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Resolving the early-stage dynamics of exciton formation following non-resonant photoexcitation in time, energy, and momentum is quite challenging due to their inherently fast timescales and the proximity of the excitonic state to the bottom of the conduction band. In this study, by combining time- and angle-resolved photoemission spectroscopy with \mathit{ab initio} numerical simulations, we capture the timing of the early-stage exciton dynamics in energy and momentum, starting from the photoexcited population in the conduction band, progressing through the formation of free excitons, and ultimately leading to their trapping in lattice deformations. The chosen material is bismuth tri-iodide ($BiI_3$), a layered semiconductor with a rich landscape of excitons in the electronic structure both in bulk and in monolayer form. The obtained results, providing a full characterization of the exciton formation, elucidate the early stages of the physical phenomena underlying the operation of the ultrafast semiconductor device.

Layered two-dimensional (2D) materials have revolutionized how we approach light-matter interactions, offering unprecedented optical and electronic properties with the potential for vertical heterostructures and manipulation of spin-valley degrees of freedom. The discovery of moir\'e physics in twisted heterostructures has further unlocked new possibilities for controlling the band structure of tailored semiconductor heterostructures. In parallel, the integration of 2D materials with hybrid photonic structures and ultrafast studies on their optical and spin-valley properties has revealed a wealth of novel physical phenomena. This perspective highlights the recent advances in our understanding of light-matter interactions in moir\'e and 2D systems, with a particular emphasis on ultrafast processes and the integration of these materials into photonic platforms. We explore the implications for optoelectronics and emerging photonic technologies, positioning 2D materials as a transformative tool for next-generation devices.

The study of open-shell nanographenes has relied on a paradigm where spins are the only low-energy degrees of freedom. Here we show that some nanographenes can host low-energy excitations that include strongly coupled spin and orbital degrees of freedom. The key ingredient is the existence of orbital degeneracy, as a consequence of leaving the benzenoid/half-filling scenario. We analyze the case of nitrogen-doped triangulenes, using both density-functional theory and Hubbard model multiconfigurational and random-phase approximation calculations. We find a rich interplay between orbital and spin degrees of freedom that confirms the need to go beyond the spin-only paradigm, opening a new venue in this field of research., Comment: 6 pages, 4 figures

The measurement and manipulation of the coherent dynamics of excitonic states constitute a forefront research challenge in semiconductor optics and in quantum coherence-based protocols for optoelectronic technologies. Layered semiconductors have emerged as an ideal platform for the study of exciton dynamics with accessible and technologically relevant energy and time scales. Here, we investigate the sub-picosecond exciton dynamics in a van-der-Waals semiconductor upon quasi-resonant excitation, and achieve to single out an incipient coherent excitonic state. Combining broadband transient reflectance spectroscopy and simulations based on many-body perturbation theory, we reveal a transient enhancement of the excitonic line intensity that originates from the photoinduced coherent polarization that is phase-locked with the interacting electromagnetic field. This finding allows us to define the spectral signature of a coherent excitonic state and to experimentally track the dynamical crossover from coherent to incoherent exciton, unlocking the prospective optical control of an exciton population on the intrinsic quantum-coherence timescale.

We carry out a detailed theoretical study of the electronic and optical properties of bulk and monolayer bismuth triiodide (BiI$_{3}$), a layered metal halide, using the ab initio GW+BSE scheme with a full spinorial formulation. We discuss in detail the effects due to the change of dimensionality and the role of spin-orbit coupling. Moreover, we compute the exciton dispersion by solving the BSE at finite momentum, also analysing transverse (TE) and longitudinal (LE) excitons, and the L-T splitting at $\bf{q}\approx\Gamma$. The results provide a reference for future experimental measurements. In addition, the interplay between spin-orbit coupling and large binding energy, together with the role of quantum confinement, confirm that BiI$_{3}$ is an interesting material for opto-electronic applications and show that it is a good candidate for the study of exciton dynamics., Comment: 12 pages, 8 figures

We provide a comprehensive theory of magnetic phases in two-dimensional triangulene crystals, using both Hubbard model and density functional theory (DFT) calculations. We consider centrosymmetric and non-centrosymmetric triangulene crystals. In all cases, DFT and mean-field Hubbard model predict the emergence of broken-symmetry antiferromagnetic (ferrimagnetic) phases for the centrosymmetric (non-centrosymmetric) crystals. This includes the special case of the [4,4]triangulene crystal, whose non-interacting energy bands feature a gap with flat valence and conduction bands. We show how the lack of contrast between the local density of states of these bands, recently measured via scanning tunneling spectroscopy, is a natural consequence of a broken-symmetry N\'eel state that blocks intermolecular hybridization. Using random phase approximation, we also compute the spin wave spectrum of these crystals, including the recently synthesized [4,4]triangulene crystal. The results are in excellent agreement with the predictions of a Heisenberg spin model derived from multi-configuration calculations for the unit cell. We conclude that experimental results are compatible with an antiferromagnetically ordered phase where each triangulene retains the spin predicted for the isolated species.

The coupling of the electron system to lattice vibrations and their time-dependent control and detection provides unique insight into the non-equilibrium physics of semiconductors. Here, we investigate the ultrafast transient response of semiconducting monolayer 2$H$-MoTe$_2$ encapsulated with $h$BN using broadband optical pump-probe microscopy. The sub-40-fs pump pulse triggers extremely intense and long-lived coherent oscillations in the spectral region of the A' and B' exciton resonances, up to $\sim$20% of the maximum transient signal, due to the displacive excitation of the out-of-plane $A_{1g}$ phonon. Ab-initio calculations reveal a dramatic rearrangement of the optical absorption of monolayer MoTe$_2$ induced by an out-of-plane stretching and compression of the crystal lattice, consistent with an $A_{1g}$-type oscillation. Our results highlight the extreme sensitivity of the optical properties of monolayer TMDs to small structural modifications and their manipulation with light., Comment: 27 pages, 4 figures, supporting information

In this work we perform a detailed first-principles analysis of the electronic and optical properties of NiBr$_2$ within the state-of-the-art $GW$+BSE scheme to determine whether this system displays negative excitonic energies, which would identify it as an (half) excitonic insulator. Particular attention is payed to the convergence of the $GW$ band structure and to the consistency between approximations employed in the ground-state calculations and approximations employed in the linear response calculations. We show that these two issues play a crucial role in identifying the excitonic nature of NiBr$_2$.

Bandgap engineering and quantum confinement in semiconductor heterostructures provide the means to fine-tune material response to electromagnetic fields and light in a wide range of the spectrum. Nonetheless, forming semiconductor heterostructures on lattice-mismatched substrates has been a challenge for several decades, leading to restrictions for device integration and the lack of efficient devices in important wavelength bands. Here, we show that the van der Waals epitaxy of two-dimensional (2D) GaSe and InSe heterostructures occur on substrates with substantially different lattice parameters, namely silicon and sapphire. The GaSe/InSe heterostructures were applied in the growth of quantum wells and superlattices presenting photoluminescence and absorption related to interband transitions. Moreover, we demonstrate a self-powered photodetector based on this heterostructure on Si that works in the visible-NIR wavelength range. Fabricated at wafer-scale, these results pave the way for an easy integration of optoelectronics based on these layered 2D materials in current Si technology., Comment: 16 Pages, 5 figures. Supplementary Information included in the end (+10 pages, +10 Figures, + 2 Tables). Partially presented at 21st ICMBE - September 2021

To calculate the conductivity of a material having full knowledge of its composition is a reasonably simple task. To do the same in reverse, i.e., to find information about the composition of a device from its conductivity response alone, is very challenging and even more so in the presence of disorder. An inversion methodology capable of decoding the information contained in the conductivity response of disordered structures has been recently proposed but despite claims of generality and robustness, the method has only been used with 2D systems possessing relatively simple electronic structures. Here we put these claims to the test and generalise the inversion method to the case of monolayer MoS$_2$, a material whose electronic structure is far more complex and elaborate. Starting from the spectral function that describes the DC conductivity of a disordered sample of a single layered MoS$_2$ containing a small concentration of randomly dispersed vacancies, we are able to invert the signal and find the exact composition of defects with an impressive degree of accuracy. Remarkably, equally accurate results are obtained with the optical conductivity. This is indicative of a methodology that is indeed suitable to extract composition information from different 2D materials, regardless of their electronic structure complexity. Calculated conductivity results were used as a proxy for their experimental counterpart and were obtained with an efficient quantum transport code (KITE) based on a real-space multi-orbital tight-binding model with parameters generated by density functional theory., Comment: Main: 7 pages, 3 figures Suplemental Material: 2 pages, 4 figures Accepted and in process of being published in New Journal of Physics

The coupling of excitons with atomic vibrations plays a pivotal role on the nonequilibrium optical properties of layered semiconductors. However, addressing the dynamical interaction between excitons and phonons represents a hard task both experimentally and theoretically. By means of time-resolved broadband optical reflectivity combined with state-of-the-art ab-initio calculations of a bismuth triiodide single crystal, we unravel the universal spectral fingerprints of exciton--phonon coupling in layered semiconductors. Furthermore, we microscopically relate a photoinduced coherent energy modulation of the excitonic resonance to coherent optical phonons, thereby tracking the extent of the photoinduced atomic displacement in real-space. Our findings represent a step forward on the road to coherent manipulation of the excitonic properties on ultrafast timescales.

We report first-principles calculations of the structural and vibrational properties of the synthesized two-dimensional van der Waals heterostructures formed by single-layers dichalcogenides MoSe2 and WSe2. We show that, when combining these systems in a periodic two-dimensional heterostructures, the intrinsic phonon characteristics of the free-standing constituents are to a large extent preserved but, furthermore, exhibit shear and breathing phonon modes that are not present in the individual building blocks. These peculiar modes depend strongly on the weak vdW forces and has a great contibution to the thermal properties of the layered materials. Besides these features, the departure of flexural modes of heterobilayer from the ones of its monolayer parents are also found., Comment: 7 pages, 5 figures

We study the electronic properties of the heterobilayer of vanadium and iron oxychlorides, VOCl and FeOCl, two layered air stable van der Waals insulating oxides with different types of antiferromagnetic order in bulk: VOCl monolayers are ferromagnetic (FM) whereas the FeOCl monolayers are antiferromagnetic (AF). We use density functional theory (DFT) calculations, with Hubbard correction that is found to be needed to describe correctly the insulating nature of these compounds. We compute the magnetic anisotropy and propose a spin model Hamiltonian. Our calculations show that interlayer coupling in weak and ferromagnetic so that magnetic order of the monolayers is preserved in the heterobilayers providing thereby a van der Waals heterostructure that combines two monolayers with different magnetic order. Interlayer exchange should lead both to exchange bias and to the emergence of hybrid collective modes that that combine FM and AF magnons. The energy band of the heterobilayer show a type II band alignment, and feature spin-splitting of the states of the AF layer due to the breaking of the inversion symmetry., Comment: 6 pages, 3 figures

In many paradigmatic materials, like Transition Metal Dichalcogenides, the role played by the spin degrees of freedom is as important as the one played by the electron-electron interaction. Thus an accurate treatment of the two effects and of their interaction is necessary for an accurate and predictive study of the optical and electronic properties of these materials. Despite the GW-BSE approach correctly accounts for electronic correlations the spin-orbit coupling effect is often neglected or treated perturbatively. Recently spinorial formulations of GW-BSE have become available in different flavours in material-science codes. Still an accurate validation and comparison of different approaches is missing. In this work we go through the derivation of non collinear GW-BSE approach. The scheme is applied to transition metal dichalcogenides comparing perturbative and full spinorial approach. Our calculations reveal that dark-bright exciton splittings are generally improved when the spin orbit coupling is included non perturbatively. The exchange-driven intravalley mixing between the A and B exciton is found to be extremely important in the case of MoSe$_2$. We finally define the excitonic spin and use it to sharply analyze the spinorial properties of Transition Metal Dichalcogenides excitonic states., Comment: 22 pages, 4 figures

The manipulation of light emitted by two-dimensional semiconductors grounds forthcoming technologies in the field of on-chip communications. However, these technologies require from the so elusive out-of-plane photon sources to achieve an efficient coupling of radiated light into planar devices. Here we propose a versatile spectroscopic method that enables the identification of the out-of-plane component of dipoles. The method is based on the selective coupling of light emitted by in-plane and out-of-plane dipoles to the whispering gallery modes of spherical dielectric microresonators, in close contact to them. We have applied this method to demonstrate the existence of dipoles with an out-of-plane orientation in monolayer WSe2 at room temperature. Micro-photoluminescent measurements, numerical simulations based on finite element methods, and ab-initio calculations have identified trions as the source responsible for this out-of-plane emission, opening new routes for realizing on-chip integrated systems with applications in information processing and quantum communications., Comment: 21 pages, 4 figures

We calculate the time evolution of the transient reflection signal in an MoS$_2$ monolayer on a SiO$_2$/Si substrate using first-principles out-of-equilibrium real-time methods. Our simulations provide a simple and intuitive physical picture for the delayed, yet ultrafast, evolution of the signal whose rise time depends on the excess energy of the pump laser: at laser energies above the A- and B-exciton, the pump pulse excites electrons and holes far away from the K valleys in the first Brillouin zone. Electron-phonon and hole-phonon scattering lead to a gradual relaxation of the carriers towards small $\textit{Active Excitonic Regions}$ around K, enhancing the dielectric screening. The accompanying time-dependent band gap renormalization dominates over Pauli blocking and the excitonic binding energy renormalization. This explains the delayed buildup of the transient reflection signal of the probe pulse, in excellent agreement with recent experimental data. Our results show that the observed delay is not a unique signature of an exciton formation process but rather caused by coordinated carrier dynamics and its influence on the screening.

Semiconducting ferromagnet-nonmagnet interfaces in van der Waals heterostructures present a unique opportunity to investigate magnetic proximity interactions dependent upon a multitude of phenomena including valley and layer pseudospins, moir\'e periodicity, or exceptionally strong Coulomb binding. Here, we report a charge-state dependency of the magnetic proximity effects between MoSe$_2$ and CrBr$_3$ in photoluminescence, whereby the valley polarization of the MoSe$_2$ trion state conforms closely to the local CrBr$_3$ magnetization, while the neutral exciton state remains insensitive to the ferromagnet. We attribute this to spin-dependent interlayer charge transfer occurring on timescales between the exciton and trion radiative lifetimes. Going further, we uncover by both the magneto-optical Kerr effect and photoluminescence a domain-like spatial topography of contrasting valley polarization, which we infer to be labyrinthine or otherwise highly intricate, with features smaller than 400 nm corresponding to our optical resolution. Our findings offer a unique insight into the interplay between short-lived valley excitons and spin-dependent interlayer tunnelling, while also highlighting MoSe$_2$ as a promising candidate to optically interface with exotic spin textures in van der Waals structures.

We show that H-phase transition metal dichalcogenides (TMDs) monolayers such as MoS$_2$ and WSe$_2$, are orbital Hall insulators. They present very large orbital Hall conductivity plateaus in their semiconducting gap, where the spin Hall conductivity vanishes. Our results open the possibility of using TMDs for orbital current injection and orbital torque transfers that surpass their spin-counterparts in spin-orbitronics devices. The orbital Hall effect (OHE) in TMD monolayers occurs even in the absence of spin-orbit coupling. It can be linked to exotic momentum-space Dresselhaus-like orbital textures, analogous to the spin-momentum locking in 2D Dirac fermions that arise from a combination of orbital attributes and lattice symmetry., Comment: main text with 6 pages and 3 figures, and a Supplementary material

We present a transient absorption setup combining broadband detection over the visible-UV range with high temporal resolution ($\sim$20fs) which is ideally suited to trigger and detect vibrational coherences in different classes of materials. We generate and detect coherent phonons (CPs) in single layer (1L) MoS$_2$, as a representative semiconducting 1L-transition metal dichalcogenide (TMD), where the confined dynamical interaction between excitons and phonons is unexplored. The coherent oscillatory motion of the out-of-plane $A'_{1}$ phonons, triggered by the ultrashort laser pulses, dynamically modulates the excitonic resonances on a timescale of few tens fs. We observe an enhancement by almost two orders of magnitude of the CP amplitude when detected in resonance with the C exciton peak, combined with a resonant enhancement of CP generation efficiency. Ab initio calculations of the change in 1L-MoS$_2$ band structure induced by the $A'_{1}$ phonon displacement confirm a strong coupling with the C exciton. The resonant behavior of the CP amplitude follows the same spectral profile of the calculated Raman susceptibility tensor. This demonstrates that CP excitation in 1L-MoS$_2$ can be described as a Raman-like scattering process. These results explain the CP generation process in 1L-TMDs, paving the way for coherent all-optical control of excitons in layered materials in the THz frequency range.

Chromium trihalides (CrI$_3$, CrBr$_3$ and CrCl$_3$) form a prominent family of isostructural insulating layered materials in which ferromagnetic order has been observed down to the monolayer. Here we provide a comprehensive computational study of magneto-optical properties that are used as probes for the monolayer ferromagnetic order: magnetic circular dichroism and magneto-optic Kerr effect. Using a combination of density functional and Bethe-Salpeter theories, we calculate both the optical absorption and the magneto-optical Kerr angle spectra, including both excitonic effects and spinorial wave functions. We compare the magneto-optical response of the chromium trihalides series and we find that its strength is governed by the spin-orbit coupling of the ligand atoms (I, Br, Cl).

Van der Waals heterostructures offer attractive opportunities to design quantum materials. For instance, transition metal dichalcogenides (TMDs) possess three quantum degrees of freedom: spin, valley index, and layer index. Further, twisted TMD heterobilayers can form moir\'e patterns that modulate the electronic band structure according to atomic registry, leading to spatial confinement of interlayer exciton (IXs). Here we report the observation of spin-layer locking of IXs trapped in moir\'e potentials formed in a heterostructure of bilayer 2H-MoSe$_2$ and monolayer WSe$_2$. The phenomenon of locked electron spin and layer index leads to two quantum-confined IX species with distinct spin-layer-valley configurations. Furthermore, we observe that the atomic registries of the moir\'e trapping sites in the three layers are intrinsically locked together due to the 2H-type stacking characteristic of bilayer TMDs. These results identify the layer index as a useful degree of freedom to engineer tunable few-level quantum systems in two-dimensional heterostructures., Comment: 10 pages, 4 figures. Supplementary Material available at: https://www.dropbox.com/s/8331cfoasdofwkq/Brotons-Gisbert_Suppl_Info.pdf?dl=0

yambo is an open source project aimed at studying excited state properties of condensed matter systems from first principles using many-body methods. As input, yambo requires ground state electronic structure data as computed by density functional theory codes such as quantum-espresso and abinit. yambo's capabilities include the calculation of linear response quantities (both independent-particle and including electron-hole interactions), quasi-particle corrections based on the GW formalism, optical absorption, and other spectroscopic quantities. Here we describe recent developments ranging from the inclusion of important but oft-neglected physical effects such as electron-phonon interactions to the implementation of a real-time propagation scheme for simulating linear and non-linear optical properties. Improvements to numerical algorithms and the user interface are outlined. Particular emphasis is given to the new and efficient parallel structure that makes it possible to exploit modern high performance computing architectures. Finally, we demonstrate the possibility to automate workflows by interfacing with the yambopy and AiiDA software tools.

Van der Waals materials offer a wide range of atomic layers with unique properties that can be easily combined to engineer novel electronic and photonic devices. A missing ingredient of the van der Waals platform is a two-dimensional crystal with naturally occurring out-of-plane luminescent dipole orientation. Here we measure the far-field photoluminescence intensity distribution of bulk InSe and two-dimensional InSe, WSe$_2$ and MoSe$_2$. We demonstrate, with the support of ab-initio calculations, that layered InSe flakes sustain luminescent excitons with an intrinsic out-of-plane orientation, in contrast with the in-plane orientation of dipoles we find in two-dimensional WSe$_2$ and MoSe$_2$ at room-temperature. These results, combined with the high tunability of the optical response and outstanding transport properties, position layered InSe as a promising semiconductor for novel optoelectronic devices, in particular for hybrid integrated photonic chips which exploit the out-of-plane dipole orientation., Comment: Published in Nature Communications. 12 pages, 5 figures. Link: https://www.nature.com/articles/s41467-019-11920-4

Hybrid organic/inorganic perovskites have emerged as efficient semiconductor materials for applications in photovoltaic solar cells with conversion efficiency above 20 \%. Recent experiments have synthesized ultra-thin two-dimensional (2D) organic perovskites with optical properties similar to those of 2D materials like monolayer MoS$_2$: large exciton binding energy and excitonic effects at room temperature. In addition, 2D perovskites are synthesized with a simple fabrication process with potential low-cost and large-scale manufacture. Up to now, state-of-the-art simulations of the excitonic states have been limited to the study of bulk organic perovskites. A large number of atoms in the unit cell and the complex role of the organic molecules make inefficient the use of \textit{ab initio} methods. In this work, we define a simplified crystal structure to calculate the optical properties of 2D perovskites, replacing the molecular cations with inorganic atoms. We can thus apply state-of-the-art, parameter-free and predictive \textit{ab initio} methods like the GW method and the Bethe-Salpeter equation to obtain the excitonic states of a model 2D perovskite. We find that optical properties of 2D perovskites are strongly influenced by excitonic effects, with binding energies up to 600 meV. Moreover, the optical absorption is carried out at the bromine and lead atoms and therefore the results are useful for a qualitatively understanding of the optical properties of organic 2D perovskites., Comment: 4 figures

We present an \textit{ab initio} method to calculate phonon-assisted absorption and emission spectra in the presence of strong excitonic effects. We apply the method to bulk hexagonal BN which has an indirect band gap and is known for its strong luminescence in the UV range. We first analyse the excitons at the wave vector $\overline{q}$ of the indirect gap. The coupling of these excitons with the various phonon modes at $\overline{q}$ is expressed in terms of a product of the mean square displacement of the atoms and the second derivative of the optical response function with respect to atomic displacement along the phonon eigenvectors. The derivatives are calculated numerically with a finite difference scheme in a supercell commensurate with $\overline{q}$. We use detailed balance arguments to obtain the intensity ratio between emission and absorption processes. Our results explain recent luminescence experiments and reveal the exciton-phonon coupling channels responsible for the emission lines., Comment: Main text: 5 pages, 3 figures. The supplementary material (10 pages, 11 figures) follows the main text

In monolayer Transition Metal Dichalcogenides (TMDs) the valence and conduction bands are spin split because of the strong spin-orbit interaction. In tungsten-based TMDs the spin-ordering of the conduction band is such that the so-called dark exciton, consisting of an electron and a hole with opposite spin orientation, has lower energy than the A exciton. A possible mechanism leading to the transition from bright to dark excitons involves the scattering of the electrons from the upper to the lower conduction band state in K. Here we exploit the valley selective optical selection rules and use two-color helicity-resolved pump-probe spectroscopy to directly measure the intravalley spin-flip relaxation dynamics of electrons in the conduction band of single-layer WS$_2$. This process occurs on a sub-ps time scale and it is significantly dependent on the temperature, indicative of a phonon-assisted relaxation. These experimental results are supported by time-dependent ab-initio calculations which show that the intra-valley spin-flip scattering occurs on significantly longer time scales only exactly at the K point. In a realistic situation the occupation of states away from the minimum of the conduction band leads to a dramatic reduction of the scattering time.

Accurately described excitonic properties of transition metal dichalcogenide heterobilayers (HBLs) are crucial to comprehend the optical response and the charge carrier dynamics of them. Excitons in multilayer systems posses inter or intralayer character whose spectral positions depend on their binding energy and the band alignment of the constituent single-layers. In this study, we report the electronic structure and the absorption spectra of MoS$_2$/WS$_2$ and MoSe$_2$/WSe$_2$ HBLs from first-principles calculations. We explore the spectral positions, binding energies and the origins of inter and intralayer excitons and compare our results with experimental observations. The absorption spectra of the systems are obtained by solving the Bethe-Salpeter equation on top of a G$_0$W$_0$ calculation which corrects the independent particle eigenvalues obtained from density functional theory calculations. Our calculations reveal that the lowest energy exciton in both HBLs possesses interlayer character which is decisive regarding their possible device applications. Due to the spatially separated nature of the charge carriers, the binding energy of inter-layer excitons might be expected to be considerably smaller than that of intra-layer ones. However, according to our calculations the binding energy of lowest energy interlayer excitons is only $\sim$ 20\% lower due to the weaker screening of the Coulomb interaction between layers of the HBLs. Therefore, it can be deduced that the spectral positions of the interlayer excitons with respect to intralayer ones are mostly determined by the band offset of the constituent single-layers. By comparing oscillator strengths and thermal occupation factors, we show that in luminescence at low temperature, the interlayer exciton peak becomes dominant, while in absorption it is almost invisible., Comment: 17 pages, 4 figures

Hexagonal boron nitride (hBN) has been attracting great attention because of its strong excitonic effects. Taking into account few-layer systems, we investigate theoretically the effects of the number of layers on quasiparticle energies, absorption spectra, and excitonic states, placing particular focus on the Davydov splitting of the lowest bound excitons. We describe how the inter-layer interaction as well as the variation in electronic screening as a function of layer number $N$ affects the electronic and optical properties. Using both \textit{ab initio} simulations and a tight-binding model for an effective Hamiltonian describing the excitons, we characterize in detail the symmetry of the excitonic wavefunctions and the selection rules for their coupling to incoming light. We show that for $N > 2$, one can distinguish between surface excitons that are mostly localized on the outer layers and inner excitons, leading to an asymmetry in the energy separation between split excitonic states. In particular, the bound surface excitons lie lower in energy than their inner counterparts. Additionally, this enables us to show how the layer thickness affects the shape of the absorption spectrum., Comment: 24 pages, 10 figures

In single-layer WSe$_2$, a paradigmatic semiconducting transition metal dichalcogenide, a circularly polarized laser field can selectively excite electronic transitions in one of the inequivalent $K^{\pm}$ valleys. Such selective valley population corresponds to a pseudospin polarization. This can be used as a degree of freedom in a valleytronic device provided that the time scale for its depolarization is sufficiently large. Yet, the mechanism behind the valley depolarization still remains heavily debated. Recent time-dependent Kerr experiments have provided an accurate way to visualize the valley dynamics by measuring the rotation of a linearly polarized probe pulse applied after a circularly polarized pump pulse. We present here a clear, accurate and parameter-free description of the valley dynamics. By using an atomistic, ab initio, approach we fully disclose the elemental mechanisms that dictate the depolarization effects. Our results are in excellent agreement with recent time-dependent Kerr experiments. We explain the Kerr dynamics and its temperature dependence in terms of electron-phonon mediated processes that induce spin-flip inter-valley transitions.