Imaging moiré excited states with photocurrent tunnelling microscopy.

Moiré superlattices provide a highly tuneable and versatile platform to explore novel quantum phases and exotic excited states ranging from correlated insulators to moiré excitons. Scanning tunnelling microscopy has played a key role in probing microscopic behaviours of the moiré correlated ground states at the atomic scale. However, imaging of quantum excited states in moiré heterostructures remains an outstanding challenge. Here we develop a photocurrent tunnelling microscopy technique that combines laser excitation and scanning tunnelling spectroscopy to directly visualize the electron and hole distribution within the photoexcited moiré exciton in twisted bilayer WS2. The tunnelling photocurrent alternates between positive and negative polarities at different locations within a single moiré unit cell. This alternating photocurrent originates from the in-plane charge transfer moiré exciton in twisted bilayer WS2, predicted by our GW-Bethe-Salpeter equation calculations, that emerges from the competition between the electron-hole Coulomb interaction and the moiré potential landscape. Our technique enables the exploration of photoexcited non-equilibrium moiré phenomena at the atomic scale.

Strain-Tunable Hyperbolic Exciton Polaritons in Monolayer Black Arsenic with Two Exciton Resonances.

Hyperbolic polaritons have been attracting increasing interest for applications in optoelectronics, biosensing, and super-resolution imaging. Here, we report the in-plane hyperbolic exciton polaritons in monolayer black-arsenic (B-As), where hyperbolicity arises strikingly from two exciton resonant peaks. Remarkably, the presence of two resonances at different momenta makes overall hyperbolicity highly tunable by strain, as the two exciton peaks can be merged into the same frequency to double the strength of hyperbolicity as well as light absorption under a 1.5% biaxial strain. Moreover, the frequency of the merged hyperbolicity can be further tuned from 1.35 to 0.8 eV by an anisotropic biaxial strain. Furthermore, electromagnetic numerical simulation reveals a strain-induced hyperbolicity, as manifested in a topological transition of iso-frequency contour of exciton polaritons. The good tunability, large exciton binding energy, and strong light absorption exhibited in the hyperbolic monolayer B-As make it highly suitable for nanophotonics applications under ambient conditions.

Anomalous excitonic phase diagram in band-gap-tuned Ta2Ni(Se,S)5.

During a band-gap-tuned semimetal-to-semiconductor transition, Coulomb attraction between electrons and holes can cause spontaneously formed excitons near the zero-band-gap point, or the Lifshitz transition point. This has become an important route to realize bulk excitonic insulators - an insulating ground state distinct from single-particle band insulators. How this route manifests from weak to strong coupling is not clear. In this work, using angle-resolved photoemission spectroscopy (ARPES) and high-resolution synchrotron x-ray diffraction (XRD), we investigate the broken symmetry state across the semimetal-to-semiconductor transition in a leading bulk excitonic insulator candidate system Ta2Ni(Se,S)5. A broken symmetry phase is found to be continuously suppressed from the semimetal side to the semiconductor side, contradicting the anticipated maximal excitonic instability around the Lifshitz transition. Bolstered by first-principles and model calculations, we find strong interband electron-phonon coupling to play a crucial role in the enhanced symmetry breaking on the semimetal side of the phase diagram. Our results not only provide insight into the longstanding debate of the nature of intertwined orders in Ta2NiSe5, but also establish a basis for exploring band-gap-tuned structural and electronic instabilities in strongly coupled systems.

Optically controlled single-valley exciton doublet states with tunable internal spin structures and spin magnetization generation.

Manipulating quantum states through light-matter interactions has been actively pursued in two-dimensional materials research. Significant progress has been made toward the optical control of the valley degrees of freedom in semiconducting monolayer transition-metal dichalcogenides, based on doubly degenerate excitons from their two distinct valleys in reciprocal space. Here, we introduce a type of optically controllable doubly degenerate exciton states that come from a single valley, dubbed as single-valley exciton doublet (SVXD) states. They are unique in that their constituent holes originate from the same valence band, making possible the direct optical control of the spin structure of the excited constituent electrons. Combining ab initio GW plus Bethe-Salpeter equation (GW-BSE) calculations and a theoretical analysis method, we demonstrate such SVXD in substrate-supported monolayer bismuthene-which has been successfully grown using molecular beam epitaxy. In each of the two distinct valleys in the Brillouin zone, strong spin-orbit coupling and [Formula: see text] symmetry lead to a pair of degenerate 1s exciton states (the SVXD states) with opposite spin configurations. Any coherent linear combinations of the SVXD in a single valley can be excited by light with a specific polarization, enabling full manipulation of their internal spin configurations. In particular, a controllable net spin magnetization can be generated through light excitation. Our findings open routes to control quantum degrees of freedom, paving the way for applications in spintronics and quantum information science.

Intralayer charge-transfer moiré excitons in van der Waals superlattices.

Moiré patterns of transition metal dichalcogenide heterobilayers have proved to be an ideal platform on which to host unusual correlated electronic phases, emerging magnetism and correlated exciton physics. Whereas the existence of new moiré excitonic states is established1-4 through optical measurements, the microscopic nature of these states is still poorly understood, often relying on empirically fit models. Here, combining large-scale first-principles GW (where G and W denote the one-particle Green's function and the screened Coulomb interaction, respectively) plus Bethe-Salpeter calculations and micro-reflection spectroscopy, we identify the nature of the exciton resonances in WSe2/WS2 moiré superlattices, discovering a rich set of moiré excitons that cannot be captured by prevailing continuum models. Our calculations show moiré excitons with distinct characters, including modulated Wannier excitons and previously unidentified intralayer charge-transfer excitons. Signatures of these distinct excitonic characters are confirmed experimentally by the unique carrier-density and magnetic-field dependences of different moiré exciton resonances. Our study highlights the highly non-trivial exciton states that can emerge in transition metal dichalcogenide moiré superlattices, and suggests new ways of tuning many-body physics in moiré systems by engineering excited-states with specific spatial characters.

Many-body effects in the X-ray absorption spectra of liquid water.

SignificanceIn X-ray absorption spectroscopy, an electron-hole excitation probes the local atomic environment. The interpretation of the spectra requires challenging theoretical calculations, particularly in a system like liquid water, where quantum many-body effects and molecular disorder play an important role. Recent advances in theory and simulation make possible new calculations that are in good agreement with experiment, without recourse to commonly adopted approximations. Based on these calculations, the three features observed in the experimental spectra are unambiguously attributed to excitonic effects with different characteristic correlation lengths, which are distinctively affected by perturbations of the underlying H-bond structure induced by temperature changes and/or by isotopic substitution. The emerging picture of the water structure is fully consistent with the conventional tetrahedral model.

Discovering and understanding materials through computation.

Materials modelling and design using computational quantum and classical approaches is by now well established as an essential pillar in condensed matter physics, chemistry and materials science research, in addition to experiments and analytical theories. The past few decades have witnessed tremendous advances in methodology development and applications to understand and predict the ground-state, excited-state and dynamical properties of materials, ranging from molecules to nanoscopic/mesoscopic materials to bulk and reduced-dimensional systems. This issue of Nature Materials presents four in-depth Review Articles on the field. This Perspective aims to give a brief overview of the progress, as well as provide some comments on future challenges and opportunities. We envision that increasingly powerful and versatile computational approaches, coupled with new conceptual understandings and the growth of techniques such as machine learning, will play a guiding role in the future search and discovery of materials for science and technology.

Unmasking the Origin of Kinks in the Photoemission Spectra of Cuprate Superconductors.

The origin of a ubiquitous bosonic coupling feature in the photoemission spectra of high-T_{c} cuprates, an energy-momentum dispersion "kink" observed at ∼70 meV binding energy, remains a two-decade-old mystery. Understanding this phenomenon requires an accurate description of the coupling between the electron and some collective modes. We report here ab initio calculations based on GW perturbation theory and show that correlation-enhanced electron-phonon interaction in cuprates gives rise to the strong kinks, which not only explains quantitatively the observations but provides new understanding of experiments. Our results reveal it is the electron density of states being the predominant factor in determining the doping dependence of the kink size, manifesting the multiband nature of the cuprates, as opposed to the prevalent belief of it being a measure of the mode-coupling strength.

Direct observation of Klein tunneling in phononic crystals.

Tunneling plays an essential role in many branches of physics and has found important applications. It is theoretically proposed that Klein tunneling occurs when, under normal incidence, quasiparticles exhibit unimpeded penetration through potential barriers independent of their height and width. We created a phononic heterojunction by sandwiching two types of artificial phononic crystals with different Dirac point energies. The direct observation of Klein tunneling as shown by the key feature of unity transmission is demonstrated. Our experiment reveals that Klein tunneling occurs over a broad band of acoustic frequency. The direct observation of Klein tunneling in phononic crystals could find applications in signal processing, supercollimated beams, and communications.

Momentum-Resolved Dielectric Response of Free-Standing Mono-, Bi-, and Trilayer Black Phosphorus.

Black phosphorus (BP), a 2D semiconducting material of interest in electronics and photonics, exhibits physical properties characterized by strong anisotropy and band gap energy that scales with reducing layer number. However, the investigation of its intrinsic properties is challenging because thin-layer BP is photo-oxidized under ambient conditions and the energy of its electronic states shifts in different dielectric environments. We prepared free-standing samples of few-layer BP under glovebox conditions and probed the dielectric response in a vacuum using scanning transmission electron microscopy and electron energy loss spectroscopy (STEM-EELS). Thresholds of the excitation energy are measured at 1.9, 1.4, and 1.1 eV for the mono-, bi-, and trilayer BP, respectively, and these values are used to estimate the corresponding optical band gaps. A comparison of our results with electronic structure calculations indicates that the variation of the quasi-particle gap is larger than that of the exciton binding energy. The dispersion of the plasmons versus momentum for one- to three-layer BP and bulk BP highlights a deviation from parabolic to linear dispersion and strong anisotropic fingerprints.

Physical origin of giant excitonic and magneto-optical responses in two-dimensional ferromagnetic insulators.

The recent discovery of magnetism in atomically thin layers of van der Waals crystals has created great opportunities for exploring light-matter interactions and magneto-optical phenomena in the two-dimensional limit. Optical and magneto-optical experiments have provided insights into these topics, revealing strong magnetic circular dichroism and giant Kerr signals in atomically thin ferromagnetic insulators. However, the nature of the giant magneto-optical responses and their microscopic mechanism remain unclear. Here, by performing first-principles GW and Bethe-Salpeter equation calculations, we show that excitonic effects dominate the optical and magneto-optical responses in the prototypical two-dimensional ferromagnetic insulator, CrI3. We simulate the Kerr and Faraday effects in realistic experimental setups, and based on which we predict the sensitive frequency- and substrate-dependence of magneto-optical responses. These findings provide physical understanding of the phenomena as well as potential design principles for engineering magneto-optical and optoelectronic devices using two-dimensional magnets.

Electron-Phonon Coupling from Ab Initio Linear-Response Theory within the GW Method: Correlation-Enhanced Interactions and Superconductivity in Ba_{1-x}K_{x}BiO_{3}.

We present a new first-principles linear-response theory of changes due to perturbations in the quasiparticle self-energy operator within the GW method. This approach, named GW perturbation theory (GWPT), is applied to calculate the electron-phonon (e-ph) interactions with the full inclusion of the GW nonlocal, energy-dependent self-energy effects, going beyond density-functional perturbation theory. Avoiding limitations of the frozen-phonon technique, GWPT gives access to e-ph matrix elements at the GW level for all phonons and scattering processes, and the computational cost scales linearly with the number of phonon modes (wave vectors and branches) investigated. We demonstrate the capabilities of GWPT by studying the e-ph coupling and superconductivity in Ba_{0.6}K_{0.4}BiO_{3}. We show that many-electron correlations significantly enhance the e-ph interactions for states near the Fermi surface, and explain the observed high superconductivity transition temperature of Ba_{0.6}K_{0.4}BiO_{3} as well as its doping dependence.

Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals.

The realization of long-range ferromagnetic order in two-dimensional van der Waals crystals, combined with their rich electronic and optical properties, could lead to new magnetic, magnetoelectric and magneto-optic applications. In two-dimensional systems, the long-range magnetic order is strongly suppressed by thermal fluctuations, according to the Mermin-Wagner theorem; however, these thermal fluctuations can be counteracted by magnetic anisotropy. Previous efforts, based on defect and composition engineering, or the proximity effect, introduced magnetic responses only locally or extrinsically. Here we report intrinsic long-range ferromagnetic order in pristine Cr2Ge2Te6 atomic layers, as revealed by scanning magneto-optic Kerr microscopy. In this magnetically soft, two-dimensional van der Waals ferromagnet, we achieve unprecedented control of the transition temperature (between ferromagnetic and paramagnetic states) using very small fields (smaller than 0.3 tesla). This result is in contrast to the insensitivity of the transition temperature to magnetic fields in the three-dimensional regime. We found that the small applied field leads to an effective anisotropy that is much greater than the near-zero magnetocrystalline anisotropy, opening up a large spin-wave excitation gap. We explain the observed phenomenon using renormalized spin-wave theory and conclude that the unusual field dependence of the transition temperature is a hallmark of soft, two-dimensional ferromagnetic van der Waals crystals. Cr2Ge2Te6 is a nearly ideal two-dimensional Heisenberg ferromagnet and so will be useful for studying fundamental spin behaviours, opening the door to exploring new applications such as ultra-compact spintronics.

Generation of Anisotropic Massless Dirac Fermions and Asymmetric Klein Tunneling in Few-Layer Black Phosphorus Superlattices.

Artificial lattices have been employed in a broad range of two-dimensional systems, including those with electrons, atoms, and photons, in the quest for massless Dirac fermions with high flexibility and controllability. Establishing triangular or hexagonal symmetry, from periodically patterned molecule assembly or electrostatic gating as well as from moiré pattern induced by substrate, has produced electronic states with linear dispersions from two-dimensional electron gas (2DEG) residing in semiconductors, metals, and graphene. Different from the commonly studied isotropic host systems, here we demonstrate that massless Dirac fermions with tunable anisotropic characteristics can, in general, be generated in highly anisotropic 2DEG under slowly varying external periodic potentials. In the case of patterned few-layer black phosphorus superlattices, the new chiral quasiparticles exist exclusively in certain isolated energy window and inherit the strong anisotropic properties of pristine black phosphorus. These states exhibit asymmetric Klein tunneling, in which the transmission probability of the wave packets with normal incidence is no longer unity and can be tuned and controlled. In general, the direction of wave packet incidence for perfect transmission and that of the normal incidence are different, and the difference can reach more than 50° under an appropriate barrier orientation in black phosphorus superlattices. Our findings provide insight into the understanding and possible utilization of these novel emergent chiral quasiparticles.

Formation and Dynamics of Electron-Irradiation-Induced Defects in Hexagonal Boron Nitride at Elevated Temperatures.

The atomic structure, stability, and dynamics of defects in hexagonal boron nitride (h-BN) are investigated using an aberration-corrected transmission electron microscope operated at 80 kV between room temperature and 1000 °C. At temperatures above 700 °C, parallelogram- and hexagon-shaped defects with zigzag edges become prominent, in contrast to the triangular defects typically observed at lower temperatures. The appearance of 120° corners at defect vertices indicates the coexistence of both N- and B-terminated zigzag edges in the same defect. In situ dynamics studies show that the hexagonal holes grow by electron-induced sputtering of B-N chains, and that at high temperatures these chains can migrate from one defect corner to another. We complement the experiments with first-principles calculation which consider the thermal equilibrium formation energy of different defect configurations. It is shown that, below a critical defect size, hexagonal defects have the lowest formation energy and therefore are the more-stable configuration, and triangular defects are energetically metastable but can be "frozen in" under experimental conditions. We also discuss the possible contributions of several dynamic processes to the temperature-dependent defect formation.

Gate Switchable Transport and Optical Anisotropy in 90° Twisted Bilayer Black Phosphorus.

Anisotropy describes the directional dependence of a material's properties such as transport and optical response. In conventional bulk materials, anisotropy is intrinsically related to the crystal structure and thus not tunable by the gating techniques used in modern electronics. Here we show that, in bilayer black phosphorus with an interlayer twist angle of 90°, the anisotropy of its electronic structure and optical transitions is tunable by gating. Using first-principles calculations, we predict that a laboratory-accessible gate voltage can induce a hole effective mass that is 30 times larger along one Cartesian axis than along the other axis, and the two axes can be exchanged by flipping the sign of the gate voltage. This gate-controllable band structure also leads to a switchable optical linear dichroism, where the polarization of the lowest-energy optical transitions (absorption or luminescence) is tunable by gating. Thus, anisotropy is a tunable degree of freedom in twisted bilayer black phosphorus.

Tunable Magnetism and Half-Metallicity in Hole-Doped Monolayer GaSe.

We find, through first-principles calculations, that hole doping induces a ferromagnetic phase transition in monolayer GaSe. Upon increasing hole density, the average spin magnetic moment per carrier increases and reaches a plateau near 1.0 µB per carrier in a range of 3×10(13)/cm(2)-1×10(14)/cm(2), with the system in a half-metal state before the moment starts to descend abruptly. The predicted itinerant magnetism originates from an exchange splitting of electronic states at the top of the valence band, where the density of states exhibits a sharp van Hove singularity in this quasi-two-dimensional system.

What are grain boundary structures in graphene?

We have developed a new global optimization method for the determination of the interface structure based on the differential evolution algorithm. Here, we applied this method to search for the ground state atomic structures of the grain boundary (GB) between armchair and zigzag oriented graphene. We find two new grain boundary structures with a considerably lower formation energy of about 1 eV nm(-1) than those of the previously widely used structural models. We also systematically investigate the symmetric GBs with the GB angle ranging from 0° to 60°, and find some new GB structures. Surprisingly, for an intermediate GB angle, the formation energy does not depend monotonically on the defect concentration. We also discovered an interesting linear relationship between the GB density and the GB angle. Our new method provides an important novel route for the determination of GB structures and other interface structures, and our comprehensive study on GB structures could provide new structural information and guidelines to this area.