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.

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.

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.

Phonon-Driven Femtosecond Dynamics of Excitons in Crystalline Pentacene from First Principles.

Nonradiative exciton relaxation processes are critical for energy transduction and transport in optoelectronic materials, but how these processes are connected to the underlying crystal structure and the associated electron, exciton, and phonon band structures, as well as the interactions of all these particles, is challenging to understand. Here, we present a first-principles study of exciton-phonon 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 analyze key scattering channels. We find that both exciton intraband scattering and interband scattering to parity-forbidden dark states occur on the same ∼100 fs timescale as a direct consequence of the longitudinal-transverse splitting of the bright exciton band. Consequently, exciton-phonon scattering exists as a dominant nonradiative relaxation channel in pentacene. We further show how the propagation of an exciton wave packet is connected with crystal anisotropy, which gives rise to the longitudinal-transverse exciton splitting and concomitant anisotropic exciton and phonon dispersions. Our results provide a framework for understanding the role of exciton-phonon interactions in exciton nonradiative lifetimes in molecular crystals and beyond.

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.

Minimal Molecular Building Blocks for Screening in Quasi-Two-Dimensional Organic-Inorganic Lead Halide Perovskites.

Layered hybrid organic-inorganic lead halide perovskites have intriguing optoelectronic properties, but some of the most interesting perovskite systems, such as defective, disordered, or mixed perovskites, require multiple unit cells to describe and are not accessible within state-of-the-art ab initio theoretical approaches for computing excited states. The principal bottleneck is the calculation of the dielectric matrix, which scales formally as O(N4). We develop here a fully ab initio approximation for the dielectric matrix, known as IPSA-2C, in which we separate the polarizability of the organic/inorganic layers into minimal building blocks, thus circumventing the undesirable power-law scaling. The IPSA-2C method reproduces the quasi-particle band structures and absorption spectra for a series of Ruddlesden-Popper perovskites to high accuracy, by including critical nonlocal effects neglected in simpler models, and sheds light on the complicated interplay of screening between the organic and inorganic sublattices.

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.

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.

Exchange-Driven Intermixing of Bulk and Topological Surface States by Chiral Excitons in Bi_{2}Se_{3}.

Topological surface states (TSS) in the prototypical topological insulator (TI) Bi_{2}Se_{3} are frequently characterized using optical probes, but electron-hole interactions and their effect on surface localization and optical response of the TSS remain unexplored. Here, we use ab initio calculations to understand excitonic effects in the bulk and surface of Bi_{2}Se_{3}. We identify multiple series of chiral excitons that exhibit both bulk and TSS character, due to exchange-driven mixing. Our results address fundamental questions about the degree to which electron-hole interactions can relax the topological protection of surface states and dipole selection rules for circularly polarized light in TIs by elucidating the complex intermixture of bulk and surface states excited in optical measurements and their coupling to light.

Screening of Excitons by Organic Cations in Quasi-Two-Dimensional Organic-Inorganic Lead-Halide Perovskites.

Interlayer organic cations in quasi-two-dimensional halide perovskites are a versatile tuning vehicle for the optoelectronic properties of these complex systems, but chemical intuition for this design route is yet to be established. Here, we use density functional theory, the GW approximation, and the Bethe-Salpeter equation approach to understand the contribution of the organic cation to the quasiparticle band gap and exciton binding energy of layered perovskites. We show that organic cations in quasi-two-dimensional perovskites contribute significantly to the dielectric screening in these systems, countering quantum confinement effects on the quasiparticle band gap and the exciton binding energy. Using a simple electrostatics model inspired by parallel-plate capacitors, we decouple the organic cation and inorganic layer contributions to the effective dielectric constants and show that dielectric properties of layered perovskites are broadly tunable via the interlayer cation, providing a direct means of tuning photophysical properties for a variety of applications.

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.

Signatures of Multiband Effects in High-Harmonic Generation in Monolayer MoS_{2}.

High-harmonic generation (HHG) in solids has been touted as a way to probe ultrafast dynamics and crystal symmetries in condensed matter systems. Here, we investigate the polarization properties of high-order harmonics generated in monolayer MoS_{2}, as a function of crystal orientation relative to the mid-infrared laser field polarization. At several different laser wavelengths we experimentally observe a prominent angular shift of the parallel-polarized odd harmonics for energies above approximately 3.5 eV, and our calculations indicate that this shift originates in subtle differences in the recombination dipole strengths involving multiple conduction bands. This observation is material specific and is in addition to the angular dependence imposed by the dynamical symmetry properties of the crystal interacting with the laser field, and may pave the way for probing the vectorial character of multiband recombination dipoles.

Signatures of Dimensionality and Symmetry in Exciton Band Structure: Consequences for Exciton Dynamics and Transport.

Exciton dynamics, lifetimes, and scattering are directly related to the exciton dispersion or band structure. Here, we present a general theory for exciton band structure within both ab initio and model Hamiltonian approaches. We show that contrary to common assumption, the exciton band structure contains nonanalytical discontinuities-a feature which is impossible to obtain from the electronic band structure 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, whose details depend on the exciton degeneracy and material thickness. We connect these features to the early stages of exciton dynamics, radiative lifetimes, and diffusion constants, in good correspondence with recent experimental observations, revealing that the discontinuities in the band structure lead to ultrafast ballistic transport and suggesting that measured exciton diffusion and dynamics are influenced by the underlying exciton dispersion.

Large Spin-Orbit Splitting of Deep In-Gap Defect States of Engineered Sulfur Vacancies in Monolayer WS_{2}.

Structural defects in 2D materials offer an effective way to engineer new material functionalities beyond conventional doping. We report on the direct experimental correlation of the atomic and electronic structure of a sulfur vacancy in monolayer WS_{2} by a combination of CO-tip noncontact atomic force microscopy and scanning tunneling microscopy. Sulfur vacancies, which are absent in as-grown samples, were deliberately created by annealing in vacuum. Two energetically narrow unoccupied defect states followed by vibronic sidebands provide a unique fingerprint of this defect. Direct imaging of the defect orbitals, together with ab initio GW calculations, reveal that the large splitting of 252±4 meV between these defect states is induced by spin-orbit coupling.

Orbital Symmetry and the Optical Response of Single-Layer MX Monochalcogenides.

We show that the absorption spectra of single-layer GaSe and GaTe in the hexagonal phase feature exciton peaks with distinct polarization selectivity. We investigate these distinct features from first-principles calculations using the GW-BSE formalism. We show that, because of the symmetry of the bands under in-plane mirror symmetry, the bound exciton states selectively couple to either in-plane or out-of-plane polarization of the light. In particular, for a p-polarized light absorption experiment, the absorption peaks of the hydrogenic s-like excitons emerge at large angle of incidence, while the overall absorbance reduces over the rest of the spectrum.

Defect-Induced Modification of Low-Lying Excitons and Valley Selectivity in Monolayer Transition Metal Dichalcogenides.

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.

Environmental Screening Effects in 2D Materials: Renormalization of the Bandgap, Electronic Structure, and Optical Spectra of Few-Layer Black Phosphorus.

Few-layer black phosphorus has recently emerged as a promising 2D semiconductor, notable for its widely tunable bandgap, highly anisotropic properties, and theoretically predicted large exciton binding energies. To avoid degradation, it has become common practice to encapsulate black phosphorus devices. It is generally assumed that this encapsulation does not qualitatively affect their optical properties. Here, we show that the contrary is true. We have performed ab initio GW and GW plus Bethe-Salpeter equation (GW-BSE) calculations to determine the quasiparticle (QP) band structure and optical spectrum of one-layer (1L) through four-layer (4L) black phosphorus, with and without encapsulation between hexagonal boron nitride and sapphire. We show that black phosphorus is exceptionally sensitive to environmental screening. Encapsulation reduces the exciton binding energy in 1L by as much as 70% and completely eliminates the presence of a bound exciton in the 4L structure. The reduction in the exciton binding energies is offset by a similarly large renormalization of the QP bandgap so that the optical gap remains nearly unchanged, but the nature of the excited states and the qualitative features of the absorption spectrum change dramatically.

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

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

Probing the role of interlayer coupling and coulomb interactions on electronic structure in few-layer MoSe2 nanostructures.

Despite the weak nature of interlayer forces in transition metal dichalcogenide (TMD) materials, their properties are highly dependent on the number of layers in the few-layer two-dimensional (2D) limit. Here, we present a combined scanning tunneling microscopy/spectroscopy and GW theoretical study of the electronic structure of high quality single- and few-layer MoSe2 grown on bilayer graphene. We find that the electronic (quasiparticle) bandgap, a fundamental parameter for transport and optical phenomena, decreases by nearly one electronvolt when going from one layer to three due to interlayer coupling and screening effects. Our results paint a clear picture of the evolution of the electronic wave function hybridization in the valleys of both the valence and conduction bands as the number of layers is changed. This demonstrates the importance of layer number and electron-electron interactions on van der Waals heterostructures and helps to clarify how their electronic properties might be tuned in future 2D nanodevices.

Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor.

Two-dimensional (2D) transition metal dichalcogenides (TMDs) are emerging as a new platform for exploring 2D semiconductor physics. Reduced screening in two dimensions results in markedly enhanced electron-electron interactions, which have been predicted to generate giant bandgap renormalization and excitonic effects. Here we present a rigorous experimental observation of extraordinarily large exciton binding energy in a 2D semiconducting TMD. We determine the single-particle electronic bandgap of single-layer MoSe2 by means of scanning tunnelling spectroscopy (STS), as well as the two-particle exciton transition energy using photoluminescence (PL) spectroscopy. These yield an exciton binding energy of 0.55 eV for monolayer MoSe2 on graphene­orders of magnitude larger than what is seen in conventional 3D semiconductors and significantly higher than what we see for MoSe2 monolayers in more highly screening environments. This finding is corroborated by our ab initio GW and Bethe-Salpeter equation calculations which include electron correlation effects. The renormalized bandgap and large exciton binding observed here will have a profound impact on electronic and optoelectronic device technologies based on single-layer semiconducting TMDs.