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A central problem in modern condensed matter physics is the understanding of materials with strong electron correlations. Despite extensive work, the essential physics of many of these systems is not understood and there is very little ability to make predictions in this class of materials. In this manuscript we share our personal views on the major open problems in the field of correlated electron systems. We discuss some possible routes to make progress in this rich and fascinating field. This manuscript is the result of the vigorous discussions and deliberations that took place at Johns Hopkins University during a three-day workshop January 27, 28, and 29, 2020 that brought together six senior scientists and 46 more junior scientists. Our hope, is that the topics we have presented will provide inspiration for others working in this field and motivation for the idea that significant progress can be made on very hard problems if we focus our collective energies., Comment: 55 pages, 19 figures

Magnetic proximity effects are crucial ingredients for engineering spintronic, superconducting, and topological phenomena in heterostructures. Such effects are highly sensitive to the interfacial electronic properties, such as electron wave function overlap and band alignment. The recent emergence of van der Waals (vdW) magnets enables the possibility of tuning proximity effects via designing heterostructures with atomically clean interfaces. In particular, atomically thin CrI3 exhibits layered antiferromagnetism, where adjacent ferromagnetic monolayers are antiferromagnetically coupled. Exploiting this magnetic structure, we uncovered a layer-resolved magnetic proximity effect in heterostructures formed by monolayer WSe2 and bi/trilayer CrI3. By controlling the individual layer magnetization in CrI3 with a magnetic field, we found that the spin-dependent charge transfer between WSe2 and CrI3 is dominated by the interfacial CrI3 layer, while the proximity exchange field is highly sensitive to the layered magnetic structure as a whole. These properties enabled us to use monolayer WSe2 as a spatially sensitive magnetic sensor to map out layered antiferromagnetic domain structures at zero magnetic field as well as antiferromagnetic/ferromagnetic domains near the spin-flip transition in bilayer CrI3. Our work reveals a new way to control proximity effects and probe interfacial magnetic order via vdW engineering., Comment: to appear in Nature Nanotechnology

X-ray scattering is one of the primary tools to determine crystallographic configuration with atomic accuracy. However, the measurement of ultrafast structural dynamics in monolayer crystals remains a long-standing challenge due to a significant reduction of diffraction volume and complexity of data analysis, prohibiting the application of ultrafast x-ray scattering to study nonequilibrium structural properties at the two-dimensional limit. Here, we demonstrate femtosecond surface x-ray diffraction in combination with crystallographic model-refinement calculations to quantify the ultrafast structural dynamics of monolayer WSe$_2$ crystals supported on a substrate. We found the absorbed optical photon energy is preferably coupled to the in-plane lattice vibrations within 2 picoseconds while the out-of-plane lattice vibration amplitude remains unchanged during the first 10 picoseconds. The model-assisted fitting suggests an asymmetric intralayer spacing change upon excitation. The observed nonequilibrium anisotropic structural dynamics in two-dimensional materials agrees with first-principles nonadiabatic modeling in both real and momentum space, marking the distinct structural dynamics of monolayer crystals from their bulk counterparts. The demonstrated methods unlock the benefit of surface sensitive x-ray scattering to quantitatively measure ultrafast structural dynamics in atomically thin materials and across interfaces.

The creation of moir\'e patterns in crystalline solids is a powerful approach to manipulate their electronic properties, which are fundamentally influenced by periodic potential landscapes. In 2D materials, a moir\'e pattern with a superlattice potential can form by vertically stacking two layered materials with a twist and/or finite lattice constant difference. This unique approach has led to emergent electronic phenomena, including the fractal quantum Hall effect, tunable Mott insulators, and unconventional superconductivity. Furthermore, theory predicts intriguing effects on optical excitations by a moir\'e potential in 2D valley semiconductors, but these signatures have yet to be experimentally detected. Here, we report experimental evidence of interlayer valley excitons trapped in a moir\'e potential in MoSe$_2$/WSe$_2$ heterobilayers. At low temperatures, we observe photoluminescence near the free interlayer exciton energy but with over 100 times narrower linewidths. The emitter g-factors are homogeneous across the same sample and only take two values, -15.9 and 6.7, in samples with twisting angles near 60{\deg} and 0\deg, respectively. The g-factors match those of the free interlayer exciton, which is determined by one of two possible valley pairing configurations. At a twist angle near 20\deg, the emitters become two orders of magnitude dimmer, but remarkably, they possess the same g-factor as the heterobilayer near 60\deg. This is consistent with the Umklapp recombination of interlayer excitons near the commensurate 21.8{\deg} twist angle. The emitters exhibit strong circular polarization, which implies the preservation of three-fold rotation symmetry by the trapping potential. Together with the power and excitation energy dependence, all evidence points to their origin as interlayer excitons trapped in a smooth moir\'e potential with inherited valley-contrasting physics.

Monolayer valley semiconductors, such as tungsten diselenide (WSe$_2$), possess valley pseudospin degrees of freedom that are optically addressable but degenerate in energy. Lifting the energy degeneracy by breaking time-reversal symmetry is vital for valley manipulation. This has been realized by directly applying magnetic fields or via pseudo-magnetic fields generated by intense circularly polarized optical pulses. However, sweeping large magnetic fields is impractical for devices, and the pseudo-magnetic fields are only effective in the presence of ultrafast laser pulses. The recent rise of two-dimensional (2D) magnets unlocks new approaches to control valley physics via van der Waals heterostructure engineering. Here we demonstrate wide continuous tuning of the valley polarization and valley Zeeman splitting with small changes in the laser excitation power in heterostructures formed by monolayer WSe$_2$ and 2D magnetic chromium triiodide (CrI$_3$). The valley manipulation is realized via optical control of the CrI$_3$magnetization, which tunes the magnetic exchange field over a range of 20 T. Our results reveal a convenient new path towards optical control of valley pseudospins and van der Waals magnetic heterostructures., Comment: 10 pages main text, 4 figures, 12 pages supplementary information, in Nano Letters

The challenge of controlling magnetism using electric fields raises fundamental questions and addresses technological needs such as low-dissipation magnetic memory. The recently reported two-dimensional (2D) magnets provide a new system for studying this problem owing to their unique magnetic properties. For instance, bilayer chromium triiodide (CrI3) behaves as a layered antiferromagnet with a magnetic field-driven metamagnetic transition. Here, we demonstrate electrostatic gate control of magnetism in CrI3 bilayers, probed by magneto-optical Kerr effect (MOKE) microscopy. At fixed magnetic fields near the metamagnetic transition, we realize voltage-controlled switching between antiferromagnetic and ferromagnetic states. At zero magnetic field, we demonstrate a time-reversal pair of layered antiferromagnetic states which exhibit spin-layer locking, leading to a remarkable linear dependence of their MOKE signals on gate voltage with opposite slopes. Our results pave the way for exploring new magnetoelectric phenomena and van der Waals spintronics based on 2D materials., Comment: To appear in Nature Nanotechnology

Magnetic multilayer devices that exploit magnetoresistance are the backbone of magnetic sensing and data storage technologies. Here we report novel multiple-spin-filter magnetic tunnel junctions (sf-MTJs) based on van der Waals (vdW) heterostructures in which atomically thin chromium triiodide (CrI3) acts as a spin-filter tunnel barrier sandwiched between graphene contacts. We demonstrate tunneling magnetoresistance which is drastically enhanced with increasing CrI3 layer thickness, reaching a record 19,000% for magnetic multilayer structures using four-layer sf-MTJs at low temperatures. These devices also show multiple resistance states as a function of magnetic field, suggesting the potential for multi-bit functionalities using an individual vdW sf-MTJ. Using magnetic circular dichroism measurements, we attribute these effects to the intrinsic layer-by-layer antiferromagnetic ordering of the atomically thin CrI3. Our work reveals the possibility to push magnetic information storage to the atomically thin limit, and highlights CrI3 as a superlative magnetic tunnel barrier for vdW heterostructure spintronic devices., Comment: Submitted

Systems that simultaneously exhibit superconductivity and spin-orbit coupling are predicted to provide a route toward topological superconductivity and unconventional electron pairing, driving significant contemporary interest in these materials. Monolayer transition-metal dichalcogenide (TMD) superconductors in particular lack inversion symmetry, enforcing a spin-triplet component of the superconducting wavefunction that increases with the strength of spin-orbit coupling. In this work, we present an experimental and theoretical study of two intrinsic TMD superconductors with large spin-orbit coupling in the atomic layer limit, metallic 2H-TaS$_2$ and 2H-NbSe$_2$. For the first time in TaS$_2$, we investigate the superconducting properties as the material is reduced to a monolayer and show that high-field measurements point to the largest upper critical field thus reported for an intrinsic TMD superconductor. In few-layer samples, we find that the enhancement of the upper critical field is sustained by the dominance of spin-orbit coupling over weak interlayer coupling, providing additional platforms for unconventional superconducting states in two dimensions., Comment: 8 pages, 4 figures, plus supplemental material

Bulk chromium triiodide (CrI$_3$) has long been known as a layered van der Waals ferromagnet. However, its monolayer form was only recently isolated and confirmed to be a truly two-dimensional (2D) ferromagnet, providing a new platform for investigating light-matter interactions and magneto-optical phenomena in the atomically thin limit. Here, we report spontaneous circularly polarized photoluminescence in monolayer CrI$_3$ under linearly polarized excitation, with helicity determined by the monolayer magnetization direction. In contrast, the bilayer CrI$_3$ photoluminescence exhibits vanishing circular polarization, supporting the recently uncovered anomalous antiferromagnetic interlayer coupling in CrI$_3$ bilayers. Distinct from the Wannier-Mott excitons that dominate the optical response in well-known 2D van der Waals semiconductors, our absorption and layer-dependent photoluminescence measurements reveal the importance of ligand-field and charge-transfer transitions to the optoelectronic response of atomically thin CrI$_3$. We attribute the photoluminescence to a parity-forbidden d-d transition characteristic of Cr$^{3+}$ complexes, which displays broad linewidth due to strong vibronic coupling and thickness-independent peak energy due to its localized molecular orbital nature., Comment: 12 pages of main text, 4 figures, 6 pages of supplementary materials

The integration of magnetic material with semiconductors has been fertile ground for fundamental science as well as of great practical interest toward the seamless integration of information processing and storage. Here we create van der Waals heterostructures formed by an ultrathin ferromagnetic semiconductor CrI3 and a monolayer of WSe2. We observe unprecedented control of the spin and valley pseudospin in WSe2, where we detect a large magnetic exchange field of nearly 13 T and rapid switching of the WSe2 valley splitting and polarization via flipping of the CrI3 magnetization. The WSe2 photoluminescence intensity strongly depends on the relative alignment between photo-excited spins in WSe2 and the CrI3 magnetization, due to ultrafast spin-dependent charge hopping across the heterostructure interface. The photoluminescence detection of valley pseudospin provides a simple and sensitive method to probe the intriguing domain dynamics in the ultrathin magnet, as well as the rich spin interactions within the heterostructure., Comment: Supplementary Materials included. To appear in Science Advances

Since the celebrated discovery of graphene, the family of two-dimensional (2D) materials has grown to encompass a broad range of electronic properties. Recent additions include spin-valley coupled semiconductors, Ising superconductors that can be tuned into a quantum metal, possible Mott insulators with tunable charge-density waves, and topological semi-metals with edge transport. Despite this progress, there is still no 2D crystal with intrinsic magnetism, which would be useful for many technologies such as sensing, information, and data storage. Theoretically, magnetic order is prohibited in the 2D isotropic Heisenberg model at finite temperatures by the Mermin-Wagner theorem. However, magnetic anisotropy removes this restriction and enables, for instance, the occurrence of 2D Ising ferromagnetism. Here, we use magneto-optical Kerr effect (MOKE) microscopy to demonstrate that monolayer chromium triiodide (CrI3) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temperature of 45 K is only slightly lower than the 61 K of the bulk crystal, consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phase transition, showcasing the hallmark thickness-dependent physical properties typical of van der Waals crystals. Remarkably, bilayer CrI3 displays suppressed magnetization with a metamagnetic effect, while in trilayer the interlayer ferromagnetism observed in the bulk crystal is restored. Our work creates opportunities for studying magnetism by harnessing the unique features of atomically-thin materials, such as electrical control for realizing magnetoelectronics, and van der Waals engineering for novel interface phenomena., Comment: To appear in Nature

Van der Waals heterostructures formed by two different monolayer semiconductors have emerged as a promising platform for new optoelectronic and spin/valleytronic applications. In addition to its atomically thin nature, a two-dimensional semiconductor heterostructure is distinct from its three-dimensional counterparts due to the unique coupled spin-valley physics of its constituent monolayers. Here, we report the direct observation that an optically generated spin-valley polarization in one monolayer can be transferred between layers of a two-dimensional MoSe2-WSe2 heterostructure. Using nondegenerate optical circular dichroism spectroscopy, we show that charge transfer between two monolayers conserves spin-valley polarization and is only weakly dependent on the twist angle between layers. Our work points to a new spin-valley pumping scheme in nanoscale devices, provides a fundamental understanding of spin-valley transfer across the two-dimensional interface, and shows the potential use of two-dimensional semiconductors as a spin-valley generator in 2D spin/valleytronic devices for storing and processing information.

Nano-resonator integrated with two-dimensional materials (e.g. transition metal dichalcogenides) have recently emerged as a promising nano-optoelectronic platform. Here we demonstrate resonatorenhanced second-harmonic generation (SHG) in tungsten diselenide using a silicon photonic crystal cavity. By pumping the device with the ultrafast laser pulses near the cavity mode at the telecommunication wavelength, we observe a near visible SHG with a narrow linewidth and near unity linear polarization, originated from the coupling of the pump photon to the cavity mode. The observed SHG is enhanced by factor of ~200 compared to a bare monolayer on silicon. Our results imply the efficacy of cavity integrated monolayer materials for nonlinear optics and the potential of building a silicon-compatible second-order nonlinear integrated photonic platform.

Combining monolayers of different two-dimensional (2D) semiconductors into heterostructures opens up a wealth of possibilities for novel electronic and optical functionalities. Exploiting them hinges on accurate measurements of the band parameters and orbital hybridization in separate and stacked monolayers, many of which are only available as small samples. The recently introduced technique of angle-resolved photoemission spectroscopy with submicron spatial resolution ({\mu}-ARPES) offers the capability to measure small samples, but the energy resolution obtained for such exfoliated samples to date (~0.5 eV) has been inadequate. Here, we show that by suitable heterostructure sample design the full potential of {\mu}-ARPES can be realized. We focus on MoSe2/WSe2 van der Waals heterostructures, which are 2D analogs of 3D semiconductor heterostructures. We find that in a MoSe2/WSe2 heterobilayer the bands in the K valleys are weakly hybridized, with the conduction and valence band edges originating in the MoSe2 and WSe2 respectively. There is stronger hybridization at the {\Gamma} point, but the valence band edge remains at the K points. This is consistent with the recent observation of interlayer excitons where the electron and hole are valley polarized but in opposite layers. We determine the valence band offset to be 300 meV, which combined with photoluminescence measurements implies that the binding energy of interlayer excitons is at least 200 meV, comparable with that of intralayer excitons., Comment: 10 pages, 4 figures; + 14 pages, 8 figures in supplementary

Heterostructures comprising different monolayer semiconductors provide a new system for fundamental science and device technologies, such as in the emerging field of valleytronics. Here, we realize valley-specific interlayer excitons in monolayer WSe2-MoSe2 vertical heterostructures. We create interlayer exciton spin-valley polarization by circularly polarized optical pumping and determine a valley lifetime of 40 nanoseconds. This long-lived polarization enables the visualization of the expansion of a valley-polarized exciton cloud over several microns. The spatial pattern of the polarization evolves into a ring with increasing exciton density, a manifestation of valley exciton exchange interactions. Our work lays a foundation for quantum optoelectronics and valleytronics based on interlayer excitons in van der Waals heterostructures., Comment: This is the original submitted version. The final version is to appear in Science

Nonlinear optical frequency conversion, in which optical fields interact with a nonlinear medium to produce new field frequencies, is ubiquitous in modern photonic systems. However, the nonlinear electric susceptibilities that give rise to such phenomena are often challenging to tune in a given material, and so far, dynamical control of optical nonlinearities remains confined to research labs as a spectroscopic tool. Here, we report a mechanism to electrically control second-order optical nonlinearities in monolayer WSe2, an atomically thin semiconductor. We show that the intensity of second-harmonic generation at the A-exciton resonance is tunable by over an order of magnitude at low temperature and nearly a factor of 4 at room temperature through electrostatic doping in a field-effect transistor. Such tunability arises from the strong exciton charging effects in monolayer semiconductors, which allow for exceptional control over the oscillator strengths at the exciton and trion resonances. The exciton-enhanced second-harmonic generation is counter-circularly polarized to the excitation laser, arising from the combination of the two-photon and one-photon valley selection rules that have opposite helicity in the monolayer. Our study paves the way towards a new platform for chip-scale, electrically tunable nonlinear optical devices based on two-dimensional semiconductors., Comment: Published in Nature Nanotechnology

Semi-metallic graphene and semiconducting monolayer transition metal dichalcogenides (TMDCs) are the two-dimensional (2D) materials most intensively studied in recent years. Recently, black phosphorus emerged as a promising new 2D material due to its widely tunable and direct bandgap, high carrier mobility and remarkable in-plane anisotropic electrical, optical and phonon properties. However, current progress is primarily limited to its thin-film form, and its unique properties at the truly 2D quantum confinement have yet to be demonstrated. Here, we reveal highly anisotropic and tightly bound excitons in monolayer black phosphorus using polarization-resolved photoluminescence measurements at room temperature. We show that regardless of the excitation laser polarization, the emitted light from the monolayer is linearly polarized along the light effective mass direction and centers around 1.3 eV, a clear signature of emission from highly anisotropic bright excitons. In addition, photoluminescence excitation spectroscopy suggests a quasiparticle bandgap of 2.2 eV, from which we estimate an exciton binding energy of around 0.9 eV, consistent with theoretical results based on first-principles. The experimental observation of highly anisotropic, bright excitons with exceedingly large binding energy not only opens avenues for the future explorations of many-electron effects in this unusual 2D material, but also suggests a promising future in optoelectronic devices such as on-chip infrared light sources.