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This paper presents a physics-based compact model for circuit simulations in a SPICE environment for HfO2-based ferroelectric capacitors (FeCaps). The model has been calibrated based on experimental data obtained from HfO2-based FeCaps. A thermal model with an accurate description of the device parasitics is included to derive precise device characteristics based on first principles. The model incorporates statistical data that enables Monte Carlo analysis based on realistic distributions, thereby making it particularly well-suited for design-technology co-optimization (DTCO). Furthermore, the model is demonstrated in circuit simulations using an integrated circuit with current programming, wherein partial switching of the ferroelectric polarization is observed. Finally, the model was benchmarked in an array simulation, reaching convergence in 1.8 s with an array size of 100 kb., Comment: 6 pages, 7 figures

Superconductivity in few-layer semiconducting transition metal dichalcogenides (TMDs) can be induced by field-effect doping through ionic-liquid gating. While several experimental observations have been collected over the years, a fully-consistent theoretical picture is still missing. Here we develop a realistic framework that combines the predictive power of first-principles simulations with the versatility and insight of Bardeen-Cooper-Schrieffer gap equations to rationalize such experiments. The multi-valley nature of semiconducting TMDs is taken into account, together with the doping- and momentum-dependent electron-phonon and Coulomb interactions. Consistently with experiments, we find that superconductivity occurs when the electron density is large enough that the Q valleys get occupied, as a result of a large enhancement of electron-phonon interactions. Despite being phonon-driven, the superconducting state is predicted to be sensitive to Coulomb interactions, which can lead to the appearance of a relative sign difference between valleys and thus to a $s_{+-}$ character. We discuss qualitatively how such scenario may account for many of the observed physical phenomena for which no microscopic explanation has been found so far, including in particular the presence of a large subgap density of states, and the sample-dependent dome-shaped dependence of $T_c$ on accumulated electron density. Our results provide a comprehensive analysis of gate-induced superconductivity in semiconducting TMDs, and introduce an approach that will likely be valuable for other multivalley electronic systems, in which superconductivity occurs at relatively low electron density., Comment: 17 pages, 8 figures

We predict that in InAs/GaSb nanowires with an inverted band alignment a transverse electric field induces a collapse of the hybridization gap, and a semimetal phase occurs. We use a self-consistent k.p approach and an adapted Bernevig-Hughes-Zhang model to show that massless Dirac points result from exact cancellation between the kinetic electron-hole coupling and the field-controlled spin-orbit coupling. End states - mid-gap states localized at the extremes of a finite nanowire - are supported up to a critical field, but suddenly fade away as the system is driven through the semimetal phase, eventually evolving to trivial surface states, which expose a spin-orbit induced topological transition to the normal phase., Comment: 18 pages, includes Supplementary Information

Recent experiments in twisted bilayer transition-metal dichalcogenides have revealed a variety of strongly correlated phenomena. To theoretically explore their origin, we combine here ab initio calculations with correlated model approaches to describe and study many-body effects in twisted bilayer WSe$_2$ under pressure. We find that the interlayer distance is a key factor for the electronic structure, as it tunes the relative energetic positions between the K and the $\Gamma$ valleys of the valence band maximum of the untwisted bilayer. As a result, applying uniaxial pressure to a twisted bilayer induces a charge-transfer from the K valley to the flat bands in the $\Gamma$ valley. Upon Wannierizing moir\'e bands from both valleys, we establish the relevant tight-binding model parameters and calculate the effective interaction strengths using the constrained random phase approximation. With this, we approximate the interacting pressure-doping phase diagram of WSe$_2$ moir\'e bilayers using self-consistent mean field theory. Our results establish twisted bilayer WSe$_2$ as a platform that allows the direct pressure-tuning of different correlated phases, ranging from Mott insulators, charge-valley-transfer insulators to Kondo lattice-like systems., Comment: 10 pages, 5 figures. Supplementary Information is separate pdf file

We investigate the c-direction conduction in CrSBr in the linear regime, not accessible in other van der Waals (vdW) magnetic semiconductors, because of the unmeasurably low current. The resistivity -- $10^8$ to $10^{11}$ times larger than in the a- and b-directions -- exhibits magnetic state dependent thermally activated and variable range hopping transport. In the spin-flip phase at 2 T, the activation energy is 20 meV lower than in the antiferromagnetic state, due to a downshift of the conduction band edge, in agreement with ab-initio calculations. In the variable range hopping regime, the average hopping length decreases from twice the interlayer distance to the interlayer distance at 2 T, because in the antiferromagnetic state the large exchange energy impedes electrons hopping between adjacent layers. Our work demonstrates that the linear transport regime provides new information about electronic processes in vdW magnetic semiconductors, and shows how magnetism influences these processes both in real and reciprocal space.

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 CrI$_3$, known to exhibit either ferromagnetic or antiferromagnetic interlayer order, depending on layer stacking. However, the very strong uniaxial anisotropy of CrI$_3$ 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 CrBr$_3$ multilayers, and reveal that the uniaxial anisotropy is significantly smaller than in CrI$_3$. These results are obtained by magnetoconductance measurements on CrBr$_3$ 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 CrBr$_3$ and the excellent agreement found between theory and experiments, provide complete information on the stacking-dependent interlayer exchange energy and establish twisted bilayer CrBr$_3$ as an ideal system to deterministically create non-collinear magnetic phases.

Hubbard-corrected density-functional theory has proven to be successful in addressing self-interaction errors in 3D magnetic materials. However, the effectiveness of this approach for 2D magnetic materials has not been extensively explored. Here, we use PBEsol+$\textit{U}$ and its extensions PBEsol+$\textit{U}$+$\textit{V}$ to investigate the electronic, structural, and vibrational properties of 2D antiferromagnetic FePS$_3$ and ferromagnetic CrI$_3$, and compare the monolayers with their bulk counterparts. Hubbard parameters (on-site $\textit{U}$ and inter-site $\textit{V}$) are computed self-consistently using density-functional perturbation theory, thus avoiding any empirical assumptions. We show that for FePS$_3$ the Hubbard corrections are crucial in obtaining the experimentally observed insulating state with the correct crystal symmetry, providing also vibrational frequencies in good agreement with Raman experiments. For ferromagnetic CrI$_3$, we discuss how a straightforward application of Hubbard corrections worsens the results and introduces a spurious separation between spin-majority and minority conduction bands. Promoting the Hubbard $\textit{U}$ to be a spin-resolved parameter - that is, applying different (first-principles) values to the spin-up and spin-down manifolds - recovers a more physical picture of the electronic bands and delivers the best comparison with experiments.

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 micro-focus angle resolved photoemission ($\mu$-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., Comment: Supporting Information available upon request

Transistors realized on 2D antiferromagnetic semiconductor CrPS$_4$ exhibit large magnetoconductance, due to magnetic-field-induced changes in magnetic state. The microscopic mechanism coupling 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 N\'eel temperature $T_N$, the magnetoconductance originates from a mobility increase due to the applied magnetic field that reduces spin fluctuation induced disorder. For $T << T_N$, 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 \emph{ab-initio} calculations. Our results demonstrate that the bandstructure of CrPS$_4$ depends on its magnetic state and reveal a mechanism for magnetoconductance that had not been identified earlier.

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, we show that exfoliated layers of CrPS$_4$ -- 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, we perform conductance measurements as a function of temperature and magnetic field, to determine the full magnetic phase diagram, which includes a spin-flop and a spin-flip phase. We find that the magnetoconductance depends strongly on gate voltage, 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 CrPS$_4$ multilayers employed in our study. Our 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., Comment: Accepted for publication in Advanced Materials

Event-based neuromorphic systems provide a low-power solution by using artificial neurons and synapses to process data asynchronously in the form of spikes. Ferroelectric Tunnel Junctions (FTJs) are ultra low-power memory devices and are well-suited to be integrated in these systems. Here, we present a hybrid FTJ-CMOS Integrate-and-Fire neuron which constitutes a fundamental building block for new-generation neuromorphic networks for edge computing. We demonstrate electrically tunable neural dynamics achievable by tuning the switching of the FTJ device.

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 couple of dozens to more than a hundred, with the number of theoretically predicted compounds reaching a few thousands. 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 to the updated versions of the two databases (ICSD and COD) used in our previous work. This expansion has led to the discovery of additional 1252 unique monolayers, bringing the total to 3077 compounds and, notably, almost doubling the number of easily exfoliable materials (2004). Moreover, we optimized the structural properties of all these monolayers and explored their electronic structure with a particular emphasis on those rare large-bandgap 2D materials that could be precious to isolate 2D field effect transistors channels. Finally, for each material containing up to 6 atoms per unit cell, we identified the best candidates to form commensurate heterostructures, balancing requirements on the supercells size and minimal strain.

Charge transport plays a crucial role in manifold potential applications of two-dimensional materials, including field effect transistors, solar cells, and transparent conductors. At most operating temperatures, charge transport is hindered by scattering of carriers by lattice vibrations. Assessing the intrinsic phonon-limited carrier mobility is thus of paramount importance to identify promising candidates for next-generation devices. Here we provide a framework to efficiently compute the drift and Hall carrier mobility of two-dimensional materials through the Boltzmann transport equation by relying on a Fourier-Wannier interpolation. Building on a recent formulation of long-range contributions to dynamical matrices and phonon dispersions [Phys. Rev. X 11, 041027 (2021)], we extend the approach to electron-phonon coupling including the effect of dynamical dipoles and quadrupoles. We identify an unprecedented contribution associated with the Berry connection that is crucial to preserve the Wannier-gauge covariance of the theory. This contribution is not specific to 2D crystals, but also concerns the 3D case, as we demonstrate via an application to bulk SrO. We showcase our method on a wide selection of relevant monolayers ranging from SnS2 to MoS2, graphene, BN, InSe, and phosphorene. We also discover a non-trivial temperature evolution of the Hall hole mobility in InSe whereby the mobility increases with temperature above 150 K due to the mexican-hat electronic structure of the InSe valence bands. Overall, we find that dynamical quadrupoles are essential and can impact the carrier mobility in excess of 75%., Comment: 31 pages and 16 figures

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., Comment: 6 pages and 2 figures

We investigate electronic transport through exfoliated multilayers of CrSBr, a 2D semiconductor that is attracting attention because of its magnetic properties. We find an extremely pronounced anisotropy that manifests itself in qualitative and quantitative differences of all quantities measured along the in-plane \textit{a} and \textit{b} crystallographic directions. In particular, we observe a qualitatively different dependence of the conductivities $\sigma_a$ and $\sigma_b$ on temperature and gate voltage, accompanied by orders of magnitude differences in their values ($\sigma_b$/$\sigma_a \approx 3\cdot10^2-10^5$ at low temperature and large negative gate voltage). We also find 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 -- together with unambiguous signatures of a 1D van Hove singularity that we detect 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. We conclude that CrSBr is the first 2D semiconductor to show distinctly quasi 1D electronic transport properties., Comment: Accepted for publication in Advanced Materials

Quantum spin Hall insulators (QSHI) have been proposed to power a number of applications, many of which rely on the possibility to switch on and off the non-trivial topology. Typically this control is achieved through strain or external electric fields, which require energy consumption to be maintained. On the contrary, a non-volatile mechanism would be highly beneficial and could be realized through ferroelectricity if opposite polarization states are associated with different topological phases. While this is not possible in a single ferroelectric material where the two polarization states are related by inversion, the necessary asymmetry could be introduced by combining a ferroelectric layer with another two-dimensional (2D) trivial insulator. Here, by means of first-principles simulations, not only we propose that this is a promising strategy to engineer non-volatile ferroelectric control of topological order in 2D heterostructures, but also that the effect is robust and can survive up to room temperature, irrespective of the weak van der Waals coupling between the layers. We illustrate the general idea by considering a heterostructure made of a well-known ferroelectric material, In$_2$Se$_3$, and a suitably chosen, easily exfoliable trivial insulator, CuI. In one polarization state the system is trivial, while it becomes a QSHI with a robust band gap upon polarization reversal. Remarkably, the topological band gap is mediated by the interlayer hybridization and allows to maximise the effect of intralayer spin-orbit coupling, promoting a robust ferroelectric topological phase that could not exist in monolayer materials and is resilient against relative orientation and lattice matching between the layers., Comment: 13 pages, 8 figures + supplementary (6 pages, 3 figures)

The electronic band structure of atomically thin semiconductors can be tuned by the application of a perpendicular electric field. The principle was demonstrated experimentally shortly after the discovery of graphene by opening a finite band gap in graphene bilayers, which naturally are zero-gap semiconductors. So far, however, the same principle could not be employed to control a broader class of materials, because the required electric fields are beyond reach in current devices. To overcome this limitation, we have realized double ionic gated transistors that enable the application of very large electric fields. Using these devices, we show that the band gap of few-layer semiconducting transition metal dichalcogenides can be continuously suppressed from 1.5 eV to zero. Our results illustrate an unprecedented level of control of the band structures of 2D semiconductors, which is important for future research and applications., Comment: Submitted paper

Recent experiments on van der Waals antiferrmagnets such as CrI3, CrCl3 and MnPS3 have shown that using atomically thin layers as tunnel barriers and measuring the temperature ($T$) and magnetic field ($H$) dependence of the conductance allows their magnetic phase diagram to be mapped. In contrast, barriers made of CrBr3 -- the sole van der Waals ferromagnet investigated in this way -- were found to exhibit small and featureless magnetoconductance, seemingly carrying little information about magnetism. Here we show that -- despite these early results -- the conductance of CrBr3 tunnel barriers does provide detailed information about the magnetic state of atomically thin CrBr3 crystals for $T$ both above and below the Curie temperature ($T_C = 32$ K). Our analysis establishes that the tunneling conductance depends on $H$ and $T$ exclusively through the magnetization $M(H,T)$, over the entire temperature range investigated (2-50 K). The phenomenon is reproduced in detail by the spin-dependent Fowler-Nordheim model for tunneling, and is a direct manifestation of the spin splitting of the CrBr3 conduction band. These findings demonstrate that the investigation of magnetism by tunneling conductance measurements is not limited to antiferromagnets, but can also be applied to ferromagnetic materials.

Layered materials (LMs), such as graphite, hexagonal boron nitride, and transition-metal dichalcogenides, are at the centre 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 and the strength of the interlayer interactions. Here, we present a general approach to predict the complete spectroscopic fan diagrams, i.e., the relations between frequencies and number of layers, $N$, for the optically-active shear and layer-breathing modes of any multilayer comprising $N \geq 2$ 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 directly available on the Materials Cloud portal, to assist any researcher in the prediction and interpretation of such diagrams. Our work will underpin all future efforts on Raman and Infrared characterization of known, and yet not investigated, LMs., Comment: 30 pages (including appendices and tables), 7 figures

Van der Waals heterostructures provide a versatile tool to not only protect or control, but also enhance the properties of a 2D material. We use ab initio calculations and semi-analytical models to find strategies which boost the mobility of a current-carrying 2D semiconductor within an heterostructure. Free-carrier screening from a metallic "screener" layer remotely suppresses electron-phonon interactions in the current-carrying layer. This concept is most effective in 2D semiconductors whose scattering is dominated by screenable electron-phonon interactions, and in particular the Fr\"ohlich coupling to polar-optical phonons. Such materials are common and characterised by overall low mobilities in the small doping limit, and much higher ones when the 2D material is doped enough for electron-phonon interactions to be screened by its own free carriers. We use GaSe as a prototype and place it in a heterostructure with doped graphene as the "screener" layer and BN as a separator. We develop an approach to determine the electrostatic response of any heterostructure by combining the responses of the individual layers computed within density-functional perturbation theory. Remote screening from graphene can suppress the long-wavelength Fr\"ohlich interaction, leading to a consistently high mobility around $500$ to $600$ cm$^2$/Vs for carrier densities in GaSe from $10^{11}$ to $10^{13}$ cm$^{-2}$. Notably, the low-doping mobility is enhanced by a factor 2.5. This remote free-carrier screening is more efficient than more conventional manipulation of the dielectric environment, and it is most effective when the separator (BN) is thin., Comment: 20 pages, 14 figures

Chromium trihalides, CrX$_3$ (with X = Cl, Br, I), are a family of layered magnetic materials that can be easily exfoliated to provide ferromagnetic monolayers. When two layers are stacked together to form a bilayer the interlayer exchange coupling can be either ferromagnetic or antiferromagnetic depending on the stacking sequence. Here we combine crystallographic arguments based on the close-packing condition with first-principles simulations to enumerate all possible stacking patterns in CrX$_3$ bilayers that preserve the spatial periodicity of each layer. We recover all configurations observed in bulk crystals and disclose stacking sequences with no bulk counterpart where the two layers have opposite chirality. Stacking sequences are ranked according to their relative stability and a preferential interlayer magnetic ordering is assigned to each of them. Simulations provide a consistent picture to frame all current experimental observations on bulk and exfoliated CrX$_3$ crystals, with interesting implications for future measurements, including synthetic bilayers with non-standard stacking patterns., Comment: 9+epsilon pages, 4 figures, 3 tables

When complex mechanisms are involved, pinpointing high-performance materials within large databases is a major challenge in materials discovery. We focus here on phonon-limited conductivities, and study 2D semiconductors doped by field effects. Using state-of-the-art density-functional perturbation theory and Boltzmann transport equation, we discuss 11 monolayers with outstanding transport properties. These materials are selected from a computational database of exfoliable materials providing monolayers that are dynamically stable and that do not have more than 6 atoms per unit cell. We first analyse electron-phonon scattering in two well-known systems: electron-doped InSe and hole-doped phosphorene. Both are single-valley systems with weak electron-phonon interactions, but they represent two distinct pathways to fast transport: a steep and deep isotropic valley for the former and strongly anisotropic electron-phonon physics for the latter. We identify similar features in the database and compute the conductivities of the relevant monolayers. This process yields several high-conductivity materials, some of them only very recently emerging in the literature (GaSe, Bi$_2$SeTe$_2$, Bi$_2$Se$_3$, Sb$_2$SeTe$_2$), others never discussed in this context (AlLiTe$_2$, BiClTe, ClGaTe, AuI). Comparing these 11 monolayers in detail, we discuss how the strength and angular dependency of the electron-phonon scattering drives key differences in the transport performance of materials despite similar valley structure. We also discuss the high conductivity of hole-doped WSe$_2$, and how this case study shows the limitations of a selection process that would be based on band properties alone.

We study free, capped and encapsulated bilayer jacutingaite Pt$_2$HgSe$_3$ from first principles. While the free standing bilayer is a large gap trivial insulator, we find that the encapsulated structure has a small trivial gap due to the competition between sublattice symmetry breaking and sublattice-dependent next-nearest-neighbor hopping. Upon the application of a small perpendicular electric field, the encapsulated bilayer undergoes a topological transition towards a quantum spin Hall insulator. We find that this topological transition can be qualitatively understood by modeling the two layers as uncoupled and described by an imbalanced Kane-Mele model that takes into account the sublattice imbalance and the corresponding inversion-symmetry breaking in each layer. Within this picture, bilayer jacutingaite undergoes a transition from a 0+0 state, where each layer is trivial, to a 0+1 state, where an unusual topological state relying on Rashba-like spin orbit coupling emerges in only one of the layers., Comment: 10 pages, 5 figures

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, very difficult to obtain otherwise. Here we show that in CrCl$_3$ multilayers, the dependence of the tunnelling conductance on applied magnetic field ($H$), temperature ($T$), and number of layers ($N$) tracks the evolution of the magnetic state, enabling the magnetic phase diagram of these systems 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. If the layer number $N$ is even, the transition occurs at $\mu_0 H \sim 0$ T due to the very small in-plane magnetic anisotropy, whereas for odd $N$ the net magnetization of the uncompensated layer causes the transition to occur at finite $H$. Through a quantitative analysis of the phenomena, we determine the interlayer exchange coupling as well as the staggered magnetization, and show that in CrCl$_3$ shape anisotropy dominates. Our results reveal the rich behaviour of atomically-thin layered antiferromagnets with weak magnetic anisotropy., Comment: 10 pages, 5 figures (supplementary information as ancillary file)

Monolayer jacutingaite (Pt$_2$HgSe$_3$) has been recently identified as a candidate quantum spin Hall system with a 0.5 eV band gap, but no transport measurements have been performed so far on this material, neither in monolayer nor in the bulk. By using a dedicated high-pressure technique, we grow crystals enabling the exfoliation of 50-100 nm thick layers and the realization of devices for controlled transport experiments. Magnetoresistance measurements indicate that jacutingaite is a semimetal, exhibiting Shubnikov-de Haas (SdH) resistance oscillations with a multi-frequency spectrum. We adapt the Lifshitz-Kosevich formula to analyze quantitatively the SdH resistance oscillations in the presence of multiple frequencies, and find that the experimental observations are overall reproduced well by band structure ab-initio calculations for bulk jacutingaite. Together with the relatively high electron mobility extracted from the experiments ($\approx 2000$ cm$^2$/Vs, comparable to what is observed in WTe$_2$ crystals of the same thickness), our results indicate that monolayer jacutingaite should provide an excellent platform to investigate transport in 2D quantum spin Hall systems., Comment: 11 pages, 4 figures + supplementary (3 pages, 2 figures)

The magnetic state of atomically thin semiconducting layered antiferromagnets such as CrI$_3$ and CrCl$_3$ 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 tunneling magnetoresistance originates from a spin-filtering effect sensitive to the relative orientation of the magnetization in different layers, i.e., to the magnetic state of the multilayers. For systems in which antiferromagnetism occurs within an individual layer, however, no spin-filtering occurs: it is unclear whether this strategy can work. To address this issue, we investigate tunnel transport through atomically thin crystals of MnPS$_3$, a van der Waals semiconductor that in the bulk exhibits easy-axis antiferromagnetic order within the layers. For thick multilayers below $T\simeq 78$ K, a $T$-dependent magnetoresistance sets-in at $\sim 5$ T, and is found to track the boundary between the antiferromagnetic and the spin-flop phases known from bulk magnetization measurements. The magnetoresistance persists down to individual MnPS$_3$ monolayers with nearly unchanged characteristic temperature and magnetic field scales, albeit with a different dependence on $H$. We discuss the implications of these finding for the magnetic state of atomically thin MnPS$_3$ crystals, conclude that antiferromagnetic correlations persist down to the level of individual monolayers, and that tunneling magnetoresistance does allow magnetism in 2D insulating materials to be detected even in the absence of spin-filtering., Comment: 19 pages, 4 figures + supplementary (10 pages, 5 figures)

The family of 2D materials grows day by day, drastically expanding the scope of possible phenomena to be explored in two dimensions, as well as the possible van der Waals heterostructures that one can create. Such 2D materials currently cover a vast range of properties. Until recently, this family has been missing one crucial member - 2D magnets. The situation has changed over the last two years with the introduction of a variety of atomically-thin magnetic crystals. Here we will discuss the difference between magnetic states in 2D materials and in bulk crystals and present an overview of the 2D magnets that have been explored recently. We will focus, in particular, on the case of the two most studied systems - semiconducting CrI$_3$ and metallic Fe$_3$GeTe$_2$ - and illustrate the physical phenomena that have been observed. Special attention will be given to the range of novel van der Waals heterostructures that became possible with the appearance of 2D magnets, offering new perspectives in this rapidly expanding field.

We report high-resolution angle resolved photoemission measurements on single crystals of Pt2HgSe3 grown by high-pressure synthesis. Our data reveal a gapped Dirac nodal line whose (001)-projection separates the surface Brillouin zone in topological and trivial areas. In the non-trivial $k$-space range we find surface states with multiple saddle-points in the dispersion resulting in two van Hove singularities in the surface density of states. Based on density functional theory calculations, we identify these surface states as signatures of a topological crystalline state which coexists with a weak topological phase.

Recently, the very first large-gap Kane-Mele quantum spin Hall insulator was predicted to be monolayer jacutingaite (Pt$_2$HgSe$_3$), a naturally-occurring exfoliable mineral discovered in Brazil in 2008. The stacking of quantum spin Hall monolayers into a van-der-Waals layered crystal typically leads to a (0;001) weak topological phase, which does not protect the existence of surface states on the (001) surface. Unexpectedly, recent angle-resolved photoemission spectroscopy experiments revealed the presence of surface states dispersing over large areas of the 001-surface Brillouin zone of jacutingaite single crystals. The 001-surface states have been shown to be topologically protected by a mirror Chern number $C_M=-2$, associated with a nodal line gapped by spin-orbit interactions. Here, we extend the two-dimensional Kane-Mele model to bulk jacutingaite and unveil the microscopic origin of the gapped nodal line and the emerging crystalline topological order. By using maximally-localized Wannier functions, we identify a large non-trivial second nearest-layer hopping term that breaks the standard paradigm of weak topological insulators. Complemented by this term, the predictions of the Kane-Mele model are in remarkable agreement with recent experiments and first-principles simulations, providing an appealing conceptual framework also relevant for other layered materials made of stacked honeycomb lattices., Comment: main text: 7 pages, 3 figures; supplementary: 3 pages, 2 figures

Using accurate first-principles calculations based on many-body perturbation theory we predict that two-dimensional MoS$_2$ hosts edge excitons with universal character, intrinsic to the existence of edges and lying well below the onset of bulk features. These excitons are largely insensitive to edge terminations or orientation, persisting even in the presence of metallic screening at zigzag edges, with large binding energies of $\sim$0.4 eV. Additional excitons can also emerge in ultranarrow ribbons, or as a function of the chemical nature of the termination. The chemical, structural, and electronic similarities with Se- or W-based transition-metal dichalcogenides suggest that these optical features could be common in this class of materials., Comment: 7 pages main text, 5 pages supplemental material, 12 figures

Chromium triiodide, CrI$_3$, is emerging as a promising magnetic two-dimensional semiconductor where spins are ferromagnetically aligned within a single layer. Potential applications in spintronics arise from an antiferromagnetic ordering between adjacent layers that gives rise to spin filtering and a large magnetoresistance in tunnelling devices. This key feature appears only in thin multilayers and it is not inherited from bulk crystals, where instead neighbouring layers share the same ferromagnetic spin orientation. This discrepancy between bulk and thin samples is unexpected, as magnetic ordering between layers arises from exchange interactions that are local in nature and should not depend strongly on thickness. Here we solve this controversy and show through polarization resolved Raman spectroscopy that thin multilayers do not undergo a structural phase transition typical of bulk crystals. As a consequence, a different stacking pattern is present in thin and bulk samples at the temperatures at which magnetism sets in and, according to previous first-principles simulations, this results in a different interlayer magnetic ordering. Our experimental findings provide evidence for the strong interplay between stacking order and magnetism in CrI$_3$, opening interesting perspectives to design the magnetic state of van der Waals multilayers., Comment: 7 pages, 3 figures

Quantum spin Hall insulators are 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, $\mathbb{Z}_2$ 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 very 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 non-trivial $\mathbb{Z}_2$ topological order at room temperature hinders development. Here, we screen a comprehensive database we recently created 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 AsCuLi$_2$ and jacutingaite (Pt$_2$HgSe$_3$). We also identify monolayer Pd$_2$HgSe$_3$ as a novel Kane-Mele quantum spin Hall insulator, and compare it with jacutingaite. Such a handful of promising materials are mechanically stable and exhibit $\mathbb{Z}_2$ topological order, either unpertubed or driven by a small amount of strain. Such screening highlights a relative abundance of $\mathbb{Z}_2$ topological order of around 1%, and provides an optimal set of candidates for experimental efforts., Comment: Supporting information as an ancillary file

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., Comment: 26 pages, 8 figures

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. While extrinsic mechanisms can in general be minimized by improving fabrication processes, the suppression of intrinsic scattering (driven e.g. by electron-phonon interactions) requires to modify the electronic or vibrational properties of the material. Since 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 4 of the 6 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., Comment: 14 pages, 14 figures

The recent discovery of ferromagnetism in 2D van der Waals (vdw) crystals has generated widespread interest, owing to their potential for fundamental and applied research. Advancing the understanding and applications of vdw magnets requires methods to quantitatively probe their magnetic properties on the nanoscale. Here, we report the study of atomically thin crystals of the vdw magnet CrI$_3$ down to individual monolayers using scanning single-spin magnetometry, and demonstrate quantitative, nanoscale imaging of magnetisation, localised defects and magnetic domains. We determine the magnetisation of CrI$_3$ monolayers to be $\approx16~\mu_B/$nm$^2$ and find comparable values in samples with odd numbers of layers, whereas the magnetisation vanishes when the number of layers is even. We also establish that this inscrutable even-odd effect is intimately connected to the material structure, and that structural modifications can induce switching between ferro- and anti-ferromagnetic interlayer ordering. Besides revealing new aspects of magnetism in atomically thin CrI$_3$ crystals, these results demonstrate the power of single-spin scanning magnetometry for the study of magnetism in 2D vdw magnets., Comment: Questions and comments are welcome. For further information and related job-openings, please visit www.quantum-sensing.ch

Through a combined theoretical and experimental effort, we uncover a yet unidentified mechanism that strengthens considerably electron-phonon coupling in materials where electron accumulation leads to population of multiple valleys. Taking atomically-thin transition-metal dichalcogenides as prototypical examples, we establish that the mechanism results from a phonon-induced out-of-phase energy shift of the different valleys, which causes inter-valley charge transfer and reduces the effectiveness of electrostatic screening, thus enhancing electron-phonon interactions. The effect is physically robust, it can play a role in many materials and phenomena, as we illustrate by discussing experimental evidence for its relevance in the occurrence of superconductivity. (short abstract due to size limitations - full abstract in the manuscript), Comment: 16 pages, 8 figures

Two-dimensional crystals of semimetallic 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'-WTe$_2$ and of a quantum spin Hall state in monolayers of the same material. Understanding these phases is particularly challenging because little is known from experiment about the momentum space electronic structure of ultrathin crystals. Here, we report direct electronic structure measurements of exfoliated mono-, bi-, and few-layer 1T'-WTe$_2$ by laser-based micro-focus angle resolved photoemission. This is achieved by encapsulating with monolayer graphene a flake of WTe$_2$ comprising regions of different thickness. Our data support the recent identification of a quantum spin Hall state in monolayer 1T'-WTe$_2$ 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., Comment: 14 pages, 5 figures

We present a first-principles approach to compute the transport properties of 2D materials in an accurate and automated framework. We use density-functional perturbation theory in the appropriate bidimensional setup with open-boundary conditions in the third direction. The materials are charged by field effect via planar counter-charges. In this approach, we obtain electron-phonon matrix elements in which dimensionality and doping effects are inherently accounted for, without the need for post-processing corrections. This treatment highlights some unexpected consequences, such as an increase of electron-phonon coupling with doping in transition-metal dichalcogenides.We use symmetries extensively and identify pockets of relevant electronic states to minimize the number of electron-phonon interactions to compute; the integrodifferential Boltzmann transport equation is then linearized and solved beyond the relaxation-time approximation. We apply the entire protocol to a set of much studied materials with diverse electronic and vibrational band structures: electron-doped MoS2, WS2, WSe2, phosphorene, arsenene, and hole-doped phosphorene. Among these, hole-doped phosphorene is found to have the highest mobility, with a room temperature value around 600 cm^2/(Vs). Last, we identify the factors that affect most phonon-limited mobilities, such as the number and the anisotropy of electron and hole pockets, to provide a broader understanding of the driving forces behind high mobilities in two-dimensional materials., Comment: 24 pages, 15 figures

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 first 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 new phenomenon that demonstrates the presence of a strong coupling between transport and magnetism in magnetic van der Waals semiconductors.

Fundamental research and technological applications of topological insulators are hindered by the rarity of materials exhibiting a robust topologically non-trivial phase, especially in two dimensions. Here, by means of extensive first-principles calculations, we propose a novel quantum spin Hall insulator with a sizeable band gap of $\sim$0.5 eV that is a monolayer of Jacutingaite, a naturally occurring layered mineral first discovered in 2008 in Brazil and recently synthesised. This system realises 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.