Hyperspectral imaging of exciton confinement within a moiré unit cell with a subnanometer electron probe.

Electronic and optical excitations in two-dimensional systems are distinctly sensitive to the presence of a moiré superlattice. We used cryogenic transmission electron microscopy and spectroscopy to simultaneously image the structural reconstruction and associated localization of the lowest-energy intralayer exciton in a rotationally aligned WS2-WSe2 moiré superlattice. In conjunction with optical spectroscopy and ab initio calculations, we determined that the exciton center-of-mass wave function is confined to a radius of approximately 2 nanometers around the highest-energy stacking site in the moiré unit cell. Our results provide direct evidence that atomic reconstructions lead to the strongly confining moiré potentials and that engineering strain at the nanoscale will enable new types of excitonic lattices.

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.

Magnetic Interactions in Substitutional Core-Doped Graphene Nanoribbons.

The design of a spin imbalance within the crystallographic unit cell of bottom-up engineered 1D graphene nanoribbons (GNRs) gives rise to nonzero magnetic moments within each cell. Here, we demonstrate the bottom-up assembly and spectroscopic characterization of a one-dimensional Kondo spin chain formed by a chevron-type GNR (cGNR) physisorbed on Au(111). Substitutional nitrogen core doping introduces a pair of low-lying occupied states per monomer within the semiconducting gap of cGNRs. Charging resulting from the interaction with the gold substrate quenches one electronic state for each monomer, leaving behind a 1D chain of radical cations commensurate with the unit cell of the ribbon. Scanning tunneling microscopy (STM) and spectroscopy (STS) reveal the signature of a Kondo resonance emerging from the interaction of S = 1/2 spin centers in each monomer core with itinerant electrons in the Au substrate. STM tip lift-off experiments locally reduce the effective screening of the unpaired radical cation being lifted, revealing a robust exchange coupling between neighboring spin centers. First-principles DFT-LSDA calculations support the presence of magnetic moments in the core of this GNR when it is placed on Au.

Tuning colour centres at a twisted hexagonal boron nitride interface.

The colour centre platform holds promise for quantum technologies, and hexagonal boron nitride has attracted attention due to the high brightness and stability, optically addressable spin states and wide wavelength coverage discovered in its emitters. However, its application is hindered by the typically random defect distribution and complex mesoscopic environment. Here, employing cathodoluminescence, we demonstrate on-demand activation and control of colour centre emission at the twisted interface of two hexagonal boron nitride flakes. Further, we show that colour centre emission brightness can be enhanced by two orders of magnitude by tuning the twist angle. Additionally, by applying an external voltage, nearly 100% brightness modulation is achieved. Our ab initio GW and GW plus Bethe-Salpeter equation calculations suggest that the emission is correlated to nitrogen vacancies and that a twist-induced moiré potential facilitates electron-hole recombination. This mechanism is further exploited to draw nanoscale colour centre patterns using electron beams.

Unconventional excitonic states with phonon sidebands in layered silicon diphosphide.

Complex correlated states emerging from many-body interactions between quasiparticles (electrons, excitons and phonons) are at the core of condensed matter physics and material science. In low-dimensional materials, quantum confinement affects the electronic, and subsequently, optical properties for these correlated states. Here, by combining photoluminescence, optical reflection measurements and ab initio theoretical calculations, we demonstrate an unconventional excitonic state and its bound phonon sideband in layered silicon diphosphide (SiP2), where the bound electron-hole pair is composed of electrons confined within one-dimensional phosphorus-phosphorus chains and holes extended in two-dimensional SiP2 layers. The excitonic state and emergent phonon sideband show linear dichroism and large energy redshifts with increasing temperature. Our ab initio many-body calculations confirm that the observed phonon sideband results from the correlated interaction between excitons and optical phonons. With these results, we propose layered SiP2 as a platform for the study of excitonic physics and many-particle effects.

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.

Intervalley Excitonic Hybridization, Optical Selection Rules, and Imperfect Circular Dichroism in Monolayer h-BN.

We perform first-principles GW plus Bethe-Salpeter equation calculations to investigate the photophysics of monolayer hexagonal boron nitride (h-BN), revealing excitons with novel k-space characteristics. The excitonic states forming the first and third peaks in its absorption spectrum are s-like, but those of the second peak are notably p-like, a first finding of strong co-occurrence of bright s-like and bright p-like states in an intrinsic 2D material. Moreover, even though the k-space wave function of these excitonic states are centered at the K and K^{'} valleys as in monolayer transition metal dichalcogenides, the k-space envelope functions of the basis excitons at one valley have significant extents to the basin of the other valley. As a consequence, the optical response of monolayer h-BN exhibits a lack of circular dichroism, as well as a coupling that induces an intervalley mixing between s- and p-like states.

Spin splitting of dopant edge state in magnetic zigzag graphene nanoribbons.

Spin-ordered electronic states in hydrogen-terminated zigzag nanographene give rise to magnetic quantum phenomena1,2 that have sparked renewed interest in carbon-based spintronics3,4. Zigzag graphene nanoribbons (ZGNRs)-quasi one-dimensional semiconducting strips of graphene bounded by parallel zigzag edges-host intrinsic electronic edge states that are ferromagnetically ordered along the edges of the ribbon and antiferromagnetically coupled across its width1,2,5. Despite recent advances in the bottom-up synthesis of GNRs featuring symmetry protected topological phases6-8 and even metallic zero mode bands9, the unique magnetic edge structure of ZGNRs has long been obscured from direct observation by a strong hybridization of the zigzag edge states with the surface states of the underlying support10-15. Here, we present a general technique to thermodynamically stabilize and electronically decouple the highly reactive spin-polarized edge states by introducing a superlattice of substitutional N-atom dopants along the edges of a ZGNR. First-principles GW calculations and scanning tunnelling spectroscopy reveal a giant spin splitting of low-lying nitrogen lone-pair flat bands by an exchange field (~850 tesla) induced by the ferromagnetically ordered edge states of ZGNRs. Our findings directly corroborate the nature of the predicted emergent magnetic order in ZGNRs and provide a robust platform for their exploration and functional integration into nanoscale sensing and logic devices15-21.

Pseudo-atomic orbital behavior in graphene nanoribbons with four-membered rings.

The incorporation of nonhexagonal rings into graphene nanoribbons (GNRs) is an effective strategy for engineering localized electronic states, bandgaps, and magnetic properties. Here, we demonstrate the successful synthesis of nanoribbons having four-membered ring (cyclobutadienoid) linkages by using an on-surface synthesis approach involving direct contact transfer of coronene-type precursors followed by thermally assisted [2 + 2] cycloaddition. The resulting coronene-cyclobutadienoid nanoribbons feature a narrow 600-meV bandgap and novel electronic frontier states that can be interpreted as linear chains of effective px and py pseudo-atomic orbitals. We show that these states give rise to exceptional physical properties, such as a rigid indirect energy gap. This provides a previously unexplored strategy for constructing narrow gap GNRs via modification of precursor molecules whose function is to modulate the coupling between adjacent four-membered ring states.

Rationally Designed Topological Quantum Dots in Bottom-Up Graphene Nanoribbons.

Bottom-up graphene nanoribbons (GNRs) have recently been shown to host nontrivial topological phases. Here, we report the fabrication and characterization of deterministic GNR quantum dots whose orbital character is defined by zero-mode states arising from nontrivial topological interfaces. Topological control was achieved through the synthesis and on-surface assembly of three distinct molecular precursors designed to exhibit structurally derived topological electronic states. Using a combination of low-temperature scanning tunneling microscopy and spectroscopy, we have characterized two GNR topological quantum dot arrangements synthesized under ultrahigh vacuum conditions. Our results are supported by density-functional theory and tight-binding calculations, revealing that the magnitude and sign of orbital hopping between topological zero-mode states can be tuned based on the bonding geometry of the interconnecting region. These results demonstrate the utility of topological zero modes as components for designer quantum dots and advanced electronic devices.

Topological Phases in Graphene Nanoribbons Tuned by Electric Fields.

Graphene nanoribbons (GNRs) possess distinct symmetry-protected topological phases. We show, through first-principles calculations, that by applying an experimentally accessible transverse electric field, certain boron and nitrogen periodically codoped GNRs have tunable topological phases. The tunability arises from a field-induced band inversion due to an opposite response of the conduction- and valence-band states to the electric field. With a spatially varying applied field, segments of GNRs of distinct topological phases are created, resulting in a field-programmable array of topological junction states, each may be occupied with charge or spin. Our findings not only show that electric field may be used as an easy tuning knob for topological phases in quasi-one-dimensional systems, but also provide new design principles for future GNR-based quantum electronic devices through their topological characters.

Giant exciton-enhanced shift currents and direct current conduction with subbandgap photo excitations produced by many-electron interactions.

Shift current is a direct current generated from nonlinear light-matter interaction in a noncentrosymmetric crystal and is considered a promising candidate for next-generation photovoltaic devices. The mechanism for shift currents in real materials is, however, still not well understood, especially if electron-hole interactions are included. Here, we employ a first-principles interacting Green's-function approach on the Keldysh contour with real-time propagation to study photocurrents generated by nonlinear optical processes under continuous wave illumination in real materials. We demonstrate a strong direct current shift current at subbandgap excitation frequencies in monolayer GeS due to strongly bound excitons, as well as a giant excitonic enhancement in the shift current coefficients at above bandgap photon frequencies. Our results suggest that atomically thin two-dimensional materials may be promising building blocks for next-generation shift current devices.

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.

Rational Passivation of Sulfur Vacancy Defects in Two-Dimensional Transition Metal Dichalcogenides.

Structural defects vary the optoelectronic properties of monolayer transition metal dichalcogenides, leading to concerted efforts to control defect type and density via materials growth or postgrowth passivation. Here, we explore a simple chemical treatment that allows on-off switching of low-lying, defect-localized exciton states, leading to tunable emission properties. Using steady-state and ultrafast optical spectroscopy, supported by ab initio calculations, we show that passivation of sulfur vacancy defects, which act as exciton traps in monolayer MoS2 and WS2, allows for controllable and improved mobilities and an increase in photoluminescence up to 275-fold, more than twice the value achieved by other chemical treatments. Our findings suggest a route for simple and rational defect engineering strategies for tunable and switchable electronic and excitonic properties through passivation.

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.

Imaging moiré flat bands in three-dimensional reconstructed WSe2/WS2 superlattices.

Moiré superlattices in transition metal dichalcogenide (TMD) heterostructures can host novel correlated quantum phenomena due to the interplay of narrow moiré flat bands and strong, long-range Coulomb interactions1-9. However, microscopic knowledge of the atomically reconstructed moiré superlattice and resulting flat bands is still lacking, which is critical for fundamental understanding and control of the correlated moiré phenomena. Here we quantitatively study the moiré flat bands in three-dimensional (3D) reconstructed WSe2/WS2 moiré superlattices by comparing scanning tunnelling spectroscopy (STS) of high-quality exfoliated TMD heterostructure devices with ab initio simulations of TMD moiré superlattices. A strong 3D buckling reconstruction accompanied by large in-plane strain redistribution is identified in our WSe2/WS2 moiré heterostructures. STS imaging demonstrates that this results in a remarkably narrow and highly localized K-point moiré flat band at the valence band edge of the heterostructure. A series of moiré flat bands are observed at different energies that exhibit varying degrees of localization. Our observations contradict previous simplified theoretical models but agree quantitatively with ab initio simulations that fully capture the 3D structural reconstruction. Our results reveal that the strain redistribution and 3D buckling in TMD heterostructures dominate the effective moiré potential and the corresponding moiré flat bands at the Brillouin zone K points.

Narrow-band high-lying excitons with negative-mass electrons in monolayer WSe2.

Monolayer transition-metal dichalcogenides (TMDCs) show a wealth of exciton physics. Here, we report the existence of a new excitonic species, the high-lying exciton (HX), in single-layer WSe2 with an energy of ~3.4 eV, almost twice the band-edge A-exciton energy, with a linewidth as narrow as 5.8 meV. The HX is populated through momentum-selective optical excitation in the K-valleys and is identified in upconverted photoluminescence (UPL) in the UV spectral region. Strong electron-phonon coupling results in a cascaded phonon progression with equidistant peaks in the luminescence spectrum, resolvable to ninth order. Ab initio GW-BSE calculations with full electron-hole correlations explain HX formation and unmask the admixture of upper conduction-band states to this complex many-body excitation. These calculations suggest that the HX is comprised of electrons of negative mass. The coincidence of such high-lying excitonic species at around twice the energy of band-edge excitons rationalizes the excitonic quantum-interference phenomenon recently discovered in optical second-harmonic generation (SHG) and explains the efficient Auger-like annihilation of band-edge excitons.

Topology Classification using Chiral Symmetry and Spin Correlations in Graphene Nanoribbons.

We apply the topological classification theory using chiral symmetry to graphene nanoribbons (GNRs). This approach eliminates the requirement of time-reversal and spatial symmetry in previous Z2 topology theory, resulting in a Z classification with the conventional Z index in a new vector-formed expression called "chiral phase index" (CPI). Our approach is applicable to GNRs of arbitrary terminations and any quasi one-dimensional chiral structures, including magnetism. It naturally solves a recent experimental puzzle of junction states at a class of asymmetric GNR junctions. We moreover derive a simple analytic formula for the CPI of armchair GNRs. Since this approach enables access to electron spin behavior, based on the CPI, we design a novel GNR with periodic localized moments and strong spin-spin exchange coupling.