Exciton-Phonon Interaction and Relaxation Times from First Principles

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.

Topologically Protected Photovoltaics in Bi Nanoribbons

Photovoltaic efficiency in solar cells is hindered by many unwanted effects. Radiative channels (emission of photons) sometimes mediated by nonradiative ones (emission of phonons) are principally responsible for the decrease in exciton population before charge separation can take place. One such mechanism is electron-hole recombination at surfaces or defects where the in-gap edge states serve as the nonradiative channels. In topological insulators (TIs), which are rarely explored from an optoelectronics standpoint, we show that their characteristic surface states constitute a nonradiative decay channel that can be exploited to generate a protected photovoltaic current. Focusing on two-dimensional TIs, and specifically for illustration purposes on a Bi(111) monolayer, we obtain the transition rates from the bulk excitons to the edge states. By breaking the appropriate symmetries of the system, one can induce an edge charge accumulation and edge currents under illumination, demonstrating the potential of TI nanoribbons for photovoltaics.

Optical Absorption and Photoluminescence of Single-Layer Boron Nitride from a First-Principles Cumulant Approach

The photoluminescence spectrum of a single-layer boron nitride remains elusive, marked by enigmatic satellites that hint at significant but unidentified exciton-phonon coupling. Here, by employing a first-principles approach based on the many-body cumulant expansion of the charge response, we calculate the optical absorption and photoluminescence of a single-layer boron nitride. We identify the specific exciton-phonon scattering channels and unravel their impact on the optical absorption and photoluminescence spectra, thereby providing an interpretation of the experimental features. Finally, we show that, even in a strongly polar material such as h-BN monolayer, the electron-hole interaction responsible for the excitonic effect results in the cancellation of the Frölich interaction at small phonon momenta. This effect is captured only if the invariance of the exciton-phonon matrix elements under unitary transformations in the Bloch function manifold is preserved in the calculation.

Ultra-Confined Phonon Polaritons and Strongly Coupled Microcavity Exciton Polaritons in Monolayer MoSi2N4 and WSi2N4

The 2D semiconductors are an ideal platform for exploration of bosonic fluids composed of coupled photons and collective excitations of atoms or excitons, primarily due to large excitonic binding energies and strong light-matter interaction. Based on first-principles calculations, it is demonstrated that the phonon polaritons formed by two infrared-active phonon modes in monolayer MoSi2N4 and WSi2N4 possess ultra-high confinement factors of around ≈105 and 103, surpassing those of conventional polaritonic thin-film materials by two orders of magnitude. It is observed that the first bright exciton possesses a substantial binding energies of 750 and 740 meV in these two monolayers, with the radiative recombination lifetimes as long as 25 and 188 ns, and the Rabi splitting of the formed cavity-exciton polaritons reaching 373 and 321 meV, respectively. The effective masses of the cavity exciton polaritons are approximately 10-5me, providing the potential for high-temperature quantum condensation. The ultra-confined and ultra-low-loss phonon polaritons, as well as strongly-coupled cavity exciton polaritons with ultra-small polaritonic effective masses in these two monolayers, offering the flexible control of light at the nanoscale, probably leading to practical applications in nanophotonics, meta-optics, and quantum materials.

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.

Strong Exciton-Phonon Coupling as a Fingerprint of Magnetic Ordering in van der Waals Layered CrSBr

The layered, air-stable van der Waals antiferromagnetic compound CrSBr exhibits pronounced coupling among its optical, electronic, and magnetic properties. As an example, exciton dynamics can be significantly influenced by lattice vibrations through exciton-phonon coupling. Using low-temperature photoluminescence spectroscopy, we demonstrate the effective coupling between excitons and phonons in nanometer-thick CrSBr. By careful analysis, we identify that the satellite peaks predominantly arise from the interaction between the exciton and an optical phonon with a frequency of 118 cm-1 (∼14.6 meV) due to the out-of-plane vibration of Br atoms. Power-dependent and temperature-dependent photoluminescence measurements support exciton-phonon coupling and indicate a coupling between magnetic and optical properties, suggesting the possibility of carrier localization in the material. The presence of strong coupling between the exciton and the lattice may have important implications for the design of light-matter interactions in magnetic semiconductors and provide insights into the exciton dynamics in CrSBr. This highlights the potential for exploiting exciton-phonon coupling to control the optical properties of layered antiferromagnetic materials.

Ab Initio Predictions of Spin Relaxation, Dephasing, and Diffusion in Solids

Spin relaxation, dephasing, and diffusion are at the heart of spin-based information technology. Accurate theoretical approaches to simulate spin lifetimes (τs), determining how fast the spin polarization and phase information will be lost, are important to the understanding of the underlying mechanism of these spin processes, and invaluable in searching for promising candidates of spintronic materials. Recently, we develop a first-principles real-time density-matrix (FPDM) approach to simulate spin dynamics for general solid-state systems. Through the complete first-principles descriptions of light-matter interaction and scattering processes including electron-phonon, electron-impurity, and electron-electron scatterings with self-consistent spin-orbit coupling, as well as ab initio Landé g-factor, our method can predict τs at various conditions as a function of carrier density and temperature, under electric and magnetic fields. By employing this method, we successfully reproduce experimental results of disparate materials and identify the key factors affecting spin relaxation, dephasing, and diffusion in different materials. Specifically, we predict that germanene has long τs (∼100 ns at 50 K), a giant spin lifetime anisotropy, and spin-valley locking effect under electric fields, making it advantageous for spin-valleytronic applications. Based on our theoretical derivations and ab initio simulations, we propose a new useful electronic quantity, named spin-flip angle θ↑↓, for the understanding of spin relaxation through intervalley spin-flip scattering processes. Our method can be further applied to other emerging materials and extended to simulate exciton spin dynamics and steady-state photocurrents due to photogalvanic effect.

Excitonic Polarons and Self-Trapped Excitons from First-Principles Exciton-Phonon Couplings

Excitons consist of electrons and holes held together by their attractive Coulomb interaction. Although excitons are neutral excitations, spatial fluctuations in their charge density couple with the ions of the crystal lattice. This coupling can lower the exciton energy and lead to the formation of a localized excitonic polaron or even a self-trapped exciton in the presence of strong exciton-phonon interactions. Here, we develop a theoretical and computational approach to compute excitonic polarons and self-trapped excitons from first principles. Our methodology combines the many-body Bethe-Salpeter approach with density-functional perturbation theory and does not require explicit supercell calculations. As a proof of concept, we demonstrate our method for a compound of the halide perovskite family.

Distinguishing Different Stackings in Layered Materials via Luminescence Spectroscopy

Despite its simple crystal structure, layered boron nitride features a surprisingly complex variety of phonon-assisted luminescence peaks. We present a combined experimental and theoretical study on ultraviolet-light emission in hexagonal and rhombohedral bulk boron nitride crystals. Emission spectra of high-quality samples are measured via cathodoluminescence spectroscopy, displaying characteristic differences between the two polytypes. These differences are explained using a fully first-principles computational technique that takes into account radiative emission from "indirect," finite-momentum excitons via coupling to finite-momentum phonons. We show that the differences in peak positions, number of peaks, and relative intensities can be qualitatively and quantitatively explained, once a full integration over all relevant momenta of excitons and phonons is performed.

Ab initio real-time quantum dynamics of charge carriers in momentum space

Application of the non-adiabatic molecular dynamics (NAMD) approach is limited to studying carrier dynamics in the momentum space, as a supercell is required to sample the phonon excitation and electron-phonon (e-ph) interaction at different momenta in a molecular dynamics simulation. Here we develop an ab initio approach for the real-time charge carrier quantum dynamics in the momentum space (NAMD_k) by directly introducing e-ph coupling into the Hamiltonian based on the harmonic approximation. The NAMD_k approach maintains the zero-point energy and includes memory effects of carrier dynamics. The application of NAMD_k to the hot carrier dynamics in graphene reveals the phonon-specific relaxation mechanism. An energy threshold of 0.2 eV-defined by two optical phonon modes-separates the hot electron relaxation into fast and slow regions with lifetimes of pico- and nanoseconds, respectively. The NAMD_k approach provides an effective tool to understand real-time carrier dynamics in the momentum space for different materials.

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.

Intrinsic Control of Interlayer Exciton Generation in Van der Waals Materials via Janus Layers

We demonstrate the possibility of engineering the optical properties of transition metal dichalcogenide heterobilayers when one of the constitutive layers has a Janus structure. We investigate different MoS₂@Janus layer combinations using first-principles methods including excitons and exciton-phonon coupling. The direction of the intrinsic electric field from the Janus layer modifies the electronic band alignments and, consequently, the energy separation between dark interlayer exciton states and bright in-plane excitons. We find that in-plane lattice vibrations strongly couple the two states, so that exciton-phonon scattering may be a viable generation mechanism for interlayer excitons upon light absorption. In particular, in the case of MoS₂@WSSe, the energy separation of the low-lying interlayer exciton from the in-plane exciton is resonant with the transverse optical phonon modes (40 meV). We thus identify this heterobilayer as a prime candidate for efficient generation of charge-separated electron-hole pairs.

Hot carrier extraction from 2D semiconductor photoelectrodes

Hot carrier-based energy conversion systems could double the efficiency of conventional solar energy technology or drive photochemical reactions that would not be possible using fully thermalized, "cool" carriers, but current strategies require expensive multijunction architectures. Using an unprecedented combination of photoelectrochemical and in situ transient absorption spectroscopy measurements, we demonstrate ultrafast (<50 fs) hot exciton and free carrier extraction under applied bias in a proof-of-concept photoelectrochemical solar cell made from earth-abundant and potentially inexpensive monolayer (ML) MoS2. Our approach facilitates ultrathin 7 Å charge transport distances over 1 cm2 areas by intimately coupling ML-MoS2 to an electron-selective solid contact and a hole-selective electrolyte contact. Our theoretical investigations of the spatial distribution of exciton states suggest greater electronic coupling between hot exciton states located on peripheral S atoms and neighboring contacts likely facilitates ultrafast charge transfer. Our work delineates future two-dimensional (2D) semiconductor design strategies for practical implementation in ultrathin photovoltaic and solar fuel applications.

Exciton dispersion and exciton-phonon interaction in solids by time-dependent density functional theory

Understanding, predicting, and ultimately controlling exciton band structure and exciton dynamics are central to diverse chemical and materials problems. Here, we have developed a first-principles method to determine exciton dispersion and exciton-phonon interaction in semiconducting and insulating solids based on time-dependent density functional theory. The first-principles method is formulated in planewave bases and pseudopotentials and can be used to compute exciton band structures, exciton charge density, ionic forces, the non-adiabatic coupling matrix between excitonic states, and the exciton-phonon coupling matrix. Based on the spinor formulation, the method enables self-consistent noncollinear calculations to capture spin-orbital coupling. Hybrid exchange-correlation functionals are incorporated to deal with long-range electron-hole interactions in solids. A sub-Hilbert space approximation is introduced to reduce the computational cost without loss of accuracy. For validations, we have applied the method to compute the exciton band structure and exciton-phonon coupling strength in transition metal dichalcogenide monolayers; both agree very well with the previous GW-Bethe-Salpeter equation and experimental results. This development paves the way for accurate determinations of exciton dynamics in a wide range of solid-state materials.

Quantifying vibronic coupling with resonant inelastic X-ray scattering

Electron–phonon interactions are fundamental to the behavior of chemical and physical systems.

Non-adiabatic Exciton Dynamics in van der Waals Heterostructures

In this Perspective, we introduce a first-principles method that combines time-dependent density functional theory with non-adiabatic molecular dynamics (NAMD) to explore exciton dynamics in two-dimensional (2D) van der Waals (vdW) heterostructures. The theoretical foundation and computational efficiency of the method are discussed and compared with those of related methods (e.g., GW-BSE). Using three 2D vdW heterostructures as examples, we demonstrate that the proposed method can provide a reliable description of many-body electron-hole interactions crucial to exciton dynamics. With much lower computational costs than the GW-BSE method, the proposed method represents a particularly promising theoretical tool to probe exciton dynamics in solids. Moreover, we find that the NAMD simulations widely used in the literature cannot capture the excitonic effect in 2D materials and often yield incorrect results because they are formulated in a single-particle picture. The instances where the single-particle picture fails are pointed out and contrasted with the many-body simulation results.

Going beyond the Cumulant Approximation: Power Series Correction to the Single-Particle Green's Function in the Holstein System

In the context of a single-electron two orbital Holstein system coupled to dispersionless bosons, we develop a general method to correct the single-particle Green's function using a power series correction (PSC) scheme. We outline the derivations of various flavors of cumulant approximation through the PSC scheme explaining the assumptions and approximations behind them. Finally, we compare the PSC spectral function with cumulant and exact diagonalized spectral functions and elucidate three regimes of this problem-two where the cumulant explains and one where the cumulant fails. We find that the exact and the PSC spectral functions match within spectral broadening across all three regimes.

Vibronic Exciton-Phonon States in Stack-Engineered van der Waals Heterojunction Photodiodes

Stack engineering, an atomic-scale metamaterial strategy, enables the design of optical and electronic properties in van der Waals heterostructure devices. Here we reveal the optoelectronic effects of stacking-induced strong coupling between atomic motion and interlayer excitons in WSe₂/MoSe₂ heterojunction photodiodes. To do so, we introduce the photocurrent spectroscopy of a stack-engineered photodiode as a sensitive technique for probing interlayer excitons, enabling access to vibronic states typically found only in molecule-like systems. The vibronic states in our stack are manifest as a palisade of pronounced periodic sidebands in the photocurrent spectrum in frequency windows close to the interlayer exciton resonances and can be shifted "on demand" through the application of a perpendicular electric field via a source-drain bias voltage. The observation of multiple well-resolved sidebands as well as their ability to be shifted by applied voltages vividly demonstrates the emergence of interlayer exciton vibronic structure in a stack-engineered optoelectronic device.

First-Principles Study of the Optical Dipole Trap for Two-Dimensional Excitons in Graphane

Recent studies on excitons in two-dimensional materials have been widely conducted for their potential usages for novel electronic and optical devices. Especially, sophisticated manipulation techniques of quantum degrees of freedom of excitons are in demand. In this Letter we propose a technique of forming an optical dipole trap for excitons in graphane, a two-dimensional wide gap semiconductor, based on first-principles calculations. We develop a first-principles method to evaluate the transition dipole matrix between excitonic states and combine it with the density functional theory and GW+BSE calculations. We reveal that in graphane the huge exciton binding energy and the large dipole moments of Wannier-like excitons enable us to induce the dipole trap of the order of meV depth and μm width. This Letter opens a new way to control light-exciton interacting systems based on newly developed numerically robust ab initio calculations.

Unconventional excitonic states with phonon sidebands in layered silicon diphosphide

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

Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods

We benchmark a set of quantum-chemistry methods, including multitrajectory Ehrenfest, fewest-switches surface-hopping, and multiconfigurational-Ehrenfest dynamics, against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model. This is a paradigmatic model in condensed matter theory incorporating a local coupling of electrons to Einstein phonons. For the two-site and three-site Holstein model, we discuss the exact and quantum-chemistry methods in terms of the Born-Huang formalism, covering different initial states, which either start on a single Born-Oppenheimer surface, or with the electron localized to a single site. For extended systems with up to 51 sites, we address both the physics of single Holstein polarons and the dynamics of charge-density waves at finite electron densities. For these extended systems, we compare the quantum-chemistry methods to exact dynamics obtained from time-dependent density matrix renormalization group calculations with local basis optimization (DMRG-LBO). We observe that the multitrajectory Ehrenfest method, in general, only captures the ultrashort time dynamics accurately. In contrast, the surface-hopping method with suitable corrections provides a much better description of the long-time behavior but struggles with the short-time description of coherences between different Born-Oppenheimer states. We show that the multiconfigurational Ehrenfest method yields a significant improvement over the multitrajectory Ehrenfest method and can be converged to the exact results in small systems with moderate computational efforts. We further observe that for extended systems, this convergence is slower with respect to the number of configurations. Our benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the quality of the quantum-chemistry methods.

Solving the time-independent Schrödinger equation for chains of coupled excitons and phonons using tensor trains

We demonstrate how to apply the tensor-train format to solve the time-independent Schrödinger equation for quasi-one-dimensional excitonic chain systems with and without periodic boundary conditions. The coupled excitons and phonons are modeled by Fröhlich-Holstein type Hamiltonians with on-site and nearest-neighbor interactions only. We reduce the memory consumption as well as the computational costs significantly by employing efficient decompositions to construct low-rank tensor-train representations, thus mitigating the curse of dimensionality. In order to compute also higher quantum states, we introduce an approach that directly incorporates the Wielandt deflation technique into the alternating linear scheme for the solution of eigenproblems. Besides systems with coupled excitons and phonons, we also investigate uncoupled problems for which (semi-)analytical results exist. There, we find that in the case of homogeneous systems, the tensor-train ranks of state vectors only marginally depend on the chain length, which results in a linear growth of the storage consumption. However, the central processing unit time increases slightly faster with the chain length than the storage consumption because the alternating linear scheme adopted in our work requires more iterations to achieve convergence for longer chains and a given rank. Finally, we demonstrate that the tensor-train approach to the quantum treatment of coupled excitons and phonons makes it possible to directly tackle the phenomenon of mutual self-trapping. We are able to confirm the main results of the Davydov theory, i.e., the dependence of the wave packet width and the corresponding stabilization energy on the exciton-phonon coupling strength, although only for a certain range of that parameter. In future work, our approach will allow calculations also beyond the validity regime of that theory and/or beyond the restrictions of the Fröhlich-Holstein type Hamiltonians.

Conditional Wave Function Theory: A Unified Treatment of Molecular Structure and Nonadiabatic Dynamics

We demonstrate that a conditional wave function theory enables a unified and efficient treatment of the equilibrium structure and nonadiabatic dynamics of correlated electron-ion systems. The conditional decomposition of the many-body wave function formally recasts the full interacting wave function of a closed system as a set of lower-dimensional (conditional) coupled "slices". We formulate a variational wave function ansatz based on a set of conditional wave function slices and demonstrate its accuracy by determining the structural and time-dependent response properties of the hydrogen molecule. We then extend this approach to include time-dependent conditional wave functions and address paradigmatic nonequilibrium processes including strong-field molecular ionization, laser-driven proton transfer, and nuclear quantum effects induced by a conical intersection. This work paves the road for the application of conditional wave function theory in equilibrium and out-of-equilibrium ab initio molecular simulations of finite and extended systems.

Organic-2D Material Heterostructures: A Promising Platform for Exciton Condensation and Multiplication

We predict that high temperature Bose-Einstein condensation of charge transfer excitons can be achieved in organic-two-dimensional (2D) material heterostructures, at ∼50-100 K. Unlike 2D bilayers that can be angle-misaligned, organic-2D systems generally have momentum-direct low-energy excitons, thus favoring condensation. Our predictions are obtained for ZnPc-MoS₂ using state-of-the-art first-principles calculations with the GW-BSE approach. The exciton energies we predict are in excellent agreement with recent experiments. The lowest energy charge transfer excitons in ZnPc-MoS₂ are strongly bound with a spatial extent of ∼1-2 nm and long lifetimes (τ₀ ∼ 1 ns), making them ideal for exciton condensation. We also predict the emergence of inter-ZnPc excitons that are stabilized by the interaction of the molecules with the 2D substrate. This novel way of stabilizing intermolecular excitons by indirect substrate mediation suggests design strategies for singlet fission and exciton multiplication, which are important to overcome the Shockley-Queisser efficiency limit in solar cells.

Computational design of quantum defects in two-dimensional materials

Missing atoms or atom substitutions (point defects) in crystal lattices in two-dimensional (2D) materials are potential hosts for emerging quantum technologies, such as single-photon emitters and spin quantum bits (qubits). First-principles-guided design of quantum defects in 2D materials is paving the way for rational spin qubit discovery. Here we discuss the frontier of first-principles theory development and the challenges in predicting the critical physical properties of point defects in 2D materials for quantum information technology, in particular for optoelectronic and spin-optotronic properties. Strong many-body interactions at reduced dimensionality require advanced electronic structure methods beyond mean-field theory. The great challenges for developing theoretical methods that are appropriate for strongly correlated defect states, as well as general approaches for predicting spin relaxation and the decoherence time of spin defects, are yet to be addressed.

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.

Revealing momentum-dependent electron-phonon and phonon-phonon coupling in complex materials with ultrafast electron diffuse scattering

ABSTRACT

Despite their fundamental role in determining many important properties of materials, detailed momentum-dependent information on the strength of electron-phonon and phonon-phonon coupling across the entire Brillouin zone has remained elusive. Ultrafast electron diffuse scattering (UEDS) is a recently developed technique that is making a significant contribution to these questions. Here, we describe both the UEDS methodology and the information content of ultrafast, photoinduced changes in phonon-diffuse scattering from single-crystal materials. We present results obtained from Ni, WSe₂, and TiSe₂, materials that are characterized by a complex interplay between electronic (charge, spin) and lattice degrees of freedom. We demonstrate the power of this technique by unraveling carrier-phonon and phonon-phonon interactions in both momentum and time and following nonequilibrium phonon dynamics in detail on ultrafast time scales. By combining ab initio calculations with ultrafast diffuse electron scattering, insights into electronic and magnetic dynamics that impact UEDS indirectly can also be obtained.

The role of chalcogen vacancies for atomic defect emission in MoS2

For two-dimensional (2D) layered semiconductors, control over atomic defects and understanding of their electronic and optical functionality represent major challenges towards developing a mature semiconductor technology using such materials. Here, we correlate generation, optical spectroscopy, atomic resolution imaging, and ab initio theory of chalcogen vacancies in monolayer MoS2. Chalcogen vacancies are selectively generated by in-vacuo annealing, but also focused ion beam exposure. The defect generation rate, atomic imaging and the optical signatures support this claim. We discriminate the narrow linewidth photoluminescence signatures of vacancies, resulting predominantly from localized defect orbitals, from broad luminescence features in the same spectral range, resulting from adsorbates. Vacancies can be patterned with a precision below 10 nm by ion beams, show single photon emission, and open the possibility for advanced defect engineering of 2D semiconductors at the ultimate scale.