The 1/2 state is incompressible and assigned to an insulating stripe crystal phase. Wide-field imaging reveals domain configurations with a preferential alignment along the high-symmetry axes of the moiré superlattice. Away from 1/2 filling, we observe additional stripe crystals at commensurate filling 1/4, 2/5 and 3/5, and compressible electronic liquid crystal states at incommensurate fillings. Our results demonstrate …

Two-dimensional (2D) magnetic materials have attracted much recent interest with unique properties emerging at the few-layer limit. Beyond the reported impacts on the static magnetic properties, the effects of reducing the dimensionality on the magnetization dynamics are also of fundamental interest and importance for 2D device development. In this report, we investigate the spin dynamics in atomically thin antiferromagnetic FePS3 of varying layer numbers using ultrafast pump–probe spectroscopy. Following the absorption of an optical pump pulse, the time evolution of the antiferromagnetic order parameter is probed by magnetic linear birefringence. We observe a strong divergence in the demagnetization time near the Néel temperature. The divergence can be characterized by a power-law dependence on the reduced temperature, with an exponent decreasing with sample thickness. We compare our results to …

Moiré superlattices offer an unprecedented opportunity for tailoring interactions between quantum particles, , , , , , , , , – and their coupling to electromagnetic fields, , , , , –. Strong superlattice potentials generate moiré minibands of excitons, –—bound pairs of electrons and holes that reside either in a single layer (intralayer excitons) or in two separate layers (interlayer excitons). Twist-angle-controlled interlayer electronic hybridization can also mix these two types of exciton to combine their strengths,,. Here we report the direct observation of layer-hybridized moiré excitons in angle-aligned WSe2/WS2 and MoSe2/WS2 superlattices by optical reflectance spectroscopy. These excitons manifest a hallmark signature of strong coupling in WSe2/WS2, that is, energy-level anticrossing and oscillator strength redistribution under a vertical electric field. They also exhibit doping-dependent renormalization and hybridization …

Ferromagnetism in two-dimensional materials presents a promising platform for the development of ultrathin spintronic devices with advanced functionalities. Recently discovered ferromagnetic van der Waals crystals such as CrI3, readily isolated two-dimensional crystals, are highly tunable through external fields or structural modifications. However, there remains a challenge because of material instability under air exposure. Here, we report the observation of an air-stable and layer-dependent ferromagnetic (FM) van der Waals crystal, CrPS4, using magneto-optic Kerr effect microscopy. In contrast to the antiferromagnetic (AFM) bulk, the FM out-of-plane spin orientation is found in the monolayer crystal. Furthermore, alternating AFM and FM properties observed in even and odd layers suggest robust antiferromagnetic exchange interactions between layers. The observed ferromagnetism in these crystals remains …

Moiré superlattices of two-dimensional van der Waals materials have emerged as a powerful platform for designing electronic band structures and discovering emergent physical phenomena. A key concept involves the creation of long-wavelength periodic potential and moiré bands in a crystal through interlayer electronic hybridization or atomic corrugation when two materials are overlaid. Here we demonstrate a new approach based on spatially periodic dielectric screening to create moiré bands in a monolayer semiconductor. This approach relies on reduced dielectric screening of the Coulomb interactions in monolayer semiconductors and their environmental dielectric-dependent electronic band structure. We observe optical transitions between moiré bands in monolayer WSe2 when it is placed close to small-angle-misaligned graphene on hexagonal boron nitride. The moiré bands are a result of long-range …

Van der Waals moiré materials have emerged as a highly controllable platform to study electronic correlation phenomena, , , , , , , , , , , , , , , –. Robust correlated insulating states have recently been discovered at both integer and fractional filling factors of semiconductor moiré systems, , , , , , –. In this study we explored the thermodynamic properties of these states by measuring the gate capacitance of MoSe2/WS2 moiré superlattices. We observed a series of incompressible states for filling factors 0–8 and anomalously large capacitance in the intervening compressible regions. The anomalously large capacitance, which was nearly 60% above the device’s geometrical capacitance, was most pronounced at small filling factors, below the melting temperature of the charge-ordered states, and for small sample–gate separation. It is a manifestation of the device-geometry-dependent Coulomb interaction between electrons …

Strong magnetization fluctuations are expected near the thermodynamic critical point of a continuous magnetic phase transition. Such critical fluctuations are highly correlated and in principle can occur at any time and length scales; they govern critical phenomena and potentially can drive new phases,. Although critical phenomena in magnetic materials have been studied using neutron scattering, magnetic a.c. susceptibility and other techniques, –, direct real-time imaging of critical magnetization fluctuations remains elusive. Here we develop a fast and sensitive magneto-optical imaging microscope to achieve wide-field, real-time monitoring of critical magnetization fluctuations in single-layer ferromagnetic insulator CrBr3. We track the critical phenomena directly from the fluctuation correlations and observe both slowing-down dynamics and enhanced correlation length. Through real-time feedback control of the …

Monolayer WSe 2 hosts bright single-photon emitters. Because of its compliance, monolayer WSe 2 conforms to patterned substrates without breaking, thus creating the potential for large local strain, which is one activation mechanism of its intrinsic quantum emitters. Here, we report an approach to creating spatially isolated quantum emitters from WSe 2 monolayers that display clean spectra with little detrimental background signal. We show that a bilayer of hexagonal boron nitride and WSe 2 placed on a nanostructured substrate can be used to create and shape wrinkles that communicate local strain to WSe 2, thus creating quantum emitters that are isolated from substrate features. We compare quantum emitters created directly on top of substrate features with quantum emitters formed along wrinkles and find that the spectra of the latter consist of mainly a single peak and a low background fluorescence. We also …

Here, we report a magnetotransport study of high-quality Sr Ru O 3 thin films with high residual resistivity ratios grown by reactive oxide molecular-beam epitaxy. The transverse resistivity exhibits clear anomalies which are typically believed to be signatures of the topological Hall effect and the presence of magnetic skyrmions. By systematically investigating these anomalies as a function of temperature, field, film thickness, and excitation currents we verify that these anomalies originate from a two-channel anomalous Hall effect arising from magnetic inhomogeneities in the samples and not from an intrinsic topological Hall effect. Using a combination of magnetic circular dichroism, scanning transmission electron microscopy, x-ray diffraction, and magnetotransport, we discover that strain relaxation effects in the films are the origin of these inhomogeneities. Our results shed light on the recently reported Hall effect …

Quantum particles on a lattice with competing long-range interactions are ubiquitous in physics; transition metal oxides,, layered molecular crystals and trapped-ion arrays are a few examples. In the strongly interacting regime, these systems often show a rich variety of quantum many-body ground states that challenge theory. The emergence of transition metal dichalcogenide moiré superlattices provides a highly controllable platform in which to study long-range electronic correlations, , , , , , –. Here we report an observation of nearly two dozen correlated insulating states at fractional fillings of tungsten diselenide/tungsten disulfide moiré superlattices. This finding is enabled by a new optical sensing technique that is based on the sensitivity to the dielectric environment of the exciton excited states in a single-layer semiconductor of tungsten diselenide. The cascade of insulating states shows an energy ordering that is …

Remarkable properties of two-dimensional (2D) layer magnetic materials, which include spin filtering in magnetic tunnel junctions and the gate control of magnetic states, were demonstrated recently, , , , , , , , , , –. Whereas these studies focused on static properties, dynamic magnetic properties, such as excitation and control of spin waves, remain elusive. Here we investigate spin-wave dynamics in antiferromagnetic CrI3 bilayers using an ultrafast optical pump/magneto-optical Kerr probe technique. Monolayer WSe2 with a strong excitonic resonance was introduced on CrI3 to enhance the optical excitation of spin waves. We identified subterahertz magnetic resonances under an in-plane magnetic field, from which the anisotropy and interlayer exchange fields were determined. We further showed tuning of the antiferromagnetic resonances by tens of gigahertz through electrostatic gating. Our results shed light on …

Isolated spins are the focus of intense scientific exploration due to their potential role as qubits for quantum information science. Optical access to single spins, demonstrated in III-V semiconducting quantum dots, has fueled research aimed at realizing quantum networks. More recently, quantum emitters in atomically thin materials such as tungsten diselenide have been demonstrated to host optically addressable single spins by means of electrostatic doping the localized excitons. Electrostatic doping is not the only route to charging localized quantum emitters and another path forward is through band structure engineering using van der Waals heterojunctions. Critical to this second approach is to interface tungsten diselenide with other van der Waals materials with relative band-alignments conducive to the phenomenon of charge transfer. In this work we show that the Type-II band-alignment between tungsten …

The Hubbard model, formulated by physicist John Hubbard in the 1960s, is a simple theoretical model of interacting quantum particles in a lattice. The model is thought to capture the essential physics of high-temperature superconductors, magnetic insulators and other complex quantum many-body ground states,. Although the Hubbard model provides a greatly simplified representation of most real materials, it is nevertheless difficult to solve accurately except in the one-dimensional case,. Therefore, the physical realization of the Hubbard model in two or three dimensions, which can act as an analogue quantum simulator (that is, it can mimic the model and simulate its phase diagram and dynamics,), has a vital role in solving the strong-correlation puzzle, namely, revealing the physics of a large number of strongly interacting quantum particles. Here we obtain the phase diagram of the two-dimensional triangular …

Achieving on-demand control of the valley degree of freedom is essential for valley-based information science and technology. Optical and magnetic control of the valley degree of freedom in monolayer transition-metal dichalcogenide (TMD) semiconductors has been studied extensively. However, electrical control of the valley polarization has remained a challenge. Here we demonstrate switching of the valley polarization in monolayer WS e 2 by electrical gating. This is achieved by coupling a WS e 2 monolayer to a two-dimensional (2D) layered magnetic insulator Cr I 3. The valley degeneracy in WS e 2 is lifted by the magnetic proximity effect. The valley polarization is switched through gate control of the interlayer spin-flip transition in 2D Cr I 3, which switches the magnetization of the Cr I 3 layer adjacent to the WS e 2 layer. The effect is manifested by a sign change in the photoluminescence handedness of WS …

Magnetostriction, coupling between the mechanical and magnetic degrees of freedom, finds a variety of applications in magnetic actuation, transduction and sensing,. The discovery of two-dimensional layered magnetic materials, , , , – presents a new platform to explore the magnetostriction effects in ultrathin solids. Here we demonstrate an exchange-driven magnetostriction effect in mechanical resonators made of two-dimensional antiferromagnetic CrI3. The mechanical resonance frequency is found to depend on the magnetic state of the material. We quantify the relative importance of the exchange and anisotropy magnetostriction by measuring the resonance frequency under a magnetic field parallel and perpendicular to the easy axis, respectively. Furthermore, we show efficient strain-tuning of the internal magnetic interactions in two-dimensional CrI3 as a result of inverse magnetostriction. Our results establish …

We report measurements of current-induced thermoelectric and spin–orbit torque effects within devices in which multilayers of the semiconducting two-dimensional van der Waals magnet Cr2Ge2Te6 (CGT) are integrated with Pt and Ta metal overlayers. We show that the magnetic orientation of the CGT can be detected accurately either electrically (using an anomalous Hall effect) or optically (using magnetic circular dichroism) with good consistency. The samples exhibit large thermoelectric effects, but nevertheless, the spin–orbit torque can be measured quantitatively using the angle-dependent second harmonic Hall technique. For CGT/Pt, we measure the spin–orbit torque efficiency to be similar to conventional metallic-ferromagnet/Pt devices with the same Pt resistivity. The interfacial transparency for spin currents is therefore similar in both classes of devices. Our results demonstrate the promise of incorporating …

Memristive devices whose resistance can be hysteretically switched by electric field or current are intensely pursued both for fundamental interest as well as potential applications in neuromorphic computing and phase‐change memory. When the underlying material exhibits additional charge or spin order, the resistive states can be directly coupled, further allowing electrical control of the collective phases. The observation of abrupt, memristive switching of tunneling current in nanoscale junctions of ultrathin CrI3, a natural layer antiferromagnet, is reported here. The coupling to spin order enables both tuning of the resistance hysteresis by magnetic field and electric‐field switching of magnetization even in multilayer samples.