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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., 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)

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

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

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., Many standard techniques for investigating magnetic properties in the bulk are ill suited to atomically thin van der Waals materials. Here, Wang et al take a prototypical van der Waals ferromagnet, Chromium Bromide, and show how tunneling conductance can elucidate the material magnetic properties.

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 semianalytical models to find strategies which boost the mobility of a current-carrying two-dimensional (2D) semiconductor within a 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 characterized 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 boron nitride 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 $500--600\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}$/V s for carrier densities in GaSe from ${10}^{11}$ to ${10}^{13}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. 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 (boron nitride) is thin.

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

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 six atoms per unit cell. We first analyze 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, Bi2SeTe2, Bi2Se3, Sb2SeTe2), others never discussed in this context (AlLiTe2, 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 WSe2, and how this case study shows the limitations of a selection process that would be based on band properties alone., Video Abstract, Video Abstract: Profiling novel high-conductivity 2D semiconductors

We report high-resolution angle-resolved photoemission measurements on single crystals of Pt_{2}HgSe_{3} 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 nontrivial 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.

The magnetic state of atomically thin semiconducting layered antiferromagnets such as CrI

The magnetic state of atomically thin semiconducting layered antiferromagnets such as CrI3 and CrCI3 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 ferromagnet cally 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 similar to 78 K, a T-dependent magnetoresistance sets in at mu H-0 similar to 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.

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

We search for novel two-dimensional materials that can be easily exfoliated from their parent compounds. Starting from 108423 unique, experimentally known three-dimensional compounds we identify a subset of 5619 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, allow to identify 1825 compounds that are either easily or potentially exfoliable, including all that are commonly exfoliated experimentally. In particular, the subset of 1036 easily exfoliable cases---layered materials held together mostly by dispersion interactions and with binding energies up to $30-35$ meV$\cdot\text{\AA}^{-2}$---provides a wealth of novel structural prototypes and simple ternary compounds, and a large portfolio to search materials for optimal properties. For the 258 compounds with up to 6 atoms per primitive cell we comprehensively explore vibrational, electronic, magnetic, and topological properties, identifying in particular 56 ferromagnetic and antiferromagnetic systems, including half-metals and half-semiconductors., Comment: 15 pages, 5 figures, supplementary material available at https://www.nature.com/articles/s41565-017-0035-5#Sec15. Data available on the Materials Cloud https://www.materialscloud.org/discover/2dstructures/dashboard/ptable

Carboxyl-functionalized graphene platelets (GP) and graphene oxide (GO) sheets were added to a commercial aqueous adhesive dispersion of thermoplastic polyurethane (TP) (Idrotex 200 from FacGB s.r.l.). For both additives, the weight percentage was of industrial interest, 0.01 and 10.1 wt %. The addition of GP/GO was carried out in a simple and scalable-up process that can be applied to other materials and additives. Mechanical, peel tests were applied on polyurethane strips (75 mm long, IS mm wide, and 1.5 mm thick) prepared cutting extruded sheets obtained using Estane 58091, a 70D aromatic polyester-based TP. The tests with 0.01 wt % of GP showed statistically significant higher forces at first failure and maximum forces with respect to the pristine adhesive. Sample characterization was carried out with scanning electron microscopy, infrared spectroscopy, X-ray diffraction, and thermal analysis. A mechanism is suggested for the improved performance of the low-dose GP adhesive.

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 AsCuLi

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., 14 pages, 14 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, which is very difficult to obtain otherwise. Here, we show that in CrCl

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

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

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, 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 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 Z(2) 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 AsCuL2 and (platinum) jacutingaite (P2HgS3). 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 Z(2) topological order, either unperturbed or driven by small amounts of strain. Such screening highlights a relative abundance of Z(2) topological order of around 1% and provides an optimal set of candidates for experimental efforts.

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)

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.

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 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'-WTe

Two-dimensional semiconductors such as MoS2 are an emerging material family with wide-ranging potential applications in electronics, optoelectronics, and energy harvesting. Large-area growth methods are needed to open the way to applications. Control over lattice orientation during growth remains a challenge. This is needed to minimize or even avoid the formation of grain boundaries, detrimental to electrical, optical, and mechanical properties of MoS2 and other 2D semiconductors. Here, we report on the growth of high-quality monolayer MoS2 with control over lattice orientation. We show that the monolayer film is composed of coalescing single islands with limited numbers of lattice orientation due to an epitaxial growth mechanism. Optical absorbance spectra acquired over large areas show significant absorbance in the high-energy part of the spectrum, indicating that MoS2 could also be interesting for harvesting this region of the solar spectrum and fabrication of UV-sensitive photodetectors. Even though the interaction between the growth substrate and MoS2 is strong enough to induce lattice alignment via van der Waals interaction, we can easily transfer the grown material and fabricate devices. Local potential mapping along channels in field-effect transistors shows that the single-crystal MoS2 grains in our film are well connected, with interfaces that do not degrade the electrical conductivity. This is also confirmed by the relatively large and length-independent mobility in devices with a channel length reaching 80 mu m.

In highest quality organic single-crystal field-effect transistors, electron transport occurs in the band-like regime, with the carrier mobility increasing upon lowering temperature. Neither the microscopic nature of this regime, nor why it occurs only in a small number of materials is currently understood. Here, comparative studies of closely related materials, exhibiting high-quality reproducible transport properties are needed. We performed a study of electron transport in single-crystals of different TCNQ (tetracyanoquinodimethane) molecules, combined with band structure calculations. We show that F2-TCNQ devices exhibit very high electron mobility and an unprecedented increase in mobility upon cooling, whereas in TCNQ and F4-TCNQ the mobility is substantially lower and decreases upon cooling. We analyze the crystal and electronic structures of these materials and find that F2-TCNQ crystals are indeed ideal to achieve outstanding transport properties. Our analysis also shows that to understand the difference between the three materials, studying their band structure is not sufficient, and that the electron-phonon coupling needs to be investigated as well. Besides the outstanding transport properties of F2-TCNQ, a key result of our work is the identification of the Fx-TCNQ family as a paradigm to investigate the most fundamental aspects of electronic transport in organic crystals.

We investigate the long-wavelength dispersion of longitudinal and transverse optical phonon modes in polar two-dimensional materials, multilayers, and their heterostructures. Using analytical models and density-functional perturbation theory in a two-dimensional framework, we show that, at variance with the three-dimensional case, these modes are degenerate at the zone center but the macroscopic electric field associated with the longitudinal-optical modes gives rise to a finite slope at the zone center in their corresponding phonon dispersions. This slope increases linearly with the number of layers and it is determined solely by the Born effective charges of the material and the dielectric properties of the surrounding media. Screening from the environment can greatly reduce the slope splitting between the longitudinal and transverse optical modes and can be seen in the experimentally relevant case of boron nitride-graphene heterostructures. As the phonon momentum increases, the intrinsic screening properties of the two-dimensional material dictate the transition to a momentum-independent splitting similar to that of three-dimensional materials. These considerations are essential to understand electrical transport and optical coupling in two-dimensional systems., Comment: 8 pages, 4 figures

The local application of mechanical stress in piezoelectric materials gives rise to boundaries across which the electric polarization changes. Polarization charges appear along such polar discontinuities and the ensuing electric fields drive a charge reconstruction with the accumulation of free carriers at the boundaries. This is particularly relevant for two-dimensional materials that can sustain very large strains and display record piezoelectric responses. Here we show by first-principles simulations the emergence of one-dimensional wires of free electrons and holes along strain interfaces, taking SnSe as a paradigmatic material. We complement this by developing a Schr\"odinger-Poisson approach specifically designed for two-dimensional materials that it is able to reproduce the ab-initio results and also to extend them to regimes of parameters and system sizes that would be unaffordable in first principles calculations. This model allows us to assess the degree of tunability for the free charge in the wires coming from strain values and profiles, and to obtain the critical size at which the interfaces start to be metallic., Comment: 8 pages, 6 figures + supplementary (5 pages, 7 figures)

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 $\ensuremath{\sim}0.5\text{ }\text{ }\mathrm{eV}$ 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.

We highlight the emergence of metallic states in two-dimensional transition-metal-dichalcogenide nanostructures -nanoribbons, islands, and inversion domain boundaries- as a widespread and universal phenomenon driven by the polar discontinuities occurring at their edges or boundaries. We show that such metallic states form one-dimensional wires of electrons or holes, with a free charge density that increases with the system size, up to complete screening of the polarization charge, and can also be controlled by the specific edge or boundary configurations, e.g. through chemisorption of hydrogen or sulfur atoms at the edges. For triangular islands, local polar discontinuities occur even in the absence of a total dipole moment for the island and lead to an accumulation of free carriers close to the edges, providing a consistent explanation of previous experimental observations. To further stress the universal character of these mechanisms, we show that polar discontinuities give rise to metallic states also at inversion domain boundaries. These findings underscore the potential of engineering transition-metal-dichalcogenide nanostructures for manifold applications in nano- and opto-electronics, spintronics, catalysis, and solar-energy harvesting., Comment: 11 pages, 10 figures

We present an ab-initio study of the spin-resolved optical conductivity of two-dimensional (2D) group-VIB transition-metal dichalcogenides (TMDs). We carry out fully-relativistic density-functional-theory calculations combined with maximally localized Wannier functions to obtain band manifolds at extremely high resolutions and focus on the photo-response of 2D TMDs to circularly-polarized light in a wide frequency range. We present extensive numerical results for monolayer TMDs involving molybdenum and tungsten combined with sulphur and selenium. Our numerical approach allows us to locate with a high degree of accuracy the positions of the points in the Brillouin zone that are responsible for van Hove singularities in the optical response. Surprisingly, some of the saddle points do not occur exactly along high-symmetry directions in the Brillouin zone, although they happen to be in their close proximity., 9 pages, 5 figures

Unprecedented and fascinating phenomena have been recently observed at oxide interfaces between centrosymmetric cubic materials, such as LaAlO$_3$ and SrTiO$_3$, where a polar discontinuity across the boundary gives rise to polarization charges and electric fields that drive a metal-insulator transition, with the appearance of free carriers at the interface. Two-dimensional analogues of these systems are possible, and honeycomb lattices could offer a fertile playground, thanks to their versatility and the extensive on-going experimental efforts in graphene and related materials. Here we suggest different realistic pathways to engineer polar discontinuities across interfaces between honeycomb lattices, and support these suggestions with extensive first-principles calculations. Two broad approaches are discussed, that are based on (i) nanoribbons, where a polar discontinuity against the vacuum emerges, and (ii) selective functionalizations, where covalent ligands are used to engineer polar discontinuities by selective or total functionalization of the parent system. All the cases considered have the potential to deliver innovative applications in ultra-thin and flexible solar-energy devices and in micro- and nano-electronics., 12+epsilon pages, 6 figures

By means of time-dependent density matrix renormalization group calculations we study topological quantum pumping in a strongly interacting system. The system under consideration is described by the Hamiltonian of a one-dimensional extended Bose-Hubbard model in the presence of a correlated hopping which breaks lattice inversion symmetry. This model has been predicted to support topological pumping [E. Berg, M. Levin, and E. Altman, Phys. Rev. Lett. 106, 110405 (2011)]. The pumped charge is quantized and of topological nature. We provide a detailed analysis of the finite-size-scaling behavior of the pumped charge and its deviations from the quantized value. Furthermore we also analyze the non-adiabatic corrections due to the finite frequency of the modulation. We consider two configurations: a closed ring where the time-dependence of the parameter induces a circulating current, and a finite open-ended chain where particles are dragged from one edge to the opposite edge, due to the pumping mechanism induced by the bulk., 11 pages, 13 figures. Published version

We study adiabatic pumping at a normal metal/class-D superconductor hybrid interface when superconductivity is induced through the proximity effect in a spin-orbit coupled nanowire in the presence of a tilted Zeeman field. When the induced order parameter in the nanowire is non-uniform, the phase diagram has isolated trivial regions surrounded by topological ones. We show that in this case the pumped charge is quantized in units of the elementary charge $e$ and has a topological nature., Comment: 7 pages, 6 figures. Published version

In the race towards high-performance ultra-scaled devices, two-dimensional materials offer an alternative paradigm thanks to their atomic thickness suppressing short-channel effects. It is thus urgent to study the most promising candidates in realistic configurations, and here we present detailed multiscale simulations of field-effect transistors based on arsenene and antimonene monolayers as channels. The accuracy of first-principles approaches in describing electronic properties is combined with the efficiency of tight-binding Hamiltonians based on maximally-localised Wannier functions to compute the transport properties of the devices. These simulations provide for the first time estimates on the upper limits for the electron and hole mobilities in the Takagi's approximation, including spin-orbit and multi-valley effects, and demonstrate that ultra-scaled devices in the sub-10 nm scale show a performance that is compliant with industry requirements., Comment: 14 pages, includes also Supplementary Information

Time-reversal invariant superconductors having nodes of vanishing excitation gap support zero-energy boundary states with topological protection. Existing expressions for the topological invariant are given in terms of the Hamiltonian of an infinite system. We give an alternative formulation in terms of the Andreev reflection matrix of a normal-metal-superconductor interface. This allows to relate the topological invariant to the angle-resolved Andreev conductance, also when the boundary state in the superconductor has merged with the continuum of states in the normal metal. A variety of symmetry classes is obtained, depending on additional unitary symmetries of the reflection matrix. We derive conditions for the quantization of the conductance in each symmetry class and test these on a model for a 2D or 3D superconductor with spin-singlet and spin-triplet pairing, mixed by Rashba spin-orbit interaction., 11 pages, 10 figures

It is widely believed that carrier-density inhomogeneities ("electron-hole puddles") in single-layer graphene on a substrate like quartz are due to charged impurities located close to the graphene sheet. Here we demonstrate by using a Kohn-Sham-Dirac density-functional scheme that corrugations in a real sample are sufficient to determine electron-hole puddles on length scales that are larger than the spatial resolution of state-of-the-art scanning tunneling microscopy., 5 pages, 3 figures, published version

We study by means of the recursive Green's function technique the local density-of-states of (finite and semi-infinite) multi-band spin-orbit coupled semiconducting nanowires in proximity to an s-wave superconductor and attached to normal-metal electrodes. When the nanowire is coupled to a normal electrode, the zero-energy peak, corresponding to the Majorana state in the topological phase, broadens with increasing transmission between the wire and the leads, eventually disappearing for ideal interfaces. Interestingly, for a finite transmission a peak is present also in the normal electrode, even though it has a smaller amplitude and broadens more rapidly with the strength of the coupling. Unpaired Majorana states can survive close to a topological phase transition even when the number of open channels (defined in the absence of superconductivity) is even. We finally study the Andreev-bound-state spectrum in superconductor-normal metal-superconductor junctions and find that in multi-band nanowires the distinction between topologically trivial and non-trivial systems based on the number of zero-energy crossings is preserved., 11 pages, 12 figures, published version

We investigate the transport properties of a bilayer exciton condensate that is contacted by four superconducting leads. We focus on the equilibrium regime and investigate how the Josephson currents induced in the bilayer by phase biases applied to the superconducting electrodes are affected by the presence of an exciton condensate in the bulk of the system. As long as the distance between the superconducting electrodes is much larger than the exciton coherence length, the Josephson current depends only on the difference between the phase biases in the two layers. This result holds true in both short- and long-junction limits. We relate it to a novel correlated four-particle Andreev process which occurs at the superconductor - exciton condensate interface. The system we investigate provides an implementation of the supercurrent mirror proposed by Kitaev as a viable way to realize topologically protected qubits., 23 pages, 6 figures, final version accepted by PRB

Electrons in artificial lattices enable explorations of the impact of repulsive Coulomb interactions in a tunable system. We have trapped two-dimensional electrons belonging to a gallium arsenide quantum well in a nanofabricated lattice with honeycomb geometry. We probe the excitation spectrum in a magnetic field identifying novel collective modes that emerge from the Coulomb interaction in the artificial lattice as predicted by the Mott-Hubbard model. These observations allow us to determine the Hubbard gap and suggest the existence of a novel Coulomb-driven ground state. This approach offers new venues for the study of quantum phenomena in a controllable solid-state system., Comment: 10 pages, 10 figures

We report the magnetotransport properties of a two-dimensional electron gas in a modulation-doped AlGaAs/GaAs heterostructure subjected to a lateral potential with honeycomb geometry. Periodic oscillations of the magnetoresistance and a delocalized-localized transition are shown by applying a gate voltage. We argue that electrons in such artificial-graphene lattices offer a promising approach for the simulation of quantum phases dictated by Coulomb interactions. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3493189]