Imaging tunable Luttinger liquid systems in van der Waals heterostructures.

One-dimensional (1D) interacting electrons are often described as a Luttinger liquid1-4 having properties that are intrinsically different from those of Fermi liquids in higher dimensions5,6. In materials systems, 1D electrons exhibit exotic quantum phenomena that can be tuned by both intra- and inter-1D-chain electronic interactions, but their experimental characterization can be challenging. Here we demonstrate that layer-stacking domain walls (DWs) in van der Waals heterostructures form a broadly tunable Luttinger liquid system, including both isolated and coupled arrays. We have imaged the evolution of DW Luttinger liquids under different interaction regimes tuned by electron density using scanning tunnelling microscopy. Single DWs at low carrier density are highly susceptible to Wigner crystallization consistent with a spin-incoherent Luttinger liquid, whereas at intermediate densities dimerized Wigner crystals form because of an enhanced magneto-elastic coupling. Periodic arrays of DWs exhibit an interplay between intra- and inter-chain interactions that gives rise to new quantum phases. At low electron densities, inter-chain interactions are dominant and induce a 2D electron crystal composed of phased-locked 1D Wigner crystal in a staggered configuration. Increased electron density causes intra-chain fluctuation potentials to dominate, leading to an electronic smectic liquid crystal phase in which electrons are ordered with algebraical correlation decay along the chain direction but disordered between chains. Our work shows that layer-stacking DWs in 2D heterostructures provides opportunities to explore Luttinger liquid physics.

Exciton-Phonon Coupling Induces a New Pathway for Ultrafast Intralayer-to-Interlayer Exciton Transition and Interlayer Charge Transfer in WS2-MoS2 Heterostructure: A First-Principles Study.

Despite the weak, van der Waals interlayer coupling, photoinduced charge transfer vertically across atomically thin interfaces can occur within surprisingly fast, sub-50 fs time scales. An early theoretical understanding of charge transfer is based on a noninteracting picture, neglecting excitonic effects that dominate optical properties of such materials. We employ an ab initio many-body perturbation theory approach, which explicitly accounts for the excitons and phonons in the heterostructure. Our large-scale first-principles calculations directly probe the role of exciton-phonon coupling in the charge dynamics of the WS2/MoS2 heterobilayer. We find that the exciton-phonon interaction induced relaxation time of photoexcited excitons at the K valley of MoS2 and WS2 is 67 and 15 fs at 300 K, respectively, which sets a lower bound to the intralayer-to-interlayer exciton transfer time and is consistent with experiment reports. We further show that electron-hole correlations facilitate novel transfer pathways that are otherwise inaccessible to noninteracting electrons and holes.

Terahertz phonon engineering with van der Waals heterostructures.

Phonon engineering at gigahertz frequencies forms the foundation of microwave acoustic filters1, acousto-optic modulators2 and quantum transducers3,4. Terahertz phonon engineering could lead to acoustic filters and modulators at higher bandwidth and speed, as well as quantum circuits operating at higher temperatures. Despite their potential, methods for engineering terahertz phonons have been limited due to the challenges of achieving the required material control at subnanometre precision and efficient phonon coupling at terahertz frequencies. Here we demonstrate the efficient generation, detection and manipulation of terahertz phonons through precise integration of atomically thin layers in van der Waals heterostructures. We used few-layer graphene as an ultrabroadband phonon transducer that converts femtosecond near-infrared pulses to acoustic-phonon pulses with spectral content up to 3 THz. A monolayer WSe2 is used as a sensor. The high-fidelity readout was enabled by the exciton-phonon coupling and strong light-matter interactions. By combining these capabilities in a single heterostructure and detecting responses to incident mechanical waves, we performed terahertz phononic spectroscopy. Using this platform, we demonstrate high-Q terahertz phononic cavities and show that a WSe2 monolayer embedded in hexagonal boron nitride can efficiently block the transmission of terahertz phonons. By comparing our measurements to a nanomechanical model, we obtained the force constants at the heterointerfaces. Our results could enable terahertz phononic metamaterials for ultrabroadband acoustic filters and modulators and could open new routes for thermal engineering.

Synthesis and characterization of low-dimensional N-heterocyclic carbene lattices.

The covalent interaction of N-heterocyclic carbenes (NHCs) with transition metal atoms gives rise to distinctive frontier molecular orbitals (FMOs). These emergent electronic states have spurred the widespread adoption of NHC ligands in chemical catalysis and functional materials. Although formation of carbene-metal complexes in self-assembled monolayers on surfaces has been explored, design and electronic structure characterization of extended low-dimensional NHC-metal lattices remains elusive. Here we demonstrate a modular approach to engineering one-dimensional (1D) metal-organic chains and two-dimensional (2D) Kagome lattices using the FMOs of NHC-Au-NHC junctions to create low-dimensional molecular networks exhibiting intrinsic metallicity. Scanning tunneling spectroscopy and first-principles density functional theory reveal the contribution of C-Au-C π-bonding states to dispersive bands that imbue 1D- and 2D-NHC lattices with exceptionally small work functions.

Regioselective On-Surface Synthesis of [3]Triangulene Graphene Nanoribbons.

The integration of low-energy states into bottom-up engineered graphene nanoribbons (GNRs) is a robust strategy for realizing materials with tailored electronic band structure for nanoelectronics. Low-energy zero-modes (ZMs) can be introduced into nanographenes (NGs) by creating an imbalance between the two sublattices of graphene. This phenomenon is exemplified by the family of [n]triangulenes (n ∈ N). Here, we demonstrate the synthesis of [3]triangulene-GNRs, a regioregular one-dimensional (1D) chain of [3]triangulenes linked by five-membered rings. Hybridization between ZMs on adjacent [3]triangulenes leads to the emergence of a narrow band gap, Eg,exp ∼ 0.7 eV, and topological end states that are experimentally verified using scanning tunneling spectroscopy. Tight-binding and first-principles density functional theory calculations within the local density approximation corroborate our experimental observations. Our synthetic design takes advantage of a selective on-surface head-to-tail coupling of monomer building blocks enabling the regioselective synthesis of [3]triangulene-GNRs. Detailed ab initio theory provides insights into the mechanism of on-surface radical polymerization, revealing the pivotal role of Au-C bond formation/breakage in driving selectivity.

Engineering Small HOMO-LUMO Gaps in Polycyclic Aromatic Hydrocarbons with Topologically Protected States.

Topological phases in laterally confined low-dimensional nanographenes have emerged as versatile design tools that can imbue otherwise unremarkable materials with exotic band structures ranging from topological semiconductors and quantum dots to intrinsically metallic bands. The periodic boundary conditions that define the topology of a given lattice have thus far prevented the translation of this technology to the quasi-zero-dimensional (0D) domain of small molecular structures. Here, we describe the synthesis of a polycyclic aromatic hydrocarbon (PAH) featuring two localized zero modes (ZMs) formed by the topological junction interface between a trivial and nontrivial phase within a single molecule. First-principles density functional theory calculations predict a strong hybridization between adjacent ZMs that gives rise to an exceptionally small HOMO-LUMO gap. Scanning tunneling microscopy and spectroscopy corroborate the molecular structure of 9/7/9-double quantum dots and reveal an experimental quasiparticle gap of 0.16 eV, corresponding to a carbon-based small molecule long-wavelength infrared (LWIR) absorber.

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.

Light-induced shift current vortex crystals in moiré heterobilayers.

Transition metal dichalcogenide (TMD) moiré superlattices provide an emerging platform to explore various light-induced phenomena. Recently, the discoveries of novel moiré excitons have attracted great interest. The nonlinear optical responses of these systems are however still underexplored. Here, we report investigation of light-induced shift currents (a second-order response generating DC current from optical illumination) in the WSe2/WS2 moiré superlattice. We identify a striking phenomenon of the formation of shift current vortex crystals-i.e., two-dimensional periodic arrays of moiré-scale current vortices and associated magnetic fields with remarkable intensity under laboratory laser setup. Furthermore, we demonstrate high optical tunability of these current vortices-their location, shape, chirality, and magnitude can be tuned by the frequency, polarization, and intensity of the incident light. Electron-hole interactions (excitonic effects) are found to play a crucial role in the generation and nature of the shift current intensity and distribution. Our findings provide a promising all-optical control route to manipulate nanoscale shift current density distributions and magnetic field patterns, as well as shed light on nonlinear optical responses in moiré quantum matter and their possible applications.

Excitonic Interactions and Mechanism for Ultrafast Interlayer Photoexcited Response in van der Waals Heterostructures.

Optical dynamics in van der Waals heterobilayers is of fundamental scientific and practical interest. Based on a time-dependent adiabatic GW approach, we discover a new many-electron (excitonic) channel for converting photoexcited intralayer to interlayer excitations and the associated ultrafast optical responses in heterobilayers, which is conceptually different from the conventional single-particle picture. We find strong electron-hole interactions drive the dynamics and enhance the pump-probe optical responses by an order of magnitude with a rise time of ∼300 fs in MoSe_{2}/WSe_{2} heterobilayers, in agreement with experiment.

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.

Fermi-Level Engineering of Nitrogen Core-Doped Armchair Graphene Nanoribbons.

Substitutional heteroatom doping of bottom-up engineered 1D graphene nanoribbons (GNRs) is a versatile tool for realizing low-dimensional functional materials for nanoelectronics and sensing. Previous efforts have largely relied on replacing C-H groups lining the edges of GNRs with trigonal planar N atoms. This type of atomically precise doping, however, only results in a modest realignment of the valence band (VB) and conduction band (CB) energies. Here, we report the design, bottom-up synthesis, and spectroscopic characterization of nitrogen core-doped 5-atom-wide armchair GNRs (N2-5-AGNRs) that yield much greater energy-level shifting of the GNR electronic structure. Here, the substitution of C atoms with N atoms along the backbone of the GNR introduces a single surplus π-electron per dopant that populates the electronic states associated with previously unoccupied bands. First-principles DFT-LDA calculations confirm that a sizable shift in Fermi energy (∼1.0 eV) is accompanied by a broad reconfiguration of the band structure, including the opening of a new band gap and the transition from a direct to an indirect semiconducting band gap. Scanning tunneling spectroscopy (STS) lift-off charge transport experiments corroborate the theoretical results and reveal the relationship among substitutional heteroatom doping, Fermi-level shifting, electronic band structure, and topological engineering for this new N-doped GNR.

Engineering Robust Metallic Zero-Mode States in Olympicene Graphene Nanoribbons.

Metallic graphene nanoribbons (GNRs) represent a critical component in the toolbox of low-dimensional functional materials technology serving as 1D interconnects capable of both electronic and quantum information transport. The structural constraints imposed by on-surface bottom-up GNR synthesis protocols along with the limited control over orientation and sequence of asymmetric monomer building blocks during the radical step-growth polymerization have plagued the design and assembly of metallic GNRs. Here, we report the regioregular synthesis of GNRs hosting robust metallic states by embedding a symmetric zero-mode (ZM) superlattice along the backbone of a GNR. Tight-binding electronic structure models predict a strong nearest-neighbor electron hopping interaction between adjacent ZM states, resulting in a dispersive metallic band. First-principles density functional theory-local density approximation calculations confirm this prediction, and the robust, metallic ZM band of olympicene GNRs is experimentally corroborated by scanning tunneling spectroscopy.

Giant self-driven exciton-Floquet signatures in time-resolved photoemission spectroscopy of MoS2 from time-dependent GW approach.

Time-resolved, angle-resolved photoemission spectroscopy (TR-ARPES) is a one-particle spectroscopic technique that can probe excitons (two-particle excitations) in momentum space. We present an ab initio, time-domain GW approach to TR-ARPES and apply it to monolayer MoS2. We show that photoexcited excitons may be measured and quantified as satellite bands and lead to the renormalization of the quasiparticle bands. These features are explained in terms of an exciton-Floquet phenomenon induced by an exciton time-dependent bosonic field, which are orders of magnitude stronger than those of laser field-induced Floquet bands in low-dimensional semiconductors. Our findings imply a way to engineer Floquet matter through the coherent oscillation of excitons and open the new door for mechanisms for band structure engineering.

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.

Exciton Lifetime and Optical Line Width Profile via Exciton-Phonon Interactions: Theory and First-Principles Calculations for Monolayer MoS2.

Exciton dynamics dictates the evolution of photoexcited carriers in photovoltaic and optoelectronic devices. However, interpreting their experimental signatures is a challenging theoretical problem due to the presence of both electron-phonon and many-electron interactions. We develop and apply here a first-principles approach to exciton dynamics resulting from exciton-phonon coupling in monolayer MoS2 and reveal the highly selective nature of exciton-phonon coupling due to the internal spin structure of excitons, which leads to a surprisingly long lifetime of the lowest-energy bright A exciton. Moreover, we show that optical absorption processes rigorously require a second-order perturbation theory approach, with photon and phonon treated on an equal footing, as proposed by Toyozawa and Hopfield. Such a treatment, thus far neglected in first-principles studies, gives rise to off-diagonal exciton-phonon self-energy, which is critical for the description of dephasing mechanisms and yields exciton line widths in excellent agreement with experiment.

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.

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.

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.