Limits on gas impermeability of graphene.

Despite being only one-atom thick, defect-free graphene is considered to be completely impermeable to all gases and liquids1-10. This conclusion is based on theory3-8 and supported by experiments1,9,10 that could not detect gas permeation through micrometre-size membranes within a detection limit of 105 to 106 atoms per second. Here, using small monocrystalline containers tightly sealed with graphene, we show that defect-free graphene is impermeable with an accuracy of eight to nine orders of magnitude higher than in the previous experiments. We are capable of discerning (but did not observe) permeation of just a few helium atoms per hour, and this detection limit is also valid for all other gases tested (neon, nitrogen, oxygen, argon, krypton and xenon), except for hydrogen. Hydrogen shows noticeable permeation, even though its molecule is larger than helium and should experience a higher energy barrier. This puzzling observation is attributed to a two-stage process that involves dissociation of molecular hydrogen at catalytically active graphene ripples, followed by adsorbed atoms flipping to the other side of the graphene sheet with a relatively low activation energy of about 1.0 electronvolt, a value close to that previously reported for proton transport11,12. Our work provides a key reference for the impermeability of two-dimensional materials and is important from a fundamental perspective and for their potential applications.

Measuring the Berry phase of graphene from wavefront dislocations in Friedel oscillations.

Electronic band structures dictate the mechanical, optical and electrical properties of crystalline solids. Their experimental determination is therefore crucial for technological applications. Although the spectral distribution in energy bands is routinely measured by various techniques1, it is more difficult to access the topological properties of band structures such as the quantized Berry phase, γ, which is a gauge-invariant geometrical phase accumulated by the wavefunction along an adiabatic cycle2. In graphene, the quantized Berry phase γ = π accumulated by massless relativistic electrons along cyclotron orbits is evidenced by the anomalous quantum Hall effect4,5. It is usually thought that measuring the Berry phase requires the application of external electromagnetic fields to force the charged particles along closed trajectories3. Contradicting this belief, here we demonstrate that the Berry phase of graphene can be measured in the absence of any external magnetic field. We observe edge dislocations in oscillations of the charge density ρ (Friedel oscillations) that are formed at hydrogen atoms chemisorbed on graphene. Following Nye and Berry6 in describing these topological defects as phase singularities of complex fields, we show that the number of additional wavefronts in the dislocation is a real-space measure of the Berry phase of graphene. Because the electronic dispersion relation can also be determined from Friedel oscillations7, our study establishes the charge density as a powerful observable with which to determine both the dispersion relation and topological properties of wavefunctions. This could have profound consequences for the study of the band-structure topology of relativistic and gapped phases in solids.

The most incompressible metal osmium at static pressures above 750 gigapascals.

Metallic osmium (Os) is one of the most exceptional elemental materials, having, at ambient pressure, the highest known density and one of the highest cohesive energies and melting temperatures. It is also very incompressible, but its high-pressure behaviour is not well understood because it has been studied so far only at pressures below 75 gigapascals. Here we report powder X-ray diffraction measurements on Os at multi-megabar pressures using both conventional and double-stage diamond anvil cells, with accurate pressure determination ensured by first obtaining self-consistent equations of state of gold, platinum, and tungsten in static experiments up to 500 gigapascals. These measurements allow us to show that Os retains its hexagonal close-packed structure upon compression to over 770 gigapascals. But although its molar volume monotonically decreases with pressure, the unit cell parameter ratio of Os exhibits anomalies at approximately 150 gigapascals and 440 gigapascals. Dynamical mean-field theory calculations suggest that the former anomaly is a signature of the topological change of the Fermi surface for valence electrons. However, the anomaly at 440 gigapascals might be related to an electronic transition associated with pressure-induced interactions between core electrons. The ability to affect the core electrons under static high-pressure experimental conditions, even for incompressible metals such as Os, opens up opportunities to search for new states of matter under extreme compression.

Magnetic Two-Dimensional Chromium Trihalides: A Theoretical Perspective.

The discovery of ferromagnetic order in monolayer two-dimensional (2D) crystals has opened a new venue in the field of 2D materials. Two-dimensional magnets are not only interesting on their own, but their integration in van der Waals heterostructures allows for the observation of new and exotic effects in the ultrathin limit. The family of chromium trihalides, CrI3, CrBr3, and CrCl3, is so far the most studied among magnetic 2D crystals. In this Mini Review, we provide a perspective of the state of the art of the theoretical understanding of magnetic 2D trihalides, most of which will also be relevant for other 2D magnets, such as vanadium trihalides. We discuss both the well-established facts, such as the origin of the magnetic moment and magnetic anisotropy, and address as well open issues such as the nature of the anisotropic spin couplings and the magnitude of the magnon gap. Recent theoretical predictions on Moiré magnets and magnetic skyrmions are also discussed. Finally, we give some prospects about the future interest of these materials and possible device applications.

Temperature-Induced Lifshitz Transition and Possible Excitonic Instability in ZrSiSe.

The nodal-line semimetals have attracted immense interest due to the unique electronic structures such as the linear dispersion and the vanishing density of states as the Fermi energy approaching the nodes. Here, we report temperature-dependent transport and scanning tunneling microscopy (spectroscopy) [STM(S)] measurements on nodal-line semimetal ZrSiSe. Our experimental results and theoretical analyses consistently demonstrate that the temperature induces Lifshitz transitions at 80 and 106 K in ZrSiSe, which results in the transport anomalies at the same temperatures. More strikingly, we observe a V-shaped dip structure around Fermi energy from the STS spectrum at low temperature, which can be attributed to co-effect of the spin-orbit coupling and excitonic instability. Our observations indicate the correlation interaction may play an important role in ZrSiSe, which owns the quasi-two-dimensional electronic structures.

Proton transport through one-atom-thick crystals.

Graphene is increasingly explored as a possible platform for developing novel separation technologies. This interest has arisen because it is a maximally thin membrane that, once perforated with atomic accuracy, may allow ultrafast and highly selective sieving of gases, liquids, dissolved ions and other species of interest. However, a perfect graphene monolayer is impermeable to all atoms and molecules under ambient conditions: even hydrogen, the smallest of atoms, is expected to take billions of years to penetrate graphene's dense electronic cloud. Only accelerated atoms possess the kinetic energy required to do this. The same behaviour might reasonably be expected in the case of other atomically thin crystals. Here we report transport and mass spectroscopy measurements which establish that monolayers of graphene and hexagonal boron nitride (hBN) are highly permeable to thermal protons under ambient conditions, whereas no proton transport is detected for thicker crystals such as monolayer molybdenum disulphide, bilayer graphene or multilayer hBN. Protons present an intermediate case between electrons (which can tunnel easily through atomically thin barriers) and atoms, yet our measured transport rates are unexpectedly high and raise fundamental questions about the details of the transport process. We see the highest room-temperature proton conductivity with monolayer hBN, for which we measure a resistivity to proton flow of about 10 Ω cm(2) and a low activation energy of about 0.3 electronvolts. At higher temperatures, hBN is outperformed by graphene, the resistivity of which is estimated to fall below 10(-3) Ω cm(2) above 250 degrees Celsius. Proton transport can be further enhanced by decorating the graphene and hBN membranes with catalytic metal nanoparticles. The high, selective proton conductivity and stability make one-atom-thick crystals promising candidates for use in many hydrogen-based technologies.

Strong Electron-Phonon Coupling and its Influence on the Transport and Optical Properties of Hole-Doped Single-Layer InSe.

We show that hole states in recently discovered single-layer InSe are strongly renormalized by the coupling with acoustic phonons. The coupling is enhanced significantly at moderate hole doping (∼10^{13} cm^{-2}) due to hexagonal warping of the Fermi surface. While the system remains dynamically stable, its electron-phonon spectral function exhibits sharp low-energy resonances, leading to the formation of satellite quasiparticle states near the Fermi energy. Such many-body renormalization is predicted to have two important consequences. First, it significantly suppresses charge carrier mobility reaching ∼1 cm^{2} V^{-1} s^{-1} at 100 K in a freestanding sample. Second, it gives rise to unusual temperature-dependent optical excitations in the midinfrared region. Relatively small charge carrier concentrations and realistic temperatures suggest that these excitations may be observed experimentally.

Effective Heisenberg Model and Exchange Interaction for Strongly Correlated Systems.

We consider the extended Hubbard model and introduce a corresponding Heisenberg-like problem written in terms of spin operators. The derived formalism is reminiscent of Anderson's idea of the effective exchange interaction and takes into account nonlocal correlation effects. The results for the exchange interaction and spin susceptibility in the magnetic phase are expressed in terms of single-particle quantities. This fact not only can be used for realistic calculations of multiband systems but also allows us to reconsider a general description of many-body effects in the most interesting physical regimes, where the physical properties of the system are dominated by collective (bosonic) fluctuations. In the strongly spin-polarized limit, when the local magnetic moment is well defined, the exchange interaction reduces to a standard expression of the density functional theory that has been successfully used in practical calculations of magnetic properties of real materials.

Excitonic Instability and Pseudogap Formation in Nodal Line Semimetal ZrSiS.

Electron correlation effects are studied in ZrSiS using a combination of first-principles and model approaches. We show that basic electronic properties of ZrSiS can be described within a two-dimensional lattice model of two nested square lattices. A high degree of electron-hole symmetry characteristic for ZrSiS is one of the key features of this model. Having determined model parameters from first-principles calculations, we then explicitly take electron-electron interactions into account and show that, at moderately low temperatures, ZrSiS exhibits excitonic instability, leading to the formation of a pseudogap in the electronic spectrum. The results can be understood in terms of Coulomb-interaction-assisted pairing of electrons and holes reminiscent of that of an excitonic insulator. Our finding allows us to provide a physical interpretation of the unusual mass enhancement of charge carriers in ZrSiS recently observed experimentally.

Impact of Many-Body Effects on Landau Levels in Graphene.

We present magneto-Raman spectroscopy measurements on suspended graphene to investigate the charge carrier density-dependent electron-electron interaction in the presence of Landau levels. Utilizing gate-tunable magnetophonon resonances, we extract the charge carrier density dependence of the Landau level transition energies and the associated effective Fermi velocity v_{F}. In contrast to the logarithmic divergence of v_{F} at zero magnetic field, we find a piecewise linear scaling of v_{F} as a function of the charge carrier density, due to a magnetic-field-induced suppression of the long-range Coulomb interaction. We quantitatively confirm our experimental findings by performing tight-binding calculations on the level of the Hartree-Fock approximation, which also allow us to estimate an excitonic binding energy of ≈6 meV contained in the experimentally extracted Landau level transitions energies.

Dynamical and Reversible Control of Topological Spin Textures.

Recent observations of topological spin textures brought spintronics one step closer to new magnetic memories. Nevertheless, the existence of Skyrmions, as well as their stabilization, require very specific intrinsic magnetic properties which are usually fixed in magnets. Here we address the possibility to dynamically control their intrinsic magnetic interactions by varying the strength of a high-frequency laser field. It is shown that drastic changes can be induced in the antiferromagnetic exchange interactions and the latter can even be reversed to become ferromagnetic, provided the direct exchange is already non-negligible in equilibrium as predicted, for example, in Si doped with C, Sn, or Pb adatoms. In the presence of Dzyaloshinskii-Moriya interactions, this enables us to tune features of ferromagnetic Skyrmions such as their radius, making them easier to stabilize. Alternatively, such topological spin textures can occur in frustrated triangular lattices. Then, we demonstrate that a high-frequency laser field can induce dynamical frustration in antiferromagnets, where the degree of frustration can subsequently be tuned suitably to drive the material toward a Skyrmionic phase.

Band Filling Control of the Dzyaloshinskii-Moriya Interaction in Weakly Ferromagnetic Insulators.

We observe and explain theoretically a dramatic evolution of the Dzyaloshinskii-Moriya interaction (DMI) in the series of isostructural weak ferromagnets, MnCO_{3}, FeBO_{3}, CoCO_{3}, and NiCO_{3}. The sign of the interaction is encoded in the phase of the x-ray magnetic diffraction amplitude, observed through interference with resonant quadrupole scattering. We find very good quantitative agreement with first-principles electronic structure calculations, reproducing both sign and magnitude through the series, and propose a simplified "toy model" to explain the change in sign with 3d shell filling. The model gives insight into the evolution of the DMI in Mott and charge transfer insulators.

Density functional based simulations of proton permeation of graphene and hexagonal boron nitride.

Using density functional theory, we study proton permeation through graphene and hexagonal boron nitride. We consider several factors influencing the barriers for permeation, including structural optimization, the role of the solvent, surface curvature and proton transport through hydrogenated samples. Furthermore, we discuss the ground state charge transfer from the membrane to the proton and the strong tendency for bond formation. If the process is assumed to be slow we find that none of these effects lead to a satisfactory answer to the observed discrepancies between theory and experiment.

Correction: Energetics, barriers and vibrational spectra of partially and fully hydrogenated hexagonal boron nitride.

Correction for 'Energetics, barriers and vibrational spectra of partially and fully hydrogenated hexagonal boron nitride' by J. M. H. Kroes et al., Phys. Chem. Chem. Phys., 2016, 18, 19359-19367.

Intrinsic Charge Carrier Mobility in Single-Layer Black Phosphorus.

We present a theory for single- and two-phonon charge carrier scattering in anisotropic two-dimensional semiconductors applied to single-layer black phosphorus (BP). We show that in contrast to graphene, where two-phonon processes due to the scattering by flexural phonons dominate at any practically relevant temperatures and are independent of the carrier concentration n, two-phonon scattering in BP is less important and can be considered negligible at n≳10^{13} cm^{-2}. At smaller n, however, phonons enter in the essentially anharmonic regime. Compared to the hole mobility, which does not exhibit strong anisotropy between the principal directions of BP (µ_{xx}/µ_{yy}∼1.4 at n=10^{13} cm^{-2} and T=300 K), the electron mobility is found to be significantly more anisotropic (µ_{xx}/µ_{yy}∼6.2). Absolute values of µ_{xx} do not exceed 250 (700) cm^{2} V^{-1} s^{-1} for holes (electrons), which can be considered as an upper limit for the mobility in BP at room temperature.

Chirality-Dependent Transmission of Spin Waves through Domain Walls.

Spin-wave technology (magnonics) has the potential to further reduce the size and energy consumption of information-processing devices. In the submicrometer regime (exchange spin waves), topological defects such as domain walls may constitute active elements to manipulate spin waves and perform logic operations. We predict that spin waves that pass through a domain wall in an ultrathin perpendicular-anisotropy film experience a phase shift that depends on the orientation of the domain wall (chirality). The effect, which is absent in bulk materials, originates from the interfacial Dzyaloshinskii-Moriya interaction and can be interpreted as a geometric phase. We demonstrate analytically and by means of micromagnetic simulations that the phase shift is strong enough to switch between constructive and destructive interference. The two chirality states of the domain wall may serve as a memory bit or spin-wave switch in magnonic devices.

Scaling Behavior and Strain Dependence of In-Plane Elastic Properties of Graphene.

We show by atomistic simulations that, in the thermodynamic limit, the in-plane elastic moduli of graphene at finite temperature vanish with system size L as a power law L(-η(u)) with η(u)≃0.325, in agreement with the membrane theory. We provide explicit expressions for the size and strain dependence of graphene's elastic moduli, allowing comparison to experimental data. Our results explain the recently experimentally observed increase of the Young modulus by more than a factor of 2 for a tensile strain of only a few per mill. The difference of a factor of 2 between the measured asymptotic value of the Young modulus for tensilely strained systems and the value from ab initio calculations remains, however, unsolved. We also discuss the asymptotic behavior of the Poisson ratio, for which our simulations disagree with the predictions of the self-consistent screening approximation.

Microscopic Origin of Heisenberg and Non-Heisenberg Exchange Interactions in Ferromagnetic bcc Fe.

By means of first principles calculations, we investigate the nature of exchange coupling in ferromagnetic bcc Fe on a microscopic level. Analyzing the basic electronic structure reveals a drastic difference between the 3d orbitals of E_{g} and T_{2g} symmetries. The latter ones define the shape of the Fermi surface, while the former ones form weakly interacting impurity levels. We demonstrate that, as a result of this, in Fe the T_{2g} orbitals participate in exchange interactions, which are only weakly dependent on the configuration of the spin moments and thus can be classified as Heisenberg-like. These couplings are shown to be driven by Fermi surface nesting. In contrast, for the E_{g} states, the Heisenberg picture breaks down since the corresponding contribution to the exchange interactions is shown to strongly depend on the reference state they are extracted from. Our analysis of the nearest-neighbor coupling indicates that the interactions among E_{g} states are mainly proportional to the corresponding hopping integral and thus can be attributed to be of double-exchange origin. By making a comparison to other magnetic transition metals, we put the results of bcc Fe into context and argue that iron has a unique behavior when it comes to magnetic exchange interactions.

Erratum: Structural and Electronic Properties of Germanene on MoS_{2} [Phys. Rev. Lett. 116, 256804 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.116.256804.

Structural and Electronic Properties of Germanene on MoS_{2}.

To date germanene has only been synthesized on metallic substrates. A metallic substrate is usually detrimental for the two-dimensional Dirac nature of germanene because the important electronic states near the Fermi level of germanene can hybridize with the electronic states of the metallic substrate. Here we report the successful synthesis of germanene on molybdenum disulfide (MoS_{2}), a band gap material. Preexisting defects in the MoS_{2} surface act as preferential nucleation sites for the germanene islands. The lattice constant of the germanene layer (3.8±0.2 Å) is about 20% larger than the lattice constant of the MoS_{2} substrate (3.16 Å). Scanning tunneling spectroscopy measurements and density functional theory calculations reveal that there are, besides the linearly dispersing bands at the K points, two parabolic bands that cross the Fermi level at the Γ point.