Polarization Saturation in Multilayered Interfacial Ferroelectrics.

Van der Waals polytypes of broken inversion and mirror symmetries  have been recently shown to exhibit switchable electric polarization even at the ultimate two-layer thin limit. Their out-of-plane polarization has been found to accumulate in a ladder-like fashion with each successive layer, offering 2D building blocks for the bottom-up construction of 3D ferroelectrics. Here, it is demonstrated experimentally that beyond a critical stack thickness, the accumulated polarization in rhombohedral polytypes of molybdenum disulfide saturates. The underlying saturation mechanism, deciphered via density functional theory and self-consistent Poisson-Schrödinger calculations, point to a purely electronic redistribution involving: 1. Polarization-induced bandgap closure that allows for cross-stack charge transfer and the emergence of free surface charge; 2. Reduction of the polarization saturation value, as well as the critical thickness at which it is obtained, by the presence of free carriers. The resilience of polar layered structures to atomic surface reconstruction, which is essentially unavoidable in polar 3D crystals, potentially allows for the design of new devices with mobile surface charges. The findings, which are of general nature, should be accounted for when designing switching and/or conductive devices based on ferroelectric layered materials.

Effect of Interlayer Bonding on Superlubric Sliding of Graphene Contacts: A Machine-Learning Potential Study.

Surface defects and their mutual interactions are anticipated to affect the superlubric sliding of incommensurate layered material interfaces. Atomistic understanding of this phenomenon is limited due to the high computational cost of ab initio simulations and the absence of reliable classical force-fields for molecular dynamics simulations of defected systems. To address this, we present a machine-learning potential (MLP) for bilayer defected graphene, utilizing state-of-the-art graph neural networks trained against many-body dispersion corrected density functional theory calculations under iterative configuration space exploration. The developed MLP is utilized to study the impact of interlayer bonding on the friction of bilayer defected graphene interfaces. While a mild effect on the sliding dynamics of aligned graphene interfaces is observed, the friction coefficients of incommensurate graphene interfaces are found to significantly increase due to interlayer bonding, nearly pushing the system out of the superlubric regime. The methodology utilized herein is of general nature and can be adapted to describe other homogeneous and heterogeneous defected layered material interfaces.

Graphene nanoribbons grown in hBN stacks for high-performance electronics.

Van der Waals encapsulation of two-dimensional materials in hexagonal boron nitride (hBN) stacks is a promising way to create ultrahigh-performance electronic devices1-4. However, contemporary approaches for achieving van der Waals encapsulation, which involve artificial layer stacking using mechanical transfer techniques, are difficult to control, prone to contamination and unscalable. Here we report the transfer-free direct growth of high-quality graphene nanoribbons (GNRs) in hBN stacks. The as-grown embedded GNRs exhibit highly desirable features being ultralong (up to 0.25 mm), ultranarrow (<5 nm) and homochiral with zigzag edges. Our atomistic simulations show that the mechanism underlying the embedded growth involves ultralow GNR friction when sliding between AA'-stacked hBN layers. Using the grown structures, we demonstrate the transfer-free fabrication of embedded GNR field-effect devices that exhibit excellent performance at room temperature with mobilities of up to 4,600 cm2 V-1 s-1 and on-off ratios of up to 106. This paves the way for the bottom-up fabrication of high-performance electronic devices based on embedded layered materials.

Nanotube Slidetronics.

One-dimensional slidetronics is predicted for double-walled boron-nitride nanotubes. Local electrostatic polarization patterns along the body of the nanotube are found to be determined by the nature of the two nanotube walls, their relative configuration, and circumferential faceting modulation during coaxial interwall sliding. By careful choice of chiral indices, chiral polarization patterns can emerge that spiral around the nanotube circumference. The potential usage of the discovered slidetronic effect for low-dimensional nanogenerators is briefly discussed.

Anisotropic Interlayer Force Field for Group-VI Transition Metal Dichalcogenides.

An anisotropic interlayer force field that describes the interlayer interactions in homogeneous and heterogeneous interfaces of group-VI transition metal dichalcogenides (MX2, where M = Mo, W, and X = S, Se) is presented. The force field is benchmarked against density functional theory calculations for bilayer systems within the Heyd-Scuseria-Ernzerhof hybrid density functional approximation, augmented by a nonlocal many-body dispersion treatment of long-range correlation. The parametrization yields good agreement with the reference calculations of binding energy curves and sliding potential energy surfaces. It is found to be transferable to transition metal dichalcogenide (TMD) junctions outside of the training set that contain the same atom types. Calculated bulk moduli agree with most previous dispersion-corrected density functional theory predictions, which underestimate the available experimental values. Calculated phonon spectra of the various junctions under consideration demonstrate the importance of appropriately treating the anisotropic nature of the layered interfaces. Considering our previous parametrization for MoS2, the anisotropic interlayer potential enables accurate and efficient large-scale simulations of the dynamical, tribological, and thermal transport properties of a large set of homogeneous and heterogeneous TMD interfaces.

Electron Dynamics in Open Quantum Systems: The Driven Liouville-von Neumann Methodology within Time-Dependent Density Functional Theory.

A first-principles approach to describe electron dynamics in open quantum systems driven far from equilibrium via external time-dependent stimuli is introduced. Within this approach, the driven Liouville-von Neumann methodology is used to impose open boundary conditions on finite model systems whose dynamics is described using time-dependent density functional theory. As a proof of concept, the developed methodology is applied to simple spin-compensated model systems, including a hydrogen chain and a graphitic molecular junction. Good agreement between steady-state total currents obtained via direct propagation and those obtained from the self-consistent solution of the corresponding Sylvester equation indicates the validity of the implementation. The capability of the new computational approach to analyze, from first principles, non-equilibrium dynamics of open quantum systems in terms of temporally and spatially resolved current densities is demonstrated. Future extensions of the approach toward the description of dynamical magnetization and decoherence effects are briefly discussed.

Chirality induced spin selectivity: A classical spin-off.

We demonstrate that angular momentum selectivity of particles traversing chiral environments is not limited to the quantum regime and can be realized in classical scenarios also. In our classical variant, the electron spin, which is central to the quantum chirality induced spin selectivity (CISS) effect, is replaced by the self-rotation of a finite-volume body. The latter is coupled to the center of mass orbital motion of the body through a helical tube via wall friction that acts as a dissipative spin-orbit coupling term. As a specific example, we study C60 molecules that are initially spinning in opposite senses and investigate the effect of various external control parameters on their spatial separation when driven through a rigid helical channel. We highlight resemblances and inherent differences between the quantum CISS effect and its classical variant and discuss the potential of the latter to formulate a new paradigm for enantio-separation.

Interlayer Registry Dictates Interfacial 2D Material Ferroelectricity.

We discover that the complex ferroelectric response of layered materials toward interlayer sliding is fully dictated by the interlayer lattice registry. Importantly, the entire sliding polarization landscape of two-dimensional (2D) layered material interfaces is fully described via a simple and intuitive geometric measure, termed the polarization registry index (PRI), that quantifies the degree of interlayer commensurability. Beyond the understanding of the fundamental origin of 2D ferroelectricity, the developed tool also provides highly efficient characterization and rationalization of existing experimental and computational evidence of 2D interfacial ferroelectricity, as well as the prediction of emergent controllable polarization in new noncentrosymmetric layered systems.

Velocity Dependence of Moiré Friction.

Friction force microscopy experiments on moiré superstructures of graphene-coated platinum surfaces demonstrate that in addition to atomic stick-slip dynamics, a new dominant energy dissipation route emerges. The underlying mechanism, revealed by atomistic molecular dynamics simulations, is related to moiré ridge elastic deformations and subsequent relaxation due to the action of the pushing tip. The measured frictional velocity dependence displays two distinct regimes: (i) at low velocities, the friction force is small and nearly constant; and (ii) above some threshold, friction increases logarithmically with velocity. The threshold velocity, separating the two frictional regimes, decreases with increasing normal load and moiré superstructure period. Based on the measurements and simulation results, a phenomenological model is derived, allowing us to calculate friction under a wide range of room temperature experimental conditions (sliding velocities of 1-104 nm/s and a broad range of normal loads) and providing excellent agreement with experimental observations.

Cumulative polarization in conductive interfacial ferroelectrics.

Ferroelectricity in atomically thin bilayer structures has been recently predicted1 and measured2-4 in two-dimensional materials with hexagonal non-centrosymmetric unit-cells. The crystal symmetry translates lateral shifts between parallel two-dimensional layers to sign changes in their out-of-plane electric polarization, a mechanism termed 'slide-tronics'4. These observations have been restricted to switching between only two polarization states under low charge carrier densities5-12, limiting the practical application of the revealed phenomena13. To overcome these issues, one should explore the nature of polarization in multi-layered van der Waals stacks, how it is governed by intra- and interlayer charge redistribution and to what extent it survives the addition of mobile charge carriers14. To explore these questions, we conduct surface potential measurements of parallel WSe2 and MoS2 multi-layers with aligned and anti-aligned configurations of the polar interfaces. We find evenly spaced, nearly decoupled potential steps, indicating highly confined interfacial electric fields that provide a means to design multi-state 'ladder-ferroelectrics'. Furthermore, we find that the internal polarization remains notable on electrostatic doping of mobile charge carrier densities as high as 1013 cm-2, with substantial in-plane conductivity. Using density functional theory calculations, we trace the extra charge redistribution in real and momentum spaces and identify an eventual doping-induced depolarization mechanism.

Magnetic control over the fundamental structure of atomic wires.

When reducing the size of materials towards the nanoscale, magnetic properties can emerge due to structural variations. Here, we show the reverse effect, where the structure of nanomaterials is controlled by magnetic manipulations. Using the break-junction technique, we find that the interatomic distance in platinum atomic wires is shorter or longer by up to ∼20%, when a magnetic field is applied parallel or perpendicular to the wires during their formation, respectively. The magnetic field direction also affects the wire length, where longer (shorter) wires are formed under a parallel (perpendicular) field. Our experimental analysis, supported by calculations, indicates that the direction of the applied magnetic field promotes the formation of suspended atomic wires with a specific magnetization orientation associated with typical orbital characteristics, interatomic distance, and stability. A similar effect is found for various metal and metal-oxide atomic wires, demonstrating that magnetic fields can control the atomistic structure of different nanomaterials when applied during their formation stage.

Catalytic Growth of Ultralong Graphene Nanoribbons on Insulating Substrates.

Graphene nanoribbons (GNRs) with widths of a few nanometers are promising candidates for future nanoelectronic applications due to their structurally tunable bandgaps, ultrahigh carrier mobilities, and exceptional stability. However, the direct growth of micrometer-long GNRs on insulating substrates, which is essential for the fabrication of nanoelectronic devices, remains an immense challenge. Here, the epitaxial growth of GNRs on an insulating hexagonal boron nitride (h-BN) substrate through nanoparticle-catalyzed chemical vapor deposition is reported. Ultranarrow GNRs with lengths of up to 10 µm are synthesized. Remarkably, the as-grown GNRs are crystallographically aligned with the h-BN substrate, forming 1D moiré superlattices. Scanning tunneling microscopy reveals an average width of 2 nm and a typical bandgap of ≈1 eV for similar GNRs grown on conducting graphite substrates. Fully atomistic computational simulations support the experimental results and reveal a competition between the formation of GNRs and carbon nanotubes during the nucleation stage, and van der Waals sliding of the GNRs on the h-BN substrate throughout the growth stage. This study provides a scalable, single-step method for growing micrometer-long narrow GNRs on insulating substrates, thus opening a route to explore the performance of high-quality GNR devices and the fundamental physics of 1D moiré superlattices.

Interlayer Registry Index of Layered Transition Metal Dichalcogenides.

Inspired by the fascinating electronic properties of twisted transition metal dichalcogenides, we extend the registry index approach to quantify the interlayer commensurability of homogeneous and heterogeneous interfaces of MoS2, WS2, MoSe2, and WSe2. The developed geometric measure provides quantitative information about their sliding energy landscape with vast mechanical and tribological implications. Furthermore, the registry index is highly suitable for characterizing surface reconstruction in twisted transition metal dichalcogenide interfaces that dictates their intricate electronic and ferroelectric properties. The simple and intuitive nature of the registry index marks it as a powerful computational tool for studying the fascinating physical phenomena demonstrated by these materials.

Edge State Quantum Interference in Twisted Graphitic Interfaces.

Zigzag edges in graphitic systems exhibit localized electronic states that drastically affect their properties. Here, room-temperature charge transport experiments across a single graphitic interface are reported, in which the interlayer current is confined to the contact edges. It is shown that the current exhibits pronounced oscillations of up to ≈40 µA with a dominant period of ≈5 Å with respect to lateral displacement that do not directly correspond to typical graphene lattice spacing. The origin of these features is computationally rationalized as quantum mechanical interference of localized edge states showing significant amplitude and interlayer coupling variations as a function of the interface stacking configuration. Such interference effects may therefore dominate the transport properties of low-dimensional graphitic interfaces.

Theory of Chirality Induced Spin Selectivity: Progress and Challenges.

A critical overview of the theory of the chirality-induced spin selectivity (CISS) effect, that is, phenomena in which the chirality of molecular species imparts significant spin selectivity to various electron processes, is provided. Based on discussions in a recently held workshop, and further work published since, the status of CISS effects-in electron transmission, electron transport, and chemical reactions-is reviewed. For each, a detailed discussion of the state-of-the-art in theoretical understanding is provided and remaining challenges and research opportunities are identified.

Stick-Slip Dynamics of Moiré Superstructures in Polycrystalline 2D Material Interfaces.

A new frictional mechanism, based on collective stick-slip motion of moiré superstructures across polycrystalline two-dimensional material interfaces, is predicted. The dissipative stick-slip behavior originates from an energetic bistability between low- and high-commensurability configurations of large-scale moiré superstructures. When the grain boundary separates between grains of small and large interfacial twist angle, the corresponding moiré periods are significantly different, resulting in forbidden grain boundary crossing of the moiré superstructures during shear induced motion. For small twist angle grains, where the moiré periods are much larger than the lattice constant, this results in multiple reflections of collective surface waves between the surrounding grain boundaries. In combination with the individual grain boundary dislocation snap-through buckling mechanism dominating at the low normal load regime, the friction exhibits nonmonotonic behavior with the normal load. While the discovered phenomenon is demonstrated for h-BN/graphene polycrystalline junctions, it is expected to be of general nature and occur in many other large-scale layered material interfaces.

Anisotropic Interlayer Force Field for Transition Metal Dichalcogenides: The Case of Molybdenum Disulfide.

An anisotropic interlayer force field that describes the interlayer interactions in molybdenum disulfide (MoS2) is presented. The force field is benchmarked against density functional theory calculations for both bilayer and bulk systems within the Heyd-Scuseria-Ernzerhof hybrid density functional approximation, augmented by a nonlocal many-body dispersion treatment of long-range correlation. The parametrization yields good agreement with the reference calculations of binding energy curves and sliding potential energy surfaces for both bilayer and bulk configurations. Benchmark calculations for the phonon spectra of bulk MoS2 provide good agreement with experimental data, and the calculated bulk modulus falls in the lower part of experimentally measured values. This indicates the accuracy of the interlayer force field near equilibrium. Under external pressures up to 20 GPa, the developed force field provides a good description of compression curves. At higher pressures, deviations from experimental data grow, signifying the validity range of the developed force field.

Registry-Dependent Potential for Interfaces of Gold with Graphitic Systems.

We present a semi-anisotropic interfacial potential (SAIP) designed to classically describe the interaction between gold and two-dimensional (2D) carbon allotropes such as graphene, fullerenes, or hydrocarbon molecules. The potential is able to accurately reproduce dispersion-corrected density functional theory (DFT+D3) calculations performed over selected configurations: a flat graphene sheet, a benzene molecule, and a C60 fullerene, physisorbed on the Au(111) surface. The effects of bending and hydrogen passivation on the potential terms are discussed. The presented SAIP provides a noticeable improvement in the state-of-the-art description of Au-C interfaces. Furthermore, its functional form is suitable to describe the interfacial interaction between other 2D and bulk materials.