Magnetism-Induced Band-Edge Shift as the Mechanism for Magnetoconductance in CrPS4 Transistors.

Transistors realized on the 2D antiferromagnetic semiconductor CrPS4 exhibit large magnetoconductance due to magnetic-field-induced changes in the magnetic state. The microscopic mechanism coupling the conductance and magnetic state is not understood. We identify it by analyzing the evolution of the parameters determining the transistor behavior─carrier mobility and threshold voltage─with temperature and magnetic field. For temperatures T near the Néel temperature TN, the magnetoconductance originates from a mobility increase due to the applied magnetic field that reduces spin fluctuation induced disorder. For T ≪ TN, instead, what changes is the threshold voltage, so that increasing the field at fixed gate voltage increases the density of accumulated electrons. The phenomenon is explained by a conduction band-edge shift correctly predicted by the ab initio calculations. Our results demonstrate that the band structure of CrPS4 depends on its magnetic state and reveal a mechanism for magnetoconductance that had not been identified earlier.

Multiple antiferromagnetic phases and magnetic anisotropy in exfoliated CrBr3 multilayers.

In twisted two-dimensional (2D) magnets, the stacking dependence of the magnetic exchange interaction can lead to regions of ferromagnetic and antiferromagnetic interlayer order, separated by non-collinear, skyrmion-like spin textures. Recent experimental searches for these textures have focused on CrI3, known to exhibit either ferromagnetic or antiferromagnetic interlayer order, depending on layer stacking. However, the very strong uniaxial anisotropy of CrI3 disfavors smooth non-collinear phases in twisted bilayers. Here, we report the experimental observation of three distinct magnetic phases-one ferromagnetic and two antiferromagnetic-in exfoliated CrBr3 multilayers, and reveal that the uniaxial anisotropy is significantly smaller than in CrI3. These results are obtained by magnetoconductance measurements on CrBr3 tunnel barriers and Raman spectroscopy, in conjunction with density functional theory calculations, which enable us to identify the stackings responsible for the different interlayer magnetic couplings. The detection of all locally stable magnetic states predicted to exist in CrBr3 and the excellent agreement found between theory and experiments, provide complete information on the stacking-dependent interlayer exchange energy and establish twisted bilayer CrBr3 as an ideal system to deterministically create non-collinear magnetic phases.

Electronic Structure of Few-Layer Black Phosphorus from µ-ARPES.

Black phosphorus (BP) stands out among two-dimensional (2D) semiconductors because of its high mobility and thickness dependent direct band gap. However, the quasiparticle band structure of ultrathin BP has remained inaccessible to experiment thus far. Here we use a recently developed laser-based microfocus angle resolved photoemission (µ-ARPES) system to establish the electronic structure of 2-9 layer BP from experiment. Our measurements unveil ladders of anisotropic, quantized subbands at energies that deviate from the scaling observed in conventional semiconductor quantum wells. We quantify the anisotropy of the effective masses and determine universal tight-binding parameters, which provide an accurate description of the electronic structure for all thicknesses.

Expansion of the Materials Cloud 2D Database.

Two-dimensional (2D) materials are among the most promising candidates for beyond-silicon electronic, optoelectronic, and quantum computing applications. Recently, their recognized importance sparked a push to discover and characterize novel 2D materials. Within a few years, the number of experimentally exfoliated or synthesized 2D materials went from a few to more than a hundred, with the number of theoretically predicted compounds reaching a few thousand. In 2018 we first contributed to this effort with the identification of 1825 compounds that are either easily (1036) or potentially (789) exfoliable from experimentally known 3D compounds. Here, we report on a major expansion of this 2D portfolio thanks to the extension of the screening protocol to an additional experimental database (MPDS) as well as the updated versions of the two databases (ICSD and COD) used in our previous work. This expansion leads to the discovery of an additional 1252 monolayers, bringing the total to 3077 compounds and, notably, almost doubling the number of easily exfoliable materials to 2004. We optimize the structural properties of all these monolayers and explore their electronic structure with a particular emphasis on those rare large-bandgap 2D materials that could be precious in isolating 2D field-effect-transistor channels. Finally, for each material containing up to 6 atoms per unit cell, we identify the best candidates to form commensurate heterostructures, balancing requirements on supercell size and minimal strain.

Accurate Prediction of Hall Mobilities in Two-Dimensional Materials through Gauge-Covariant Quadrupolar Contributions.

Despite considerable efforts, accurate computations of electron-phonon and carrier transport properties of low-dimensional materials from first principles have remained elusive. By building on recent advances in the description of long-range electrostatics, we develop a general approach to the calculation of electron-phonon couplings in two-dimensional materials. We show that the nonanalytic behavior of the electron-phonon matrix elements depends on the Wannier gauge, but that a missing Berry connection restores invariance to quadrupolar order. We showcase these contributions in a MoS_{2} monolayer, calculating intrinsic drift and Hall mobilities with precise Wannier interpolations. We also find that the contributions of dynamical quadrupoles to the scattering potential are essential, and that their neglect leads to errors of 23% and 76% in the room-temperature electron and hole Hall mobilities, respectively.

Gate-Controlled Magnetotransport and Electrostatic Modulation of Magnetism in 2D Magnetic Semiconductor CrPS4.

Using field-effect transistors (FETs) to explore atomically thin magnetic semiconductors with transport measurements is difficult, because the very narrow bands of most 2D magnetic semiconductors cause carrier localization, preventing transistor operation. Here, it is shown that exfoliated layers of CrPS4 -a 2D layered antiferromagnetic semiconductor whose bandwidth approaches 1 eV-allow the realization of FETs that operate properly down to cryogenic temperature. Using these devices, conductance measurements as a function of temperature and magnetic field are performed to determine the full magnetic phase diagram, which includes a spin-flop and a spin-flip phase. The magnetoconductance, which depends strongly on gate voltage, is determined. reaching values as high as 5000% near the threshold for electron conduction. The gate voltage also allows the magnetic states to be tuned, despite the relatively large thickness of the CrPS4 multilayers employed in the study. The results show the need to employ 2D magnetic semiconductors with sufficiently large bandwidth to realize properly functioning transistors, and identify a candidate material to realize a fully gate-tunable half-metallic conductor.

Quenching the bandgap of two-dimensional semiconductors with a perpendicular electric field.

Perpendicular electric fields can tune the electronic band structure of atomically thin semiconductors. In bilayer graphene, which is an intrinsic zero-gap semiconductor, a perpendicular electric field opens a finite bandgap. So far, however, the same principle could not be applied to control the properties of a broader class of 2D materials because the required electric fields are beyond reach in current devices. To overcome this limitation, we design double ionic gated transistors that enable the application of large electric fields of up to 3 V nm-1. Using such devices, we continuously suppress the bandgap of few-layer semiconducting transition metal dichalcogenides (that is, bilayer to heptalayer WSe2) from 1.6 V to zero. Our results illustrate an excellent level of control of the band structure of 2D semiconductors.

Quasi-1D Electronic Transport in a 2D Magnetic Semiconductor.

Electronic transport through exfoliated multilayers of CrSBr, a 2D semiconductor of interest because of its magnetic properties, is investigated. An extremely pronounced anisotropy manifesting itself in qualitative and quantitative differences of all quantities measured along the in-plane a and b crystallographic directions is found. In particular, a qualitatively different dependence of the conductivities σa and σb on temperature and gate voltage, accompanied by orders of magnitude differences in their values (σb /σa  ≈ 3 × 102  to 105 at low temperature and negative gate voltage) are observed, together with a different behavior of the longitudinal magnetoresistance in the two directions and the complete absence of the Hall effect in transverse resistance measurements. These observations appear not to be compatible with a description in terms of conventional band transport of a 2D doped semiconductor. The observed phenomenology-and unambiguous signatures of a 1D van Hove singularity detected in energy-resolved photocurrent measurements-indicate that electronic transport through CrSBr multilayers is better interpreted by considering the system as formed by weakly and incoherently coupled 1D wires, than by conventional 2D band transport. It is concluded that CrSBr is the first 2D semiconductor to show distinctly quasi-1D electronic transport properties.

Magnetization dependent tunneling conductance of ferromagnetic barriers.

Recent experiments on van der Waals antiferromagnets have shown that measuring the temperature (T) and magnetic field (H) dependence of the conductance allows their magnetic phase diagram to be mapped. Similarly, experiments on ferromagnetic CrBr3 barriers enabled the Curie temperature to be determined at H = 0, but a precise interpretation of the magnetoconductance data at H ≠ 0 is conceptually more complex, because at finite H there is no well-defined phase boundary. Here we perform systematic transport measurements on CrBr3 barriers and show that the tunneling magnetoconductance depends on H and T exclusively through the magnetization M(H, T) over the entire temperature range investigated. The phenomenon is reproduced by the spin-dependent Fowler-Nordheim model for tunneling, and is a direct manifestation of the spin splitting of the CrBr3 conduction band. Our analysis unveils a new approach to probe quantitatively different properties of atomically thin ferromagnetic insulators related to their magnetization by performing simple conductance measurements.

Shear and Breathing Modes of Layered Materials.

Layered materials (LMs), such as graphite, hexagonal boron nitride, and transition-metal dichalcogenides, are at the center of an ever-increasing research effort, due to their scientific and technological relevance. Raman and infrared spectroscopies are accurate, non-destructive approaches to determine a wide range of properties, including the number of layers, N, and the strength of the interlayer interactions. We present a general approach to predict the complete spectroscopic fan diagrams, i.e., the relations between frequencies and N for the optically active shear and layer-breathing modes of any multilayer comprising N ≥ 2 identical layers. In order to achieve this, we combine a description of the normal modes in terms of a one-dimensional mechanical model, with symmetry arguments that describe the evolution of the point group as a function of N. Group theory is then used to identify which modes are Raman- and/or infrared-active, and to provide diagrams of the optically active modes for any stack composed of identical layers. We implement the method and algorithms in an open-source tool to assist researchers in the prediction and interpretation of such diagrams. Our work will underpin future efforts on Raman and infrared characterization of known, and yet not investigated, LMs.

Persistence of Magnetism in Atomically Thin MnPS3 Crystals.

The magnetic state of atomically thin semiconducting layered antiferromagnets such as CrI3 and CrCl3 can be probed by forming tunnel barriers and measuring their resistance as a function of magnetic field (H) and temperature (T). This is possible because the spins within each individual layer are ferromagnetically aligned and the tunneling magnetoresistance depends on the relative orientation of the magnetization in adjacent layers. The situation is different for systems that are antiferromagnetic within the layers in which case it is unclear whether magnetoresistance measurements can provide information about the magnetic state. Here, we address this issue by investigating tunnel transport through atomically thin crystals of MnPS3, a van der Waals semiconductor that in the bulk exhibits easy-axis antiferromagnetic order within the layers. For thick multilayers below T ∼ 78 K, a T-dependent magnetoresistance sets in at µ0H ∼ 5 T and is found to track the boundary between the antiferromagnetic and the spin-flop phases known from bulk measurements. We show that the magnetoresistance persists as thickness is reduced with nearly unchanged characteristic temperature and magnetic field scales, albeit with a different dependence on H, indicating the persistence of magnetism in the ultimate limit of individual monolayers.

Wannier90 as a community code: new features and applications.

Wannier90 is an open-source computer program for calculating maximally-localised Wannier functions (MLWFs) from a set of Bloch states. It is interfaced to many widely used electronic-structure codes thanks to its independence from the basis sets representing these Bloch states. In the past few years the development of Wannier90 has transitioned to a community-driven model; this has resulted in a number of new developments that have been recently released in Wannier90 v3.0. In this article we describe these new functionalities, that include the implementation of new features for wannierisation and disentanglement (symmetry-adapted Wannier functions, selectively-localised Wannier functions, selected columns of the density matrix) and the ability to calculate new properties (shift currents and Berry-curvature dipole, and a new interface to many-body perturbation theory); performance improvements, including parallelisation of the core code; enhancements in functionality (support for spinor-valued Wannier functions, more accurate methods to interpolate quantities in the Brillouin zone); improved usability (improved plotting routines, integration with high-throughput automation frameworks), as well as the implementation of modern software engineering practices (unit testing, continuous integration, and automatic source-code documentation). These new features, capabilities, and code development model aim to further sustain and expand the community uptake and range of applicability, that nowadays spans complex and accurate dielectric, electronic, magnetic, optical, topological and transport properties of materials.

Determining the phase diagram of atomically thin layered antiferromagnet CrCl3.

Changes in the spin configuration of atomically thin, magnetic van der Waals multilayers can cause drastic modifications in their opto-electronic properties. Conversely, the opto-electronic response of these systems provides information about the magnetic state, which is very difficult to obtain otherwise. Here, we show that in CrCl3 multilayers, the dependence of the tunnelling conductance on applied magnetic field, temperature and number of layers tracks the evolution of the magnetic state, enabling the magnetic phase diagram to be determined experimentally. Besides a high-field spin-flip transition occurring for all thicknesses, the in-plane magnetoconductance exhibits an even-odd effect due to a low-field spin-flop transition. Through a quantitative analysis of the phenomena, we determine the interlayer exchange coupling as well as the layer magnetization and show that in CrCl3 shape anisotropy dominates. Our results reveal the rich behaviour of atomically thin layered antiferromagnets with weak magnetic anisotropy.

Relative Abundance of [Formula: see text] Topological Order in Exfoliable Two-Dimensional Insulators.

Quantum spin Hall insulators make up a class of two-dimensional materials with a finite electronic band gap in the bulk and gapless helical edge states. In the presence of time-reversal symmetry, [Formula: see text] topological order distinguishes the topological phase from the ordinary insulating one. Some of the phenomena that can be hosted in these materials, from one-dimensional low-dissipation electronic transport to spin filtering, could be promising for many technological applications in the fields of electronics, spintronics, and topological quantum computing. Nevertheless, the rarity of two-dimensional materials that can exhibit nontrivial [Formula: see text] topological order at room temperature hinders development. Here, we screen a comprehensive database we recently identified of 1825 monolayers that can be exfoliated from experimentally known compounds to search for novel quantum spin Hall insulators. Using density-functional and many-body perturbation theory simulations, we identify 13 monolayers that are candidates for quantum spin Hall insulators including high-performing materials such as AsCuLi2 and (platinum) jacutingaite (Pt2HgSe3). We also identify monolayer Pd2HgSe3 (palladium jacutingaite) as a novel Kane-Mele quantum spin Hall insulator and compare it with platinum jacutingaite. A handful of promising materials are mechanically stable and exhibit [Formula: see text] topological order, either unperturbed or driven by small amounts of strain. Such screening highlights a relative abundance of [Formula: see text] topological order of around 1% and provides an optimal set of candidates for experimental efforts.

Valley-Engineering Mobilities in Two-Dimensional Materials.

Two-dimensional materials are emerging as a promising platform for ultrathin channels in field-effect transistors. To this aim, novel high-mobility semiconductors need to be found or engineered. Although extrinsic mechanisms can in general be minimized by improving fabrication processes, the suppression of intrinsic scattering (driven, for example, by electron-phonon interactions) requires modification of the electronic or vibrational properties of the material. Because intervalley scattering critically affects mobilities, a powerful approach to enhance transport performance relies on engineering the valley structure. We show here the power of this strategy using uniaxial strain to lift degeneracies and suppress scattering into entire valleys, dramatically improving performance. This is shown in detail for arsenene, where a 2% strain stops scattering into four of the six valleys and leads to a 600% increase in mobility. The mechanism is general and can be applied to many other materials, including in particular the isostructural antimonene and blue phosphorene.

Microfocus Laser-Angle-Resolved Photoemission on Encapsulated Mono-, Bi-, and Few-Layer 1T'-WTe2.

Two-dimensional crystals of semi-metallic van der Waals materials hold much potential for the realization of novel phases, as exemplified by the recent discoveries of a polar metal in few-layer 1T'-WTe2 and of a quantum spin Hall state in monolayers of the same material. Understanding these phases is particularly challenging because little is known from experiments about the momentum space electronic structure of ultrathin crystals. Here, we report direct electronic structure measurements of exfoliated mono-, bi-, and few-layer 1T'-WTe2 by laser-based microfocus angle-resolved photoemission. This is achieved by encapsulating with monolayer graphene a flake of WTe2 comprising regions of different thickness. Our data support the recent identification of a quantum spin Hall state in monolayer 1T'-WTe2 and reveal strong signatures of the broken inversion symmetry in the bilayer. We finally discuss the sensitivity of encapsulated samples to contaminants following exposure to ambient atmosphere.

Very large tunneling magnetoresistance in layered magnetic semiconductor CrI3.

Magnetic layered van der Waals crystals are an emerging class of materials giving access to new physical phenomena, as illustrated by the recent observation of 2D ferromagnetism in Cr2Ge2Te6 and CrI3. Of particular interest in semiconductors is the interplay between magnetism and transport, which has remained unexplored. Here we report magneto-transport measurements on exfoliated CrI3 crystals. We find that tunneling conduction in the direction perpendicular to the crystalline planes exhibits a magnetoresistance as large as 10,000%. The evolution of the magnetoresistance with magnetic field and temperature reveals that the phenomenon originates from multiple transitions to different magnetic states, whose possible microscopic nature is discussed on the basis of all existing experimental observations. This observed dependence of the conductance of a tunnel barrier on its magnetic state is a phenomenon that demonstrates the presence of a strong coupling between transport and magnetism in magnetic van der Waals semiconductors.

Prediction of a Large-Gap and Switchable Kane-Mele Quantum Spin Hall Insulator.

Fundamental research and technological applications of topological insulators are hindered by the rarity of materials exhibiting a robust topologically nontrivial phase, especially in two dimensions. Here, by means of extensive first-principles calculations, we propose a novel quantum spin Hall insulator with a sizable band gap of ∼0.5 eV that is a monolayer of jacutingaite, a naturally occurring layered mineral first discovered in 2008 in Brazil and recently synthesized. This system realizes the paradigmatic Kane-Mele model for quantum spin Hall insulators in a potentially exfoliable two-dimensional monolayer, with helical edge states that are robust and that can be manipulated exploiting a unique strong interplay between spin-orbit coupling, crystal-symmetry breaking, and dielectric response.

Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds.

Two-dimensional (2D) materials have emerged as promising candidates for next-generation electronic and optoelectronic applications. Yet, only a few dozen 2D materials have been successfully synthesized or exfoliated. Here, we search for 2D materials that can be easily exfoliated from their parent compounds. Starting from 108,423 unique, experimentally known 3D compounds, we identify a subset of 5,619 compounds that appear layered according to robust geometric and bonding criteria. High-throughput calculations using van der Waals density functional theory, validated against experimental structural data and calculated random phase approximation binding energies, further allowed the identification of 1,825 compounds that are either easily or potentially exfoliable. In particular, the subset of 1,036 easily exfoliable cases provides novel structural prototypes and simple ternary compounds as well as a large portfolio of materials to search from for optimal properties. For a subset of 258 compounds, we explore vibrational, electronic, magnetic and topological properties, identifying 56 ferromagnetic and antiferromagnetic systems, including half-metals and half-semiconductors.