Quantum simulator to emulate lower-dimensional molecular structure.

Bottom-up quantum simulators have been developed to quantify the role of various interactions, dimensionality, and structure in creating electronic states of matter. Here, we demonstrated a solid-state quantum simulator emulating molecular orbitals, based solely on positioning individual cesium atoms on an indium antimonide surface. Using scanning tunneling microscopy and spectroscopy, combined with ab initio calculations, we showed that artificial atoms could be made from localized states created from patterned cesium rings. These artificial atoms served as building blocks to realize artificial molecular structures with different orbital symmetries. These corresponding molecular orbitals allowed us to simulate two-dimensional structures reminiscent of well-known organic molecules. This platform could further be used to monitor the interplay between atomic structures and the resulting molecular orbital landscape with submolecular precision.

Strongly Correlated Exciton-Magnetization System for Optical Spin Pumping in CrBr3 and CrI3 .

Ferromagnetism in van der Waals systems, preserved down to a monolayer limit, attracted attention to a class of materials with general composition CrX3 (X=I, Br, and Cl), which are treated now as canonical 2D ferromagnets. Their diverse magnetic properties, such as different easy axes or varying and controllable character of in-plane or interlayer ferromagnetic coupling, make them promising candidates for spintronic, photonic, optoelectronic, and other applications. Still, significantly different magneto-optical properties between the three materials have been presenting a challenging puzzle for researchers over the last few years. Herewith, it is demonstrated that despite similar structural and magnetic configurations, the coupling between excitons and magnetization is qualitatively different in CrBr3 and CrI3 films. Through a combination of the optical spin pumping experiments with the state-of-the-art theory describing bound excitonic states in the presence of magnetization, we concluded that the hole-magnetization coupling has the opposite sign in CrBr3 and CrI3 and also between the ground and excited exciton state. Consequently, efficient spin pumping capabilities are demonstrated in CrBr3 driven by magnetization via spin-dependent absorption, and the different origins of the magnetic hysteresis in CrBr3 and CrI3 are unraveled.

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.

Direct Observation of Incommensurate-Commensurate Transition in Graphene-hBN Heterostructures via Optical Second Harmonic Generation.

Commensurability effects play a crucial role in the formation of electronic properties of novel layered heterostructures. The interest in these moiré superstructures has increased tremendously since the recent observation of a superconducting state (Nature 2018, 556, 43-50) and metal-insulator transition (Nature 2018, 556, 80-84) in twisted bilayer graphene. In this regard, a straightforward and efficient experimental technique for detection of the alignment of layered materials is desired. In this work, we use optical second harmonic generation, which is sensitive to the inversion symmetry breaking, to investigate the alignment of graphene/hexagonal boron nitride heterostructures. To achieve that, we activate a commensurate-incommensurate phase transition by a thermal annealing of the sample. We find that this structural change in the system can be directly observed via a strong modification of a nonlinear optical signal. Unambiguous interpretation of obtained results reveals the potential of a second harmonic generation technique for probing of structural changes in layered systems.

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.

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.

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.

Heisenberg-exchange-free nanoskyrmion mosaic.

Isotropic Heisenberg exchange naturally appears as the main interaction in magnetism, usually favouring long-range spin-ordered phases. The anisotropic Dzyaloshinskii-Moriya interaction arises from relativistic corrections and is a priori much weaker, even though it may sufficiently compete with the isotropic one to yield new spin textures. In this work, we challenge this well-established paradigm, and propose to explore a Heisenberg-exchange-free magnetic world. In this case, the Dzyaloshinskii-Moriya interaction induces magnetic frustration in two dimensions, from which the competition with an external magnetic field results in a new mechanism producing skyrmions of nanoscale size. A single nanoskyrmion can already be stabilized in a few-atom cluster, and may then be used as LEGO® block to build a large magnetic mosaic. The realization of such topological spin nanotextures in sp- and p -electron compounds or in ultracold atomic gases would open a new route toward robust and compact magnetic memories.

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.

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.

Erratum: The Bethe-Slater curve revisited; new insights from electronic structure theory.

A correction to this article has been published and is linked from the HTML version of this paper. The error has been fixed in the paper.

The Bethe-Slater curve revisited; new insights from electronic structure theory.

The Bethe-Slater (BS) curve describes the relation between the exchange coupling and interatomic distance. Based on a simple argument of orbital overlaps, it successfully predicts the transition from antiferromagnetism to ferromagnetism, when traversing the 3d series. In a previous article [Phys. Rev. Lett. 116, 217202 (2016)] we reported that the dominant nearestneighbour (NN) interaction for 3d metals in the bcc structure indeed follows the BS curve, but the trends through the series showed a richer underlying physics than was initially assumed. The orbital decomposition of the inter-site exchange couplings revealed that various orbitals contribute to the exchange interactions in a highly non-trivial and sometimes competitive way. In this communication we perform a deeper analysis by comparing 3d metals in the bcc and fcc structures. We find that there is no coupling between the E g orbitals of one atom and T 2g orbitals of its NNs, for both cubic phases. We demonstrate that these couplings are forbidden by symmetry and formulate a general rule allowing to predict when a similar situation is going to happen. In γ-Fe, as in α-Fe, we find a strong competition in the symmetry-resolved orbital contributions and analyse the differences between the high-spin and low-spin solutions.

Exchange interactions in transition metal oxides: the role of oxygen spin polarization.

Magnetism of transition metal (TM) oxides is usually described in terms of the Heisenberg model, with orientation-independent interactions between the spins. However, the applicability of such a model is not fully justified for TM oxides because spin polarization of oxygen is usually ignored. In the conventional model based on the Anderson principle, oxygen effects are considered as a property of the TM ion and only TM interactions are relevant. Here, we perform a systematic comparison between two approaches for spin polarization on oxygen in typical TM oxides. To this end, we calculate the exchange interactions in NiO, MnO and hematite (Fe2O3) for different magnetic configurations using the magnetic force theorem. We consider the full spin Hamiltonian including oxygen sites, and also derive an effective model where the spin polarization on oxygen renormalizes the exchange interactions between TM sites. Surprisingly, the exchange interactions in NiO depend on the magnetic state if spin polarization on oxygen is neglected, resulting in non-Heisenberg behavior. In contrast, the inclusion of spin polarization in NiO makes the Heisenberg model more applicable. Just the opposite, MnO behaves as a Heisenberg magnet when oxygen spin polarization is neglected, but shows strong non-Heisenberg effects when spin polarization on oxygen is included. In hematite, both models result in non-Heisenberg behavior. The general applicability of the magnetic force theorem as well as the Heisenberg model to TM oxides is discussed.

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.

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.

Simultaneous loss of interlayer coherence and long-range magnetism in quasi-two-dimensional PdCrO2.

In many layered metals, coherent propagation of electronic excitations is often confined to the highly conducting planes. While strong electron correlations and/or proximity to an ordered phase are believed to be the drivers of this electron confinement, it is still not known what triggers the loss of interlayer coherence in a number of layered systems with strong magnetic fluctuations, such as cuprates. Here, we show that a definitive signature of interlayer coherence in the metallic-layered triangular antiferromagnet PdCrO2 vanishes at the Néel transition temperature. Comparison with the relevant energy scales and with the isostructural non-magnetic PdCoO2 reveals that the interlayer incoherence is driven by the growth of short-range magnetic fluctuations. This establishes a connection between long-range order and interlayer coherence in PdCrO2 and suggests that in many other low-dimensional conductors, incoherent interlayer transport also arises from the strong interaction between the (tunnelling) electrons and fluctuations of some underlying order.

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.