Multi-Objective Optimization for Rapid Identification of Novel Compound Metals for Interconnect Applications.

Interconnect materials play the critical role of routing energy and information in integrated circuits. However, established bulk conductors, such as copper, perform poorly when scaled down beyond 10 nm, limiting the scalability of logic devices. Here, a multi-objective search is developed, combined with first-principles calculations, to rapidly screen over 15,000 materials and discover new interconnect candidates. This approach simultaneously optimizes the bulk electronic conductivity, surface scattering time, and chemical stability using physically motivated surrogate properties accessible from materials databases. Promising local interconnects are identified that have the potential to outperform ruthenium, the current state-of-the-art post-Cu material, and also semi-global interconnects with potentially large skin depths at the GHz operation frequency. The approach is validated on one of the identified candidates, CoPt, using both ab initio and experimental transport studies, showcasing its potential to supplant Ru and Cu for future local interconnects.

Mixed Stochastic-Deterministic Approach for Many-Body Perturbation Theory Calculations.

We present an approach for GW calculations of quasiparticle energies with quasiquadratic scaling by approximating high-energy contributions to the Green's function in its Lehmann representation with effective stochastic vectors. The method is easy to implement without altering the GW code, converges rapidly with stochastic parameters, and treats systems of various dimensionality and screening response. Our calculations on a 5.75° twisted MoS_{2} bilayer show how large-scale GW methods include geometry relaxations and electronic correlations on an equal basis in structurally nontrivial materials.

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.

Hidden phonon highways promote photoinduced interlayer energy transfer in twisted transition metal dichalcogenide heterostructures.

Vertically stacked van der Waals (vdW) heterostructures exhibit unique electronic, optical, and thermal properties that can be manipulated by twist-angle engineering. However, the weak phononic coupling at a bilayer interface imposes a fundamental thermal bottleneck for future two-dimensional devices. Using ultrafast electron diffraction, we directly investigated photoinduced nonequilibrium phonon dynamics in MoS2/WS2 at 4° twist angle and WSe2/MoSe2 heterobilayers with twist angles of 7°, 16°, and 25°. We identified an interlayer heat transfer channel with a characteristic timescale of ~20 picoseconds, about one order of magnitude faster than molecular dynamics simulations assuming initial intralayer thermalization. Atomistic calculations involving phonon-phonon scattering suggest that this process originates from the nonthermal phonon population following the initial interlayer charge transfer and scattering. Our findings present an avenue for thermal management in vdW heterostructures by tailoring nonequilibrium phonon populations.

Edge-Confined Excitons in Monolayer Black Phosphorus.

Quantum confinement of two-dimensional excitons in van der Waals materials via electrostatic trapping, lithographic patterning, Moiré potentials, and chemical implantation has enabled significant advances in tailoring light emission from nanostructures. While such approaches rely on complex preparation of materials, natural edges are a ubiquitous feature in layered materials and provide a different approach for investigating quantum-confined excitons. Here, we observe that certain edge sites of monolayer black phosphorus (BP) strongly localize the intrinsic quasi-one-dimensional excitons, yielding sharp spectral lines in photoluminescence, with nearly an order of magnitude line width reduction. Through structural characterization of BP edges using transmission electron microscopy and first-principles GW plus Bethe-Salpeter equation (GW-BSE) calculations of exemplary BP nanoribbons, we find that certain atomic reconstructions can strongly quantum-confine excitons resulting in distinct emission features, mediated by local strain and screening. We observe linearly polarized luminescence emission from edge reconstructions that preserve the mirror symmetry of the parent BP lattice, in agreement with calculations. Furthermore, we demonstrate efficient electrical switching of localized edge excitonic luminescence, whose sites act as excitonic transistors for emission. Localized emission from BP edges motivates exploration of nanoribbons and quantum dots as hosts for tunable narrowband light generation, with future potential to create atomic-like structures for quantum information processing applications as well as exploration of exotic phases that may reside in atomic edge structures.

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.

Quasiparticle and Optical Properties of Carrier-Doped Monolayer MoTe2 from First Principles.

The intrinsic weak and highly nonlocal dielectric screening of two-dimensional materials is well-known to lead to high sensitivity of their optoelectronic properties to environment. Less studied theoretically is the role of free carriers in those properties. Here, we use ab initio GW and Bethe-Salpeter equation calculations, with a rigorous treatment of dynamical screening and local-field effects, to study the doping dependence of the quasiparticle and optical properties of a monolayer transition-metal dichalcogenide, 2H MoTe2. We predict a quasiparticle band gap renormalization of several hundreds of meV for experimentally attainable carrier densities and a similarly sizable decrease in the exciton binding energy. This results in an almost constant excitation energy for the lowest-energy exciton resonance with an increasing doping density. Using a newly developed and generally applicable plasmon-pole model and a self-consistent solution of the Bethe-Salpeter equation, we reveal the importance of accurately capturing both dynamical and local-field effects to understand detailed photoluminescence measurements.

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.

Rydberg Excitons and Trions in Monolayer MoTe2.

Monolayer transition metal dichalcogenide (TMDC) semiconductors exhibit strong excitonic optical resonances, which serve as a microscopic, noninvasive probe into their fundamental properties. Like the hydrogen atom, such excitons can exhibit an entire Rydberg series of resonances. Excitons have been extensively studied in most TMDCs (MoS2, MoSe2, WS2, and WSe2), but detailed exploration of excitonic phenomena has been lacking in the important TMDC material molybdenum ditelluride (MoTe2). Here, we report an experimental investigation of excitonic luminescence properties of monolayer MoTe2 to understand the excitonic Rydberg series, up to 3s. We report a significant modification of emission energies with temperature (4 to 300 K), thereby quantifying the exciton-phonon coupling. Furthermore, we observe a strongly gate-tunable exciton-trion interplay for all the Rydberg states governed mainly by free-carrier screening, Pauli blocking, and band gap renormalization in agreement with the results of first-principles GW plus Bethe-Salpeter equation approach calculations. Our results help bring monolayer MoTe2 closer to its potential applications in near-infrared optoelectronics and photonic devices.

Bidirectional phonon emission in two-dimensional heterostructures triggered by ultrafast charge transfer.

Photoinduced charge transfer in van der Waals heterostructures occurs on the 100 fs timescale despite weak interlayer coupling and momentum mismatch. However, little is understood about the microscopic mechanism behind this ultrafast process and the role of the lattice in mediating it. Here, using femtosecond electron diffraction, we directly visualize lattice dynamics in photoexcited heterostructures of WSe2/WS2 monolayers. Following the selective excitation of WSe2, we measure the concurrent heating of both WSe2 and WS2 on a picosecond timescale-an observation that is not explained by phonon transport across the interface. Using first-principles calculations, we identify a fast channel involving an electronic state hybridized across the heterostructure, enabling phonon-assisted interlayer transfer of photoexcited electrons. Phonons are emitted in both layers on the femtosecond timescale via this channel, consistent with the simultaneous lattice heating observed experimentally. Taken together, our work indicates strong electron-phonon coupling via layer-hybridized electronic states-a novel route to control energy transport across atomic junctions.

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.

Optical absorption of interlayer excitons in transition-metal dichalcogenide heterostructures.

Interlayer excitons, electron-hole pairs bound across two monolayer van der Waals semiconductors, offer promising electrical tunability and localizability. Because such excitons display weak electron-hole overlap, most studies have examined only the lowest-energy excitons through photoluminescence. We directly measured the dielectric response of interlayer excitons, which we accessed using their static electric dipole moment. We thereby determined an intrinsic radiative lifetime of 0.40 nanoseconds for the lowest direct-gap interlayer exciton in a tungsten diselenide/molybdenum diselenide heterostructure. We found that differences in electric field and twist angle induced trends in exciton transition strengths and energies, which could be related to wave function overlap, moiré confinement, and atomic reconstruction. Through comparison with photoluminescence spectra, this study identifies a momentum-indirect emission mechanism. Characterization of the absorption is key for applications relying on light-matter interactions.

Structure of the moiré exciton captured by imaging its electron and hole.

Interlayer excitons (ILXs) - electron-hole pairs bound across two atomically thin layered semiconductors - have emerged as attractive platforms to study exciton condensation1-4, single-photon emission and other quantum information applications5-7. Yet, despite extensive optical spectroscopic investigations8-12, critical information about their size, valley configuration and the influence of the moiré potential remains unknown. Here, in a WSe2/MoS2 heterostructure, we captured images of the time-resolved and momentum-resolved distribution of both of the particles that bind to form the ILX: the electron and the hole. We thereby obtain a direct measurement of both the ILX diameter of around 5.2 nm, comparable with the moiré-unit-cell length of 6.1 nm, and the localization of its centre of mass. Surprisingly, this large ILX is found pinned to a region of only 1.8 nm diameter within the moiré cell, smaller than the size of the exciton itself. This high degree of localization of the ILX is backed by Bethe-Salpeter equation calculations and demonstrates that the ILX can be localized within small moiré unit cells. Unlike large moiré cells, these are uniform over large regions, allowing the formation of extended arrays of localized excitations for quantum technology.

Identifying Hidden Intracell Symmetries in Molecular Crystals and Their Impact for Multiexciton Generation.

Organic molecular crystals are appealing for next-generation optoelectronic applications due to their multiexciton generation processes that can increase the efficiency of photovoltaic devices. However, a general understanding of how crystal structures affect these processes is lacking, requiring computationally demanding calculations for each material. Here we present an approach to understand and classify organic crystals and elucidate multiexciton processes. We show that organic crystals that are composed of two sublattices are well-approximated by effective fictitious systems of higher translational symmetry. Within this framework, we derive hidden selection rules in crystal pentacene and predict that the bulk polymorph supports fast Coulomb-mediated singlet fission with a transition rate about 2 orders of magnitude faster than that of the thin-film polymorph, a result confirmed with many-body perturbation theory calculations. Our approach is based on density-functional theory calculations and provides design principles for the experimental and computational discovery of new materials with tailored excitonic properties.

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.

Experimental measurement of the intrinsic excitonic wave function.

An exciton, a two-body composite quasiparticle formed of an electron and hole, is a fundamental optical excitation in condensed matter systems. Since its discovery nearly a century ago, a measurement of the excitonic wave function has remained beyond experimental reach. Here, we directly image the excitonic wave function in reciprocal space by measuring the momentum distribution of electrons photoemitted from excitons in monolayer tungsten diselenide. By transforming to real space, we obtain a visual of the distribution of the electron around the hole in an exciton. Further, by also resolving the energy coordinate, we confirm the elusive theoretical prediction that the photoemitted electron exhibits an inverted energy-momentum dispersion relationship reflecting the valence band where the partner hole remains, rather than that of conduction band states of the electron.

Universal slow plasmons and giant field enhancement in atomically thin quasi-two-dimensional metals.

Plasmons depend strongly on dimensionality: while plasmons in three-dimensional systems start with finite energy at wavevector q = 0, plasmons in traditional two-dimensional (2D) electron gas disperse as [Formula: see text]. However, besides graphene, plasmons in real, atomically thin quasi-2D materials were heretofore not well understood. Here we show that the plasmons in real quasi-2D metals are qualitatively different, being virtually dispersionless for wavevectors of typical experimental interest. This stems from a broken continuous translational symmetry which leads to interband screening; so, dispersionless plasmons are a universal intrinsic phenomenon in quasi-2D metals. Moreover, our ab initio calculations reveal that plasmons of monolayer metallic transition metal dichalcogenides are tunable, long lived, able to sustain field intensity enhancement exceeding 107, and localizable in real space (within ~20 nm) with little spreading over practical measurement time. This opens the possibility of tracking plasmon wave packets in real time for novel imaging techniques in atomically thin materials.

Accelerating GW-Based Energy Level Alignment Calculations for Molecule-Metal Interfaces Using a Substrate Screening Approach.

The physics of electronic energy level alignment at interfaces formed between molecules and metals can in general be accurately captured by the ab initio GW approach. However, the computational cost of such GW calculations for typical interfaces is significant, given their large system size and chemical complexity. In the past, approximate self-energy corrections, such as those constructed from image-charge models together with gas-phase molecular level corrections, have been used to compute level alignment with good accuracy. However, these approaches often neglect dynamical effects of the polarizability and require the definition of an image plane. In this work, we propose a new approximation to enable more efficient GW-quality calculations of interfaces, where we greatly simplify the calculation of the noninteracting polarizability, a primary bottleneck for large heterogeneous systems. This is achieved by first computing the noninteracting polarizability of each individual component of the interface, e.g., the molecule and the metal, without the use of large supercells, and then using folding and spatial truncation techniques to efficiently combine these quantities. Overall this approach significantly reduces the computational cost for conventional GW calculations of level alignment without sacrificing the accuracy. Moreover, this approach captures both dynamical and nonlocal polarization effects without the need to invoke a classical image-charge expression or to define an image plane. We demonstrate our approach by considering a model system of benzene at relatively low coverage on the aluminum (111) surface. Although developed for such interfaces, the method can be readily extended to other heterogeneous interfaces.