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We explore the optical dipole orientation of single photon emitters in monolayer MoS2 as produced by a focused helium ion beam. The single photon emitters can be understood as single sulfur vacancies. The corresponding far-field luminescence spectra reveal several photoluminescence lines below the dominating luminescence of the exciton in MoS2. These sub-bandgap emission lines were predicted by ab initio theory, but they have never been resolved in luminescence experiments because of their small amplitude. We reveal the lines by their dependence as a function of the photon energy and momentum as measured in the back focal plane of the optical circuitry. The agreement between theory and experiment suggests that the defect states interact strongly within the Brillouin zone.

Understanding complex quantum dynamics in realistic materials requires insight into the underlying correlations dominating the interactions between the participating particles. Due to the wealth of information involved in these processes, applying artificial intelligence methods is compelling. Yet, unsupervised data-driven approaches typically focus on maximal variations of the individual components, rather than considering the correlations between them. Here we present an approach that recognizes correlation patterns to explore convoluted dynamical processes. Our scheme is using singular value decomposition (SVD) to extract dynamical features, unveiling the internal temporal-spatial interrelations that generate the dynamical mechanisms. We apply our approach to study light-induced wavepacket propagation in organic crystals, of interest for applications in material based quantum computing and quantum information science. We show how transformation from the input momentum and time coordinates onto a new correlation-induced coordinate space allows direct recognition of the relaxation and dephasing components dominating the dynamics and demonstrate their dependence on the initial pulse shape. Entanglement of the dynamical features is suggested as a pathway to reproduce the information required for further explainability of these mechanisms. Our method offers a route for elucidating complex dynamical processes using unsupervised AI-based analysis in multi-component systems.

Optical properties of heterostructures composed of layered 2D materials, such as transition metal dichalcogenides (TMDs) and graphene, are broadly explored. Of particular interest are light-induced energy transfer mechanisms in these materials and their structural roots. Here, we use state-of-the-art first-principles calculations to study the excitonic composition and the absorption properties of WS$_2$-graphene heterostructures as a function of interlayer alignment and the local strain resulting from it. We find that Brillouin zone mismatch and the associated energy level alignment between the graphene Dirac cone and the TMD bands dictate an interplay between interlayer and intralayer excitons, mixing together in the many-body representation upon the strain-induced symmetry breaking in the interacting layers. Examining the representative cases of the 0$^\circ$ and 30$^\circ$ interlayer twist angles, we find that this exciton mixing strongly varies as a function of the relative alignment. We quantify the effect of these structural modifications on exciton charge separation between the layers and the associated graphene-induced homogeneous broadening of the absorption resonances. Our findings provide guidelines for controllable optical excitations upon interface design and shed light on the importance of many-body effects in the understanding of optical phenomena in complex heterostructures., Comment: 8 pages, 4 figures

Heterostructures of layered transition metal dichalcogenides (TMDs) host long-lived, tunable excitons, making them intriguing candidates for material-based quantum information applications. Light absorption in these systems induces a plethora of optically excited states that hybridize both interlayer and intralayer characteristics, providing a distinctive starting point for their relaxation processes, in which the interplay between generated electron-hole pairs and their scattering with phonons play a key role. We present a first-principles theoretical approach to compute phonon-induced exciton decomposition due to rapid occupation of electron-hole pairs with finite momentum and opposite spin. Using the MoSe$_2$/WSe$_2$ heterostructure as a case study, we observe a reduction in the optical activity of bright states upon phonon scattering already in the first few femtoseconds proceeding the photoexcitation, driving exciton interlayer delocalization and subsequent variations in the exciton spin. Our results reveal an unexpected and previously unexplored starting point for exciton relaxation dynamics, suggesting increased availability for coherent interactions and non-radiative processes through ultrafast changes in exciton momentum, spatial, and spin properties upon light excitation.

Non-radiative exciton relaxation processes are critical for energy transduction efficiencies in optoelectronic materials, but how these processes are connected to the underlying crystal structure and its associated electron, exciton, and phonon band structures is poorly understood. Here, we present a first-principles approach to explore exciton relaxation pathways in pentacene, a paradigmatic molecular crystal and optoelectronic semiconductor. We compute the momentum- and band-resolved exciton-phonon interactions, and use them to analyse key scattering channels. We find that exciton intraband transitions on femtosecond timescales leading to dark-state occupation is a dominant nonradiative relaxation channel in pentacene. We further show how the nature of real-time propagation of the exciton wavepacket is connected with the longitudinal-transverse exciton splitting, stemming from crystal anisotropy, and concomitant anisotropic exciton and phonon dispersions. Our results provide a framework for understanding time-resolved exciton propagation and energy transfer in molecular crystals and beyond.

Associating the presence of atomic vacancies to excited-state transport phenomena in two dimensional semiconductors is of emerging interest, and demands detailed understanding of the involved exciton transitions. Here we study the effect of such defects on the electronic and optical properties of WS$_2$-graphene and MoS$_2$-graphene van der Waals heterobilayers by employing many-body perturbation theory. We find that the combination of chalcogen defects and graphene adsorption onto the transition metal dichalcogenide layer can radically alter the optical properties of the heterobilayer, due to a combination of dielectric screening, the impact of the missing chalcogen atoms in the intralayer and interlayer optical transitions, and the different nature of each layer. By analyzing the intrinsic radiative rates of the most stable subgap excitonic features, we find that while the presence of defects introduces low-lying optical transitions, resulting in excitons with larger oscillator strength, it also decreases the optical response associated to the pristine-like transition-metal dichalcogenide intralayer excitons. Our findings relate excitonic features with interface design for defect engineering in photovoltaic and transport applications., Comment: 7 pages + 3 figures; Supporting Information (20 pages + 13 figures)

We study the dynamical properties of point-like defects, represented by monoatomic chalcogen vacancies, in WS$_2$-graphene and MoS$_2$-graphene heterobilayers. Employing a multidisciplinary approach based on the combination of ab initio, model Hamiltonian and density matrix techniques, we propose a minimal interacting model that allows for the calculation of electronic transition times associated to population and depopulation of the vacancy by an additional electron. We obtain the "coarse-grained" semiclassical dynamics by means of a master equation approach and discuss the potential role of virtual charge fluctuations in the internal dynamics of impurity quasi-degenerate states. The interplay between the symmetry of the lattice and the spin degree of freedom through the spin-orbit interaction and its impact on charge quenching is studied in detail., Comment: 17 pages + 9 figures; Supplemental Material (10 pages + 4 figures)

Moir\'e superlattices of transition metal dichalcogenide (TMD) heterostructures give rise to rich excitonic phenomena associated with the interlayer twist angle and induced changes in the involved quantum states. Theoretical calculations of excitons in such systems are typically based on model moir\'e potentials to mitigate the computational cost. However, an ab initio understanding of the electron-hole coupling dominating the excitations is crucial to realize the twist-induced modifications of the optical selection rules. In this work we use many-body perturbation theory to compute and analyze the relation between twist angle and exciton properties in twisted TMD heterostructures. We present a general approach for unfolding excitonic states from the moir\'e Brillouin zone onto the Brillouin zones of the separate layers. Applying this method to a twisted MoS$_2$/MoSe$_2$ bilayer, we find that the optical excitation spectrum is dominated by mixed transitions between electrons and holes with different momenta in the separate monolayers, leading to unexpected and angle-dependent hybridization between interlayer and intralayer excitons. Our findings offer a design pathway for tuning exciton layer-localization in TMD heterostructures as a function of twist angle.

Single spin defects in 2D transition-metal dichalcogenides are natural spin-photon interfaces for quantum applications. Here we report high-field magneto-photoluminescence spectroscopy from three emission lines (Q1, Q2 and Q*) of He-ion induced sulfur vacancies in monolayer $\text{MoS}_2$. Analysis of the asymmetric PL lineshapes in combination with the diamagnetic shift of Q1 and Q2 yields a consistent picture of localized emitters with a wavefunction extent of $\sim$ 3.5 nm. The distinct valley-Zeeman splitting in out-of-plane $B$-fields and the brightening of dark states through in-plane $B$-fields necessitates spin-valley selectivity of the defect states and lifted spin-degeneracy at zero field. Comparing our results to ab-initio calculations identifies the nature of Q1 and Q2 and suggests that Q* is the emission from a chemically functionalized defect. Analysis of the optical degree of circular polarization reveals that the Fermi level is a parameter that enables the tunability of the emitter. These results show that defects in 2D semiconductors may be utilized for quantum technologies.

The presence of chalcogen vacancies in monolayer transition metal dichalcogenides (TMDs) leads to excitons with mixed localized-delocalized character and to reduced valley selectivity. Recent experimental advances in defect design in TMDs allow for a close examination of such mixed exciton states as a function of their degree of circular polarization under external magnetic fields, revealing strongly varying defect-induced magnetic properties. A theoretical understanding of these observations and their physical origins demands a predictive, structure-sensitive theory. In this work, we study the effect of chalcogen vacancies on the exciton magnetic properties in monolayer MoS$_2$. Using many-body perturbation theory, we show how the complex excitonic picture associated with the presence of defects -- with reduced valley and spin selectivity due to hybridized electron-hole transitions -- leads to structurally-controllable exciton magnetic response. We find a variety of g-factors with changing magnitudes and sign depending on the exciton energy and character. Our findings suggest a pathway to tune the nature of the excitons -- and by that their magneto-optical properties -- through defect architecture.

BiVO$_4$ is a promising photocatalyst for efficient water oxidation, with surface reactivity determined by the structure of active catalytic sites. Surface oxidation in the presence of oxygen vacancies induces electron localization, suggesting an atomistic route to improve the charge transfer efficiency within the catalytic cycle. In this work, we study the effect of oxygen vacancies on the electronic and optical properties at BiVO$_4$ surfaces upon water oxidation. We use density functional theory and many-body perturbation theory to explore the change in the electronic and quasiparticle energy levels and to evaluate the electron-hole coupling as a function of the underlying structure. We show that while the presence of defects alters the atomic structure and largely modifies the wavefunction nature, leading to defect-localized states at the quasipatricle gap region, the optical excitations remain largely unchanged due to substantial hybridization of defect and non-defect electron-hole transitions. Our findings suggest that defect-induced surface oxidation supports improved electron transport, both through bound and tunable electronic states and via a mixed nature of the optical transitions, expected to reduce electron-hole defect trapping.

Organic molecular crystals are appealing for next-generation optoelectronic applications, most notably due to their multiexciton generation process that can increase the efficiency of photovoltaic devices. However, a general understanding of how crystal structures affects multiexciton generation processes is lacking, requiring computationally demanding calculations for each material. Here we present an approach to understand and classify such 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 common bulk polymorph supports fast Coulomb-mediated singlet fission about one order of magnitude more than the thin-film polymorph, a result confirmed with many-body perturbation theory calculations. Our approach is fully based on density-functional theory calculations, and provides design principles for the experimental and computational discovery of new materials with efficient non-radiative exciton decay rates.

We provide a critical overview of the theory of the chirality-induced spin selectivity (CISS) effect, i.e., phenomena in which the chirality of molecular species imparts significant spin selectivity to various electron processes. Based on discussions in a recently held workshop, and further work published since, we review the status of CISS effects - in electron transmission, electron transport, and chemical reactions. For each, we provide a detailed discussion of the state-of-the-art in theoretical understanding and identify remaining challenges and research opportunities.

Exciton dynamics, lifetimes and scattering are directly related to the exciton dispersion, or bandstructure. While electron and phonon bandstructures are well understood and can be easily calculated from first principles, the exciton bandstructure is commonly conflated with the underlying electronic bandstructure, where the exciton dispersion is assumed to follow the same dispersion as the electron and hole bands from which it is composed (i.e., the effective mass model). Here, we present a general theory of exciton bandstructure within both ab initio and model Hamiltonian approaches. We show that contrary to common assumption, the exciton bandstructure contains non-analytical discontinuities -- a feature which is impossible to obtain from the electronic bandstructure alone. These discontinuities are purely quantum phenomena, arising from the exchange scattering of electron-hole pairs. We show that the degree of these discontinuities depends on materials' symmetry and dimensionality, with jump discontinuities occurring in 3D and different orders of removable discontinuities in 2D and 1D. We connect these unexpected features to the early stages of exciton dynamics, which shows remarkable correspondence with recent experimental observations and suggests that the measured diffusion patterns are influenced by the underlying exciton bandstructure.

Control of impurity concentrations in semiconducting materials is essential to device technology. Because of their intrinsic confinement, the properties of two-dimensional semiconductors such as transition metal dichalcogenides (TMDs) are more sensitive to defects than traditional bulk materials. The technological adoption of TMDs is dependent on the mitigation of deleterious defects and guided incorporation of functional foreign atoms. The first step towards impurity control is the identification of defects and assessment of their electronic properties. Here, we present a comprehensive study of point defects in monolayer tungsten disulfide (WS$_2$) grown by chemical vapor deposition (CVD) using scanning tunneling microscopy/spectroscopy, CO-tip noncontact atomic force microscopy, Kelvin probe force spectroscopy, density functional theory, and tight-binding calculations. We observe four different substitutional defects: chromium (Cr$_{\text{W}}$) and molybdenum (Mo$_{\text{W}}$) at a tungsten site, oxygen at sulfur sites in both bottom and top layers (O$_{\text{S}}$ top/bottom), as well as two negatively charged defects (CDs). Their electronic fingerprints unambiguously corroborate the defect assignment and reveal the presence or absence of in-gap defect states. The important role of charge localization, spin-orbit coupling, and strain for the formation of deep defect states observed at substitutional defects in WS$_2$ as reported here will guide future efforts of targeted defect engineering and doping of TMDs.

A prototypical organic photovoltaic material is a heterojunction composed of the blend of regioregular poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl-C$_{61}$-butyric acid methyl ester (PCBM). Microscopic understanding of the energy conversion mechanism in this system involves the relationship between the electronic structure and the atomistic geometry of P3HT:PCBM interfaces. In this work, the effect of the number of P3HT layers on the electronic structure of the P3HT:PCBM interface is studied by means of first-principles $GW$. We apply the substrate screening approach to accelerate such calculations and to better understand the many-body dielectric screening at the interface. The quasiparticle band gap of the entire interface is found to decrease as the number of P3HT layers increases. The gaps of the individual components of the interface are found to be smaller than their isolated counterparts, with strong dependence on the number of P3HT layers. Importantly, when comparing the system of P3HT:PCBM - where a single interface is present - and the system of P3HT:PCBM:P3HT, where an interface is formed on either side of PCBM, we find that the two systems exhibit very different quasiparticle energy level alignments. We discuss possible implications of our findings in related experiments. The observed trends in layer-dependent quasiparticle electronic structure of P3HT:PCBM interfaces provide computational insight into energy conversion pathways in these materials., Comment: 26 pages, 4 figures

We determine the zero temeperature phase diagram of excitons in the symmetric transition-metal dichalcogenide tri-layer heterosctructure WSe2/MoSe2/WSe2. First principle calculations reveal two distinct types of interlayer excitonic states, a lower energy symmetric quadrupole and a higher energy asymmetric dipole. While interaction between quadrupolar excitons is always repulsive, anti-parallel dipolar excitons attract at large distances. We find quantum phase transitions between a repulsive quadrupole lattice phase and a staggered (anti-parallel) dipolar lattice phase, driven by the competition between the exciton-exciton interactions and the single exciton energies. Remarkably, the intrinsic nature of each interlayer exciton is completely different in each phase. This is a striking example for the possible rich quantum physics in a system where the single particle properties and the many-body state are dynamically coupled through the particle interactions.

Structural defects are widely regarded as detrimental to the optoelectronic properties of monolayer transition metal dichalcogenides, leading to concerted efforts to eliminate defects via improved materials growth or post-growth passivation. Here, using steady-state and ultrafast optical spectroscopy, supported by ab initio calculations, we demonstrate that sulfur vacancy defects act as exciton traps. Current chemical treatments do not passivate these sites, leading to decreased mobility and trap-limited photoluminescence. We present a generalizable treatment protocol based on the use of passivating agents such as thiols or sulfides in combination with a Lewis acid to passivate sulfur vacancies in monolayer MoS$_2$ and WS$_2$, increasing photoluminescence up to 275 fold, while maintaining mobilities. Our findings suggest a route for simple and rational defect engineering strategies, where the passivating agent varies the electronic properties, thereby allowing the design of new heterostructures.

Chalcogen vacancies are considered to be the most abundant point defects in two-dimensional (2D) transition-metal dichalcogenide (TMD) semiconductors, and predicted to result in deep in-gap states (IGS). As a result, important features in the optical response of 2D-TMDs have typically been attributed to chalcogen vacancies, with indirect support from Transmission Electron Microscopy (TEM) and Scanning Tunneling Microscopy (STM) images. However, TEM imaging measurements do not provide direct access to the electronic structure of individual defects; and while Scanning Tunneling Spectroscopy (STS) is a direct probe of local electronic structure, the interpretation of the chemical nature of atomically-resolved STM images of point defects in 2D-TMDs can be ambiguous. As a result, the assignment of point defects as vacancies or substitutional atoms of different kinds in 2D-TMDs, and their influence on their electronic properties, has been inconsistent and lacks consensus. Here, we combine low-temperature non-contact atomic force microscopy (nc-AFM), STS, and state-of-the-art ab initio density functional theory (DFT) and GW calculations to determine both the structure and electronic properties of the most abundant individual chalcogen-site defects common to 2D-TMDs. Surprisingly, we observe no IGS for any of the chalcogen defects probed. Our results and analysis strongly suggest that the common chalcogen defects in our 2D-TMDs, prepared and measured in standard environments, are substitutional oxygen rather than vacancies.

Structural defects in 2D materials offer an effective way to engineer new material functionalities beyond conventional doping in semiconductors. Specifically, deep in-gap defect states of chalcogen vacancies have been associated with intriguing phenomena in monolayer transition metal dichalcogenides (TMDs). Here, we report the direct experimental correlation of the atomic and electronic structure of a sulfur vacancy in monolayer WS2 by a combination of CO-tip noncontact atomic force microscopy (nc-AFM) and scanning tunneling microscopy (STM). Sulfur vacancies, which are absent in as-grown samples, were deliberately created by annealing in vacuum. Two energetically narrow unoccupied defect states of the vacancy provide a unique fingerprint of this defect. Direct imaging of the defect orbitals by STM and state-of-the-art GW calculations reveal that the large splitting of 252 meV between these defect states is induced by spin-orbit coupling. The controllable incorporation and potential decoration of chalcogen vacancies provide a new route to tailor the optical, catalytic and magnetic properties of TMDs.

We study the effect of point-defect chalcogen vacancies on the optical properties of monolayer transition metal dichalcogenides using ab initio GW and Bethe-Salpeter equation calculations. We find that chalcogen vacancies introduce unoccupied in-gap states and occupied resonant defect states within the quasiparticle continuum of the valence band. These defect states give rise to a number of strongly-bound defect excitons and hybridize with excitons of the pristine system, reducing the valley-selective circular dichroism. Our results suggest a pathway to tune spin-valley polarization and other optical properties through defect engineering.

We develop a new first-principles approach to predict and understand rates of singlet fission with an ab initio Green's-function formalism based on many-body perturbation theory. Starting with singlet and triplet excitons computed from a GW plus Bethe-Salpeter equation approach, we calculate the exciton--bi-exciton coupling to lowest order in the Coulomb interaction, assuming a final state consisting of two non-interacting spin-correlated triplets with finite center-of-mass momentum. For crystalline pentacene, symmetries dictate that the only purely Coulombic fission decay from a bright singlet state requires a final state consisting of two inequivalent nearly degenerate triplets of nonzero, equal and opposite, center-of-mass momenta. For such a process, we predict a singlet lifetime of 40 to 150 fs, in very good agreement with experimental data, indicating that this process can dominate singlet fission in crystalline pentacene. Our approach is general and provides a framework for predicting and understanding multiexciton interactions in solids.

The alignment of the frontier orbital energies of an adsorbed molecule with the substrate Fermi level at metal-organic interfaces is a fundamental observable of significant practical importance in nanoscience and beyond. Typical density functional theory calculations, especially those using local and semi-local functionals, often underestimate level alignment leading to inaccurate electronic structure and charge transport properties. In this work, we develop a new fully self-consistent predictive scheme to accurately compute level alignment at certain classes of complex heterogeneous molecule-metal interfaces based on optimally-tuned range-separated hybrid functionals. Starting from a highly accurate description of the gas-phase electronic structure, our method by construction captures important nonlocal surface polarization effects via tuning of the long-range screened exchange in a range-separated hybrid in a non-empirical and system-specific manner. We implement this functional in a plane-wave code and apply it to several physisorbed and chemisorbed molecule-metal interface systems. Our results are in quantitative agreement with experiments, both the level alignment and work function changes. Our approach constitutes a new practical scheme for accurate and efficient calculations of the electronic structure of molecule-metal interfaces., Comment: 15 pages, 8 figures

The energy positions of frontier orbitals in organic electronic materials are often studied experimentally by (inverse) photoemission spectroscopy and theoretically within density functional theory. However, standard exchange-correlation functionals often result in too small fundamental gaps, may lead to wrong orbital energy ordering, and do not capture polarization-induced gap renormalization. Here, we examine these issues and a strategy for overcoming them by studying the gas phase and bulk electronic structure of the organic molecule quinacridone (5Q), a promising material with many interesting properties for organic devices. Experimentally, we perform angle-resolved photoemission spectroscopy (ARUPS) on thin films of the crystalline $\beta$-phase of 5Q. Theoretically, we employ an optimally-tuned range-separated hybrid functional (OT-RSH) within density functional theory. For the gas phase molecule, our OT-RSH result for the ionization potential (IP) represents a substantial improvement over the semi-local PBE and the PBE0 hybrid functional results, producing an IP in quantitative agreement with experiment. For the bulk crystal, we take into account the correct screening in the bulk, using the recently developed OT-SRSH approach, while retaining the optimally-tuned parameters for the range-separation and the short-range Fock exchange. This leads to a band gap narrowing due to polarization effects and results in a valence band spectrum in excellent agreement with experimental ARUPS data, with respect to both peak positions and heights. Finally, full-frequency $G_0W_0$ results based on a hybrid functional starting point are shown to agree with the OT-SRSH approach, improving substantially on the PBE-starting point.

We present a framework for obtaining reliable solid-state charge and optical excitations and spectra from optimally-tuned range-separated hybrid density functional theory. The approach, which is fully couched within the formal framework of generalized Kohn-Sham theory, allows for accurate prediction of exciton binding energies. We demonstrate our approach through first principles calculations of one- and two-particle excitations in pentacene, a molecular semiconducting crystal, where our work is in excellent agreement with experiments and prior computations. We further show that with one adjustable parameter, set to produce an accurate bandgap, this method accurately predicts band structures and optical spectra of silicon and lithium flouride, prototypical covalent and ionic solids. Our findings indicate that for a broad range of extended bulk systems, this method may provide a computationally inexpensive alternative to many-body perturbation theory, opening the door to studies of materials of increasing size and complexity.

We present a method for obtaining outer valence quasiparticle excitation energies from a DFT-based calculation, with accuracy that is comparable to that of many-body perturbation theory within the GW approximation. The approach uses a range-separated hybrid density functional, with asymptotically exact and short-range fractional Fock exchange. The functional contains two parameters - the range separation and the short-range Fock fraction. Both are determined non-empirically, per system, based on satisfaction of exact physical constraints for the ionization potential and many-electron self-interaction, respectively. The accuracy of the method is demonstrated on four important benchmark organic molecules: perylene, pentacene, 3,4,9,10-perylene-tetracarboxylic-dianydride (PTCDA) and 1,4,5,8-naphthalene-tetracarboxylic dianhydride (NTCDA). We envision that for finite systems the approach could provide an inexpensive alternative to GW, opening the door to the study of presently out of reach large-scale systems.