Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers.

The formation of moiré patterns in crystalline solids can be used to manipulate their electronic properties, which are fundamentally influenced by periodic potential landscapes. In two-dimensional materials, a moiré pattern with a superlattice potential can be formed by vertically stacking two layered materials with a twist and/or a difference in lattice constant. This approach has led to electronic phenomena including the fractal quantum Hall effect1-3, tunable Mott insulators4,5 and unconventional superconductivity6. In addition, theory predicts that notable effects on optical excitations could result from a moiré potential in two-dimensional valley semiconductors7-9, but these signatures have not been detected experimentally. Here we report experimental evidence of interlayer valley excitons trapped in a moiré potential in molybdenum diselenide (MoSe2)/tungsten diselenide (WSe2) heterobilayers. At low temperatures, we observe photoluminescence close to the free interlayer exciton energy but with linewidths over one hundred times narrower (around 100 microelectronvolts). The emitter g-factors are homogeneous across the same sample and take only two values, -15.9 and 6.7, in samples with approximate twist angles of 60 degrees and 0 degrees, respectively. The g-factors match those of the free interlayer exciton, which is determined by one of two possible valley-pairing configurations. At twist angles of approximately 20 degrees the emitters become two orders of magnitude dimmer; however, they possess the same g-factor as the heterobilayer at a twist angle of approximately 60 degrees. This is consistent with the umklapp recombination of interlayer excitons near the commensurate 21.8-degree twist angle7. The emitters exhibit strong circular polarization of the same helicity for a given twist angle, which suggests that the trapping potential retains three-fold rotational symmetry. Together with a characteristic dependence on power and excitation energy, these results suggest that the origin of the observed effects is interlayer excitons trapped in a smooth moiré potential with inherited valley-contrasting physics. This work presents opportunities to control two-dimensional moiré optics through variation of the twist angle.

Harnessing interpretable and unsupervised machine learning to address big data from modern X-ray diffraction.

The information content of crystalline materials becomes astronomical when collective electronic behavior and their fluctuations are taken into account. In the past decade, improvements in source brightness and detector technology at modern X-ray facilities have allowed a dramatically increased fraction of this information to be captured. Now, the primary challenge is to understand and discover scientific principles from big datasets when a comprehensive analysis is beyond human reach. We report the development of an unsupervised machine learning approach, X-ray diffraction (XRD) temperature clustering (X-TEC), that can automatically extract charge density wave order parameters and detect intraunit cell ordering and its fluctuations from a series of high-volume X-ray diffraction measurements taken at multiple temperatures. We benchmark X-TEC with diffraction data on a quasi-skutterudite family of materials, (CaxSr[Formula: see text])3Rh4Sn13, where a quantum critical point is observed as a function of Ca concentration. We apply X-TEC to XRD data on the pyrochlore metal, Cd2Re2O7, to investigate its two much-debated structural phase transitions and uncover the Goldstone mode accompanying them. We demonstrate how unprecedented atomic-scale knowledge can be gained when human researchers connect the X-TEC results to physical principles. Specifically, we extract from the X-TEC-revealed selection rules that the Cd and Re displacements are approximately equal in amplitude but out of phase. This discovery reveals a previously unknown involvement of [Formula: see text] Re, supporting the idea of an electronic origin to the structural order. Our approach can radically transform XRD experiments by allowing in operando data analysis and enabling researchers to refine experiments by discovering interesting regions of phase space on the fly.

Discrete scale invariance of the quasi-bound states at atomic vacancies in a topological material.

Recently, log-periodic quantum oscillations have been detected in the topological materials zirconium pentatelluride (ZrTe5) and hafnium pentatelluride (HfTe5), displaying an intriguing discrete scale invariance (DSI) characteristic. In condensed materials, the DSI is considered to be related to the quasi-bound states formed by massless Dirac fermions with strong Coulomb attraction, offering a feasible platform to study the long-pursued atomic-collapse phenomenon. Here, we demonstrate that a variety of atomic vacancies in the topological material HfTe5 can host the geometric quasi-bound states with a DSI feature, resembling an artificial supercritical atom collapse. The density of states of these quasi-bound states is enhanced, and the quasi-bound states are spatially distributed in the "orbitals" surrounding the vacancy sites, which are detected and visualized by low-temperature scanning tunneling microscope/spectroscopy. By applying the perpendicular magnetic fields, the quasi-bound states at lower energies become wider and eventually invisible; meanwhile, the energies of quasi-bound states move gradually toward the Fermi energy (EF). These features are consistent with the theoretical prediction of a magnetic field-induced transition from supercritical to subcritical states. The direct observation of geometric quasi-bound states sheds light on the deep understanding of the DSI in quantum materials.

Accelerated Nano-Optical Imaging through Sparse Sampling.

The integration time and signal-to-noise ratio are inextricably linked when performing scanning probe microscopy based on raster scanning. This often yields a large lower bound on the measurement time, for example, in nano-optical imaging experiments performed using a scanning near-field optical microscope (SNOM). Here, we utilize sparse scanning augmented with Gaussian process regression to bypass the time constraint. We apply this approach to image charge-transfer polaritons in graphene residing on ruthenium trichloride (α-RuCl3) and obtain key features such as polariton damping and dispersion. Critically, nano-optical SNOM imaging data obtained via sparse sampling are in good agreement with those extracted from traditional raster scans but require 11 times fewer sampled points. As a result, Gaussian process-aided sparse spiral scans offer a major decrease in scanning time.

Planar thermal Hall effect of topological bosons in the Kitaev magnet α-RuCl3.

The honeycomb magnet α-RuCl3 has attracted considerable interest because it is proximate to the Kitaev Hamiltonian whose excitations are Majoranas and vortices. The thermal Hall conductivity κxy of Majorana fermions is predicted to be half-quantized. Half-quantization of κxy/T (T, temperature) was recently reported, but this observation has proven difficult to reproduce. Here, we report detailed measurements of κxy on α-RuCl3 with the magnetic field B ∥ a (zigzag axis). In our experiment, κxy/T is observed to be strongly temperature dependent between 0.5 and 10 K. We show that its temperature profile matches the distinct form expected for topological bosonic modes in a Chern-insulator-like model. Our analysis yields magnon band energies in agreement with spectroscopic experiments. At high B, the spin excitations evolve into magnon-like modes with a Chern number of ~1. The bosonic character is incompatible with half-quantization of κxy/T.

Magnetism in two-dimensional van der Waals materials.

The discovery of materials has often introduced new physical paradigms and enabled the development of novel devices. Two-dimensional magnetism, which is associated with strong intrinsic spin fluctuations, has long been the focus of fundamental questions in condensed matter physics regarding our understanding and control of new phases. Here we discuss magnetic van der Waals materials: two-dimensional atomic crystals that contain magnetic elements and thus exhibit intrinsic magnetic properties. These cleavable materials provide the ideal platform for exploring magnetism in the two-dimensional limit, where new physical phenomena are expected, and represent a substantial shift in our ability to control and investigate nanoscale phases. We present the theoretical background and motivation for investigating this class of crystals, describe the material landscape and the current experimental status of measurement techniques as well as devices, and discuss promising future directions for the study of magnetic van der Waals materials.

Current-Phase Relation of a WTe2 Josephson Junction.

When a topological insulator is incorporated into a Josephson junction, the system is predicted to reveal the fractional Josephson effect with a 4π-periodic current-phase relation. Here, we report the measurement of a 4π-periodic switching current through an asymmetric SQUID, formed by the higher-order topological insulator WTe2. Contrary to the established opinion, we show that a high asymmetry in critical current and negligible loop inductance are not sufficient by themselves to reliably measure the current-phase relation. Instead, we find that our measurement is heavily influenced by additional inductances originating from the self-formed PdTex inside the junction. We therefore develop a method to numerically recover the current-phase relation of the system and find the 1.5 µm long junction to be best described in the short ballistic limit. Our results highlight the complexity of subtle inductance effects that can give rise to misleading topological signatures in transport measurements.

Direct Visualization of the Charge Transfer in a Graphene/α-RuCl3 Heterostructure via Angle-Resolved Photoemission Spectroscopy.

We investigate the electronic properties of a graphene and α-ruthenium trichloride (α-RuCl3) heterostructure using a combination of experimental techniques. α-RuCl3 is a Mott insulator and a Kitaev material. Its combination with graphene has gained increasing attention due to its potential applicability in novel optoelectronic devices. By using a combination of spatially resolved photoemission spectroscopy and low-energy electron microscopy, we are able to provide a direct visualization of the massive charge transfer from graphene to α-RuCl3, which can modify the electronic properties of both materials, leading to novel electronic phenomena at their interface. A measurement of the spatially resolved work function allows for a direct estimate of the interface dipole between graphene and α-RuCl3. Their strong coupling could lead to new ways of manipulating electronic properties of a two-dimensional heterojunction. Understanding the electronic properties of this structure is pivotal for designing next generation low-power optoelectronics devices.

Polaritonic Probe of an Emergent 2D Dipole Interface.

The use of work-function-mediated charge transfer has recently emerged as a reliable route toward nanoscale electrostatic control of individual atomic layers. Using α-RuCl3 as a 2D electron acceptor, we are able to induce emergent nano-optical behavior in hexagonal boron nitride (hBN) that arises due to interlayer charge polarization. Using scattering-type scanning near-field optical microscopy (s-SNOM), we find that a thin layer of α-RuCl3 adjacent to an hBN slab reduces the propagation length of hBN phonon polaritons (PhPs) in significant excess of what can be attributed to intrinsic optical losses. Concomitant nano-optical spectroscopy experiments reveal a novel resonance that aligns energetically with the region of excess PhP losses. These experimental observations are elucidated by first-principles density-functional theory and near-field model calculations, which show that the formation of a large interfacial dipole suppresses out-of-plane PhP propagation. Our results demonstrate the potential utility of charge-transfer heterostructures for tailoring optoelectronic properties of 2D insulators.

Tiny Sc Allows the Chains to Rattle: Impact of Lu and Y Doping on the Charge-Density Wave in ScV6Sn6.

The kagome metals display an intriguing variety of electronic and magnetic phases arising from the connectivity of atoms on a kagome lattice. A growing number of these materials with vanadium-kagome nets host charge-density waves (CDWs) at low temperatures, including ScV6Sn6, CsV3Sb5, and V3Sb2. Curiously, only the Sc version of the RV6Sn6 materials with a HfFe6Ge6-type structure hosts a CDW (R = Gd-Lu, Y, Sc). In this study, we investigate the role of rare earth size in CDW formation in the RV6Sn6 compounds. Magnetization measurements on our single crystals of (Sc,Lu)V6Sn6 and (Sc,Y)V6Sn6 establish that the CDW is suppressed by substituting Sc by larger Lu or Y. Single-crystal X-ray diffraction reveals that compressible Sn-Sn bonds accommodate the larger rare earth atoms within loosely packed R-Sn-Sn chains without significantly expanding the lattice. We propose that Sc provides extra room in these chains crucial to CDW formation in ScV6Sn6. Our rattling chain model explains why both physical pressure and substitution by larger rare earth atoms hinder CDW formation despite opposite impacts on lattice size. We emphasize the cooperative effect of pressure and rare earth size by demonstrating that pressure further suppresses the CDW in a Lu-doped ScV6Sn6 crystal. Our model not only addresses why a CDW only forms in the RV6Sn6 materials with tiny Sc but also advances our understanding of why unusual CDWs form in the kagome metals.

Deterministic switching of a perpendicularly polarized magnet using unconventional spin-orbit torques in WTe2.

Spin-orbit torque (SOT)-driven deterministic control of the magnetic state of a ferromagnet with perpendicular magnetic anisotropy is key to next-generation spintronic applications including non-volatile, ultrafast and energy-efficient data-storage devices. However, field-free deterministic switching of perpendicular magnetization remains a challenge because it requires an out-of-plane antidamping torque, which is not allowed in conventional spin-source materials such as heavy metals and topological insulators due to the system's symmetry. The exploitation of low-crystal symmetries in emergent quantum materials offers a unique approach to achieve SOTs with unconventional forms. Here we report an experimental realization of field-free deterministic magnetic switching of a perpendicularly polarized van der Waals magnet employing an out-of-plane antidamping SOT generated in layered WTe2, a quantum material with a low-symmetry crystal structure. Our numerical simulations suggest that the out-of-plane antidamping torque in WTe2 is essential to explain the observed magnetization switching.

Observation of Giant Surface Second-Harmonic Generation Coupled to Nematic Orders in the van der Waals Antiferromagnet FePS3.

Second-harmonic generation has been applied to study lattice, electronic, and magnetic proprieties in atomically thin materials. However, inversion symmetry breaking is usually required for the materials to generate a large signal. In this work, we report a giant second-harmonic generation that arises below the Néel temperature in few-layer centrosymmetric FePS3. A layer-dependent study indicates the detected signal is from the second-order nonlinearity of the surface. The magnetism-induced surface second-harmonic response is 2 orders of magnitude larger than those reported in other magnetic systems, with the surface nonlinear susceptibility reaching 0.08-0.13 nm2/V in 2-5 L samples. By combing linear dichroism and second-harmonic generation experiments, we further confirm the giant second-harmonic generation is coupled to nematic orders formed by the three possible Zigzag antiferromagnetic domains. Our study shows that the surface second-harmonic generation is also a sensitive tool to study antiferromagnetic states in centrosymmetric atomically thin materials.

Quantum Spin Hall Edge States and Interlayer Coupling in Twisted Bilayer WTe2.

The quantum spin Hall (QSH) effect, characterized by topologically protected spin-polarized edge states, was recently demonstrated in monolayers of the transition metal dichalcogenide (TMD) WTe2. However, the robustness of this topological protection remains largely unexplored in van der Waals heterostructures containing one or more layers of a QSH insulator. In this work, we use scanning tunneling microscopy and spectroscopy (STM/STS) to explore the topological nature of twisted bilayer (tBL) WTe2. At the tBL edges, we observe the characteristic spectroscopic signatures of the QSH edge states. For small twist angles, a rectangular moiré pattern develops, which results in local modifications of the band structure. Using first-principles calculations, we quantify the interactions in tBL WTe2 and its topological edge states as a function of interlayer distance and conclude that it is possible to engineer the topology of WTe2 bilayers via the twist angle as well as interlayer interactions.

Interlayer Exciton Diode and Transistor.

Controlling the flow of charge neutral interlayer exciton (IX) quasiparticles can potentially lead to low loss excitonic circuits. Here, we report unidirectional transport of IXs along nanoscale electrostatically defined channels in an MoSe2-WSe2 heterostructure. These results are enabled by a lithographically defined triangular etch in a graphene gate to create a potential energy "slide". By performing spatially and temporally resolved photoluminescence measurements, we measure smoothly varying IX energy along the structure and high speed exciton flow with a drift velocity up to 2 × 106 cm/s, an order of magnitude larger than previous experiments. Furthermore, exciton flow can be controlled by saturating exciton population in the channel using a second laser pulse, demonstrating an optically gated excitonic transistor. Our work paves the way toward low loss excitonic circuits, the study of bosonic transport in one-dimensional channels, and custom potential energy landscapes for excitons in van der Waals heterostructures.

Ultrasharp Lateral p-n Junctions in Modulation-Doped Graphene.

We demonstrate ultrasharp (≲10 nm) lateral p-n junctions in graphene using electronic transport, scanning tunneling microscopy, and first-principles calculations. The p-n junction lies at the boundary between differentially doped regions of a graphene sheet, where one side is intrinsic and the other is charge-doped by proximity to a flake of α-RuCl3 across a thin insulating barrier. We extract the p-n junction contribution to the device resistance to place bounds on the junction width. We achieve an ultrasharp junction when the boundary between the intrinsic and doped regions is defined by a cleaved crystalline edge of α-RuCl3 located 2 nm from the graphene. Scanning tunneling spectroscopy in heterostructures of graphene, hexagonal boron nitride, and α-RuCl3 shows potential variations on a sub 10 nm length scale. First-principles calculations reveal that the charge-doping of graphene decays sharply over just nanometers from the edge of the α-RuCl3 flake.

Nanometer-Scale Lateral p-n Junctions in Graphene/α-RuCl3 Heterostructures.

The ability to create nanometer-scale lateral p-n junctions is essential for the next generation of two-dimensional (2D) devices. Using the charge-transfer heterostructure graphene/α-RuCl3, we realize nanoscale lateral p-n junctions in the vicinity of graphene nanobubbles. Our multipronged experimental approach incorporates scanning tunneling microscopy (STM) and spectroscopy (STS) and scattering-type scanning near-field optical microscopy (s-SNOM) to simultaneously probe the electronic and optical responses of nanobubble p-n junctions. Our STM/STS results reveal that p-n junctions with a band offset of ∼0.6 eV can be achieved with widths of ∼3 nm, giving rise to electric fields of order 108 V/m. Concurrent s-SNOM measurements validate a point-scatterer formalism for modeling the interaction of surface plasmon polaritons (SPPs) with nanobubbles. Ab initio density functional theory (DFT) calculations corroborate our experimental data and reveal the dependence of charge transfer on layer separation. Our study provides experimental and conceptual foundations for generating p-n nanojunctions in 2D materials.

Charge Density Wave in Kagome Lattice Intermetallic ScV_{6}Sn_{6}.

Materials hosting kagome lattices have drawn interest for the diverse magnetic and electronic states generated by geometric frustration. In the AV_{3}Sb_{5} compounds (A=K, Rb, Cs), stacked vanadium kagome layers give rise to unusual charge density waves (CDW) and superconductivity. Here we report single-crystal growth and characterization of ScV_{6}Sn_{6}, a hexagonal HfFe_{6}Ge_{6}-type compound that shares this structural motif. We identify a first-order phase transition at 92 K. Single crystal x-ray and neutron diffraction reveal a charge density wave modulation of the atomic lattice below this temperature. This is a distinctly different structural mode than that observed in the AV_{3}Sb_{5} compounds, but both modes have been anticipated in kagome metals. The diverse HfFe_{6}Ge_{6} family offers more opportunities to tune ScV_{6}Sn_{6} and explore density wave order in kagome lattice materials.

Line-Graph Approach to Spiral Spin Liquids.

Competition among exchange interactions is able to induce novel spin correlations on a bipartite lattice without geometrical frustration. A prototype example is the spiral spin liquid, which is a correlated paramagnetic state characterized by subdimensional degenerate propagation vectors. Here, using spectral graph theory, we show that spiral spin liquids on a bipartite lattice can be approximated by a further-neighbor model on the corresponding line-graph lattice that is nonbipartite, thus broadening the space of candidate materials that may support the spiral spin liquid phases. As illustrations, we examine neutron scattering experiments performed on two spinel compounds, ZnCr_{2}Se_{4} and CuInCr_{4}Se_{8}, to demonstrate the feasibility of this new approach and expose its possible limitations in experimental realizations.

Nanoscale Trapping of Interlayer Excitons in a 2D Semiconductor Heterostructure.

For quantum technologies based on single excitons and spins, the deterministic placement and control of a single exciton is a longstanding goal. MoSe2-WSe2 heterostructures host spatially indirect interlayer excitons (IXs) that exhibit highly tunable energies and unique spin-valley physics, making them promising candidates for quantum information processing. Previous IX trapping approaches involving moiré superlattices and nanopillars do not meet the quantum technology requirements of deterministic placement and energy tunability. Here, we use a nanopatterned graphene gate to create a sharply varying electric field in close proximity to a MoSe2-WSe2 heterostructure. The dipole interaction between the IX and the electric field creates an ∼20 nm trap. The trapped IXs show the predicted electric-field-dependent energy, saturation at low excitation power, and increased lifetime, all signatures of strong spatial confinement. The demonstrated architecture is a crucial step toward the deterministic trapping of single IXs, which has broad applications to scalable quantum technologies.

Excitations of Intercalated Metal Monolayers in Transition Metal Dichalcogenides.

We combine Raman scattering spectroscopy and lattice dynamics calculations to reveal the fundamental excitations of the intercalated metal monolayers in the FexTaS2 (x = 1/4, 1/3) family of materials. Both in- and out-of-plane modes are identified, each of which has trends that depend upon the metal-metal distance, the size of the van der Waals gap, and the metal-to-chalcogenide slab mass ratio. We test these trends against the response of similar systems, including Cr-intercalated NbS2 and RbFe(SO4)2, and demonstrate that the metal monolayer excitations are both coherent and tunable. We discuss the consequences of intercalated metal monolayer excitations for material properties and developing applications.