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We consider structural vector autoregressions identified through stochastic volatility. Our focus is on whether a particular structural shock is identified by heteroskedasticity without the need to impose any sign or exclusion restrictions. Three contributions emerge from our exercise: (i) a set of conditions under which the matrix containing structural parameters is partially or globally unique; (ii) a statistical procedure to assess the validity of the conditions mentioned above; and (iii) a shrinkage prior distribution for conditional variances centred on a hypothesis of homoskedasticity. Such a prior ensures that the evidence for identifying a structural shock comes only from the data and is not favoured by the prior. We illustrate our new methods using a U.S. fiscal structural model.

The exploration of two-dimensional (2D) antiferromagnetic (AFM) materials has shown great promise and interest in tuning the magnetic and electronic properties as well as studying magneto-optical effects. The current work investigates the control of magneto-optical interactions in alloyed MnxZn1-xPS3 lamellar semiconductor single crystals, with the Mn/Zn ratio regulating the coupling strength. Magnetic susceptibility results show a retention of AFM order followed by a decrease in N\'eel temperatures down to ~ 40% Mn concentration, below which a paramagnetic behavior is observed. Absorption measurements reveal an increase in bandgap energy with higher Zn(II) concentration, and the presence of Mn(II) d-d transition below the absorption edge. DFT+U approach qualitatively explained the origin and the position of the experimentally observed mid band-gap states in pure MnPS3, and corresponding peaks visible in the alloyed systems MnxZn1-xPS3. Accordingly, emission at 1.3 eV in all alloyed compounds results from recombination from a 4T1g Mn(II) excited state to a hybrid p-d state at the valence band. Most significant, temperature-dependent photoluminescence (PL) intensity trends demonstrate strong magneto-optical coupling in compositions with x > 0.65. This study underscores the potential of tailored alloy compositions as a means to control magnetic and optical properties in 2D materials, paving the way for advances in spin-based technologies.

The effect of pressure on Raman scattering (RS) in the bulk HfS$_2$ is investigated under hydrostatic and non-hydrostatic conditions. The RS lineshape does not change significantly in the hydrostatic regime, showing a systematic blueshift of the spectral features. In a non-hydrostatic environment, seven peaks emerge in the spectrum ($P$=7 GPa) dominating the lineshape up to $P$=10.5 GPa. The change in the RS lineshape manifests a pressure-induced phase transition in HfS$_2$. The simultaneous observation of both low-pressure (LP) and high-pressure (HP) related RS peaks suggests the corresponding coexistence of two different phases over a large pressure range. We found that the HP-related phase is metastable, persisting during the decompression cycle down to $P$=1.2 GPa with the LP-related features finally recovering at even lower pressures. The angle-resolved polarized RS (ARPRS) performed under $P$=7.4 GPa revealed a strong in-plane anisotropy of both the LP-related A$_{1g}$ mode and the HP peaks. The anisotropy is related to the possible distortion of the structure induced by the non-hydrostatic component of the pressure. We describe the obtained results by the influence of the non-hydrostatic pressure on the observed phase transition. We interpret our results in terms of a distorted $Pnma$ phase as a possible HP induced structure of HfS$_2$.

We investigate the vibrational and magnetic properties of thin layers of chromium tribromide (CrBr$_3$) with a thickness ranging from three to twenty layers (3~L to 20~L) revealed by the Raman scattering (RS) technique. Systematic dependence of the RS process efficiency on the energy of the laser excitation is explored for four different excitation energies: 1.96 eV, 2.21 eV, 2.41 eV, and 3.06 eV. Our characterization demonstrates that for 12 L CrBr$_3$, 3.06~eV excitation could be considered resonant with interband electronic transitions due to the enhanced intensity of the Raman-active scattering resonances and the qualitative change in the Raman spectra. Polarization-resolved RS measurements for 12 L CrBr$_3$ and first-principles calculations allow us to identify five observable phonon modes characterized by distinct symmetries, classified as the A$_\textrm{g}$ and E$_\textrm{g}$ modes. The evolution of phonon modes with temperature for a 20 L CrBr$_3$ encapsulated in hexagonal boron nitride flakes demonstrates alterations of phonon energies and/or linewidths of resonances indicative of a transition between the paramagnetic and ferromagnetic state at Curie temperature ($T_\textrm{C} \approx 50$ K). The exploration of the effects of thickness on the phonon energies demonstrated small variations pronounces exclusively for the thinnest layers in the vicinity of 3 - 5 L. This observation is attributed to strong localization in the real space of interband electronic excitations, limiting the effects of confinement for resonantly excited Raman modes to atomically thin layers., Comment: 12 pages, 5 figures

We propose a new Bayesian heteroskedastic Markov-switching structural vector autoregression with data-driven time-varying identification. The model selects alternative exclusion restrictions over time and, as a condition for the search, allows to verify identification through heteroskedasticity within each regime. Based on four alternative monetary policy rules, we show that a monthly six-variable system supports time variation in US monetary policy shock identification. In the sample-dominating first regime, systematic monetary policy follows a Taylor rule extended by the term spread, effectively curbing inflation. In the second regime, occurring after 2000 and gaining more persistence after the global financial and COVID crises, it is characterized by a money-augmented Taylor rule. This regime's unconventional monetary policy provides economic stimulus, features the liquidity effect, and is complemented by a pure term spread shock. Absent the specific monetary policy of the second regime, inflation would be over one percentage point higher on average after 2008., Comment: Keywords: Structural VARs, Markov Switching, Identification Via Heteroskedasticity, Extended Taylor Rule, Effects of Monetary Policy JEL classification: C11, C32, E52

The recent synthesis of MoSi2N4 material, along with theoretical predictions encompassing the entire family of chemical analogs, has opened up a new array of low-dimensional materials for a diverse range of optoelectronics and photovoltaics applications. In this study, we conducted state-of-the-art many-body first-principles calculations to analyze the quasi-particle electronic structure of the material class MSi2Z4 (where M = Mo, W, and Z = N, P, As, Sb). All monolayers display a direct band gap at the K point, with the exception of MoSi2N4. In tungsten-based compounds, the fundamental-gap can be adjusted over a significantly broader energy range compared to their molybdenum-based counterparts. Additionally, increasing atomic weight of the Z, both the band gap and exciton binding energies decrease. A noteworthy feature is the absence of a lateral valley ({\Lambda} or Q) near the conduction band minimum, indicating potential higher photoluminescence efficiencies compared to conventional transition-metal dichalcogenide monolayers. The optical spectra of these materials are predominantly characterized by tightly bound excitons, leading to an absorption onset in the visible range (for N-based) and in the infrared region (for others). This diversity offers promising opportunities to incorporate these materials and their heterostructures into optoelectronic devices, with tandem solar cells being particularly promising.

Here we systematically investigate the impact of the spin direction on the electronic and optical properties of transition metal phosphorus trichalcogenides (MPX$_3$, M=Mn, Ni, Fe; X=S, Se) exhibiting various antiferromagnetic arrangement within the 2D limit. Our analysis based on the density functional theory and versatile formalism of Bethe-Salpeter equation reveals larger exciton binding energies for MPS$_3$ (up to 1.1 eV in air) than MPSe$_3$(up to 0.8 eV in air), exceeding the values of transition metal dichalcogenides (TMDs). For the (Mn,Fe)PX$_3$ we determine the optically active band edge transitions, revealing that they are sensitive to in-plane magnetic order, irrespective of the type of chalcogen atom. We predict the anistropic effective masses and the type of linear polarization as an important fingerprints for sensing the type of magnetic AFM arrangements. Furthermore, we identify the spin-orientation-dependent features such as the valley splitting, the effective mass of holes, and the exciton binding energy. In particular, we demonstrate that for MnPX$_3$ (X=S, Se) a pair of non equivalent K+ and K- points exists yielding the valley splittings that strongly depend on the direction of AFM aligned spins. Notably, for the out-of-plane direction of spins, two distinct peaks are expected to be visible below the absorption onset, whereas one peak should emerge for the in-plane configuration of spins. These spin-dependent features provide an insight into spin flop transitions of 2D materials. Finally, we propose a strategy how the spin valley polarization can be realized in 2D AFM within honeycomb lattice., Comment: 20 pages, 8 figures, 11 tables

Raman scattering (RS) in bulk hafnium disulfide (HfS$_2$) is investigated as a function of temperature (5 K $-$ 350 K) with polarization resolution and excitation of several laser energies. An unexpected temperature dependence of the energies of the main Raman-active (A$_{\textrm{1g}}$ and E$_{\textrm{g}}$) modes with the temperature-induced blueshift in the low-temperature limit is observed. The low-temperature quenching of a mode $\omega_1$ (134 cm$^{-1}$) and the emergence of a new mode at approx. 184 cm$^{-1}$, labeled Z, is reported. The optical anisotropy of the RS in HfS$_2$ is also reported, which is highly susceptible to the excitation energy. The apparent quenching of the A$_{\textrm{1g}}$ mode at $T$=5 K and of the E$_{\textrm{g}}$ mode at $T$=300 K in the RS spectrum excited with 3.06~eV excitation is also observed. We discuss the results in the context of possible resonant character of light-phonon interactions. Analyzed is also a possible effect of the iodine molecules intercalated in the van der Waals gaps between neighboring HfS$_2$ layers, which inevitably result from the growth procedure., Comment: 9 pages, 7 figures +SI

Excitons in thin layers of semiconducting transition metal dichalcogenides are highly subject to the strongly modified Coulomb electron-hole interaction in these materials. Therefore, they do not follow the model system of a two-dimensional hydrogen atom. We investigate experimentally and theoretically excitonic properties in both the monolayer (ML) and the bilayer (BL) of MoSe$_2$ encapsulated in hexagonal BN. The measured magnetic field evolutions of the reflectance contrast spectra of the MoSe$_2$ ML and BL allow us to determine $g$-factors of intralayer A and B excitons, as well as the $g$-factor of the interlayer exciton. We explain the dependence of $g$-factors on the number of layers and excitation state using first principles calculations. Furthermore, we demonstrate that the experimentally measured ladder of excitonic $s$ states in the ML can be reproduced using the $\mathbf{k\cdot p}$ approach with the Rytova-Keldysh potential that describes the electron-hole interaction. In contrast, the analogous calculation for the BL case requires taking into account the out-of-plane dielectric response of the MoSe$_2$ BL., Comment: 10 pages, 4 figures, + SM

Optical measurements under externally applied stresses allow us to study the materials' electronic structure by comparing the pressure evolution of optical peaks obtained from experiments and theoretical calculations. We examine the stress-induced changes in electronic structure for the thermodynamically stable 1T polytype of selected MX2 compounds (M=Hf, Zr, Sn; X=S, Se), using the density functional theory. We demonstrate that considered 1T-MX2 materials are semiconducting with indirect character of the band gap, irrespective to the employed pressure as predicted using modified Becke-Johnson potential. We determine energies of direct interband transitions between bands extrema and in band-nesting regions close to Fermi level. Generally, the studied transitions are optically active, exhibiting in-plane polarization of light. Finally, we quantify their energy trends under external hydrostatic, uniaxial, and biaxial stresses by determining the linear pressure coefficients. Generally, negative pressure coefficients are obtained implying the narrowing of the band gap. The semiconducting-to-metal transition are predicted under hydrostatic pressure. We discuss these trends in terms of orbital composition of involved electronic bands. In addition, we demonstrate that the measured pressure coefficients of HfS2 and HfSe2 absorption edges are in perfect agreement with our predictions. Comprehensive and easy-to-interpret tables containing the optical features are provided to form the basis for assignation of optical peaks in future measurements., Comment: 19 pages, 9 figures, 71 references. This is the author created version of an article accepted for publication in Nanomaterials (MDPI) journal. The article has been published on a gold open access basis under a CC BY 4.0 licence

MA2Z4 monolayers form a new class of hexagonal non-centrosymmetric materials hosting extraordinary spin-valley physics. While only two compounds (MoSi2N4 and WSi2N4) were recently synthesized, theory predicts interesting (opto)electronic properties of a whole new family of such two-dimensional materials. Here, the chemical trends of band gaps and spin-orbit splittings of bands in selected MSi2Z4 (M = Mo, W; Z = N, P, As, Sb) compounds are studied from first-principles. Effective Bethe-Salpeter-equation-based calculations reveal high exciton binding energies. Evolution of excitonic energies under external magnetic field is predicted by providing their effective g-factors and diamagnetic coefficients, which can be directly compared to experimental values. In particular, large positive g-factors are predicted for excitons involving higher conduction bands. In view of these predictions, MSi2Z4 monolayers yield a new platform to study excitons and are attractive for optoelectronic devices, also in the forms of heterostructures. In addition, a spin-orbit induced bands inversion is observed in the heaviest studied compound, WSi2Sb4, a hallmark of its topological nature.

The temperature evolution of the resonant Raman scattering from high-quality bilayer 2H-MoS$_{2}$ encapsulated in hexagonal BN flakes is presented. The observed resonant Raman scattering spectrum as initiated by the laser energy of 1.96 eV, close to the A excitonic resonance, shows rich and distinct vibrational features that are otherwise not observed in non-resonant scattering. The appearance of 1$^{st}$ and 2$^{nd}$ order phonon modes is unambiguously observed in a broad range of temperatures from 5 K to 320 K. The spectrum includes the Raman-active modes, $i.e.$ E$_\textrm{1g}^{2}$($\Gamma$) and A$_\textrm{1g}$($\Gamma$) along with their Davydov-split counterparts, $i.e.$ E$_\textrm{1u}$($\Gamma$) and B$_\textrm{1u}$($\Gamma$). The temperature evolution of the Raman scattering spectrum brings forward key observations, as the integrated intensity profiles of different phonon modes show diverse trends. The Raman-active A$_{1g}$($\Gamma$) mode, which dominates the Raman scattering spectrum at $T$=5~K quenches with increasing temperature. Surprisingly, at room temperature the B$_\textrm{1u}$($\Gamma$) mode, which is infrared-active in the bilayer, is substantially stronger than its nominally Raman-active A$_\textrm{1g}$($\Gamma$) counterpart., Comment: 7 pages, 3 figures

The optical properties of two-dimensional materials can be effectively tuned by strain induced from a deformable substrate. In the present work we combine first-principles calculations based on density functional theory and the effective Bethe-Salpeter equation with high-pressure optical measurements in order to thoroughly describe the effect of strain and dielectric environment onto the electronic band structure and optical properties of a few-layered transition metal dichalcogenide. Our results show that WS2 remains fully adhered to the substrate at least up to a -0.6% in-plane compressive strain for a wide range of substrate materials. We provide a useful model to describe effect of strain on the optical gap energy. The corresponding experimentally-determined out-of-plane and in-plane stress gauge factors for WS2 monolayers are -8 and 24 meV/GPa, respectively. The exceptionally large in-plane gauge factor confirm transition metal dichalcogenides as very promising candidates for flexible functionalities. Finally, we discuss the pressure evolution of an optical transition closely-lying to the A exciton for bulk WS2 as well as the direct-to-indirect transition of the monolayer upon compression., Comment: 39 pages, 13 figures

The optical response of bulk germanium sulfide (GeS) is investigated systematically using different polarization-resolved experimental techniques, such as photoluminescence (PL), reflectance contrast (RC), and Raman scattering (RS). It is shown that while the low-temperature ($T$=5 K) optical band-gap absorption is governed by a single resonance related to the neutral exciton, the corresponding emission is dominated by the disorder/impurity- and/or phonon-assisted recombination processes. Both the RC and PL spectra are found to be linearly polarized along the armchair direction. The low and room ($T$=300 K) temperature RS spectra consist of six Raman peaks identified with the help of Density Fuctional Theory (DFT) calculations: A$^1_{\textrm{g}}$, A$^2_{\textrm{g}}$, A$^3_{\textrm{g}}$, A$^4_{\textrm{g}}$, B$^1_{\textrm{1g}}$, and B$^2_{\textrm{1g}}$, which polarization properties are studied under four different excitation energies. We found that the polarization orientations of the A$^2_{\textrm{g}}$ and A$^4_{\textrm{g}}$ modes under specific excitation energy can be useful tools to determine the GeS crystallographic directions: armchair and zigzag., Comment: 7 pages, 7 figures

Lamellar structures of transition metal phosphorus trisulfides possess strong intralayer bonding, albeit adjacent layers are held by weak van der Waals interactions. Those compounds received enormous interest due to their unique combination of optical and long-range magnetic properties. Among them, iron phosphorus trisulfide (FePS$_3$) gathered special attention for being a semiconductor with an absorption edge in the near-infrared, as well as showing an Ising-like anti-ferromagnetism. We report a successful growth of centimeter size bulk FePS$_3$ crystals with a chemical yield above 70%, whose crystallographic structure and composition were carefully identified by advanced electron microscopy methodologies, including atomic resolution elemental mapping, along with photoelectron spectroscopy. The knowledge on the optical activity of FePS$_3$ is extended utilizing temperature-dependent absorption and photoacoustic spectroscopies, while measurements were corroborated with density-functional theory calculations. Temperature-dependent experiments showed a small and monotonic band-edge energy shift down to 115 K and exposed the interconnected importance of electron-phonon coupling. Most of all, the correlation between the optical behavior and the magnetic phase transition is revealed, which shows the practical utilization of temperature-dependent optical absorption to investigate magnetic interactions., Comment: 40 pages, 13 figures, 1 table

Markov switching models are a popular family of models that introduces time-variation in the parameters in the form of their state- or regime-specific values. Importantly, this time-variation is governed by a discrete-valued latent stochastic process with limited memory. More specifically, the current value of the state indicator is determined only by the value of the state indicator from the previous period, thus the Markov property, and the transition matrix. The latter characterizes the properties of the Markov process by determining with what probability each of the states can be visited next period, given the state in the current period. This setup decides on the two main advantages of the Markov switching models. Namely, the estimation of the probability of state occurrences in each of the sample periods by using filtering and smoothing methods and the estimation of the state-specific parameters. These two features open the possibility for improved interpretations of the parameters associated with specific regimes combined with the corresponding regime probabilities, as well as for improved forecasting performance based on persistent regimes and parameters characterizing them., Comment: Keywords: Transition Probabilities, Exogenous Markov Switching, Infinite Hidden Markov Model, Endogenous Markov Switching, Markov Process, Finite Mixture Model, Change-point Model, Non-homogeneous Markov Switching, Time Series Analysis, Business Cycle Analysis

External fields are a powerful tool to probe optical excitations in a material. The linear energy shift of an excitation in a magnetic field is quantified by its effective g-factor. Here we show how exciton g-factors and their sign can be determined by converged first principles calculations. We apply the method to monolayer excitons in semiconducting transition metal dichalcogenides and to interlayer excitons in MoSe$_2$/WSe$_2$ heterobilayers and obtain good agreement with recent experimental data. The precision of our method allows to assign measured g-factors of optical peaks to specific transitions in the band structure and also to specific regions of the samples. This revealed the nature of various, previously measured interlayer exciton peaks. We further show that, due to specific optical selection rules, g-factors in van der Waals heterostructures are strongly spin- and stacking-dependent. The calculation of orbital angular momenta requires the summation over hundreds of bands, indicating that for the considered two-dimensional materials the basis set size is a critical numerical issue. The presented approach can potentially be applied to a wide variety of semiconductors., Comment: 29 pages, 4 figures, 2 tables

We report the experimental observation of radiative recombination from Rydberg excitons in a two-dimensional semiconductor, monolayer WSe2, encapsulated in hexagonal boron nitride. Excitonic emission up to the 4s excited state is directly observed in photoluminescence spectroscopy in an out-of-plane magnetic field up to 31 Tesla. We confirm the progressively larger exciton size for higher energy excited states through diamagnetic shift measurements. This also enables us to estimate the 1s exciton binding energy to be about 170 meV, which is significantly smaller than most previous reports. The Zeeman shift of the 1s to 3s states, from both luminescence and absorption measurements, exhibits a monotonic increase of g-factor, reflecting nontrivial magnetic-dipole-moment differences between ground and excited exciton states. This systematic evolution of magnetic dipole moments is theoretically explained from the spreading of the Rydberg states in momentum space.

In this study, Bayesian inference is developed for structural vector autoregressive models in which the structural parameters are identified via Markov-switching heteroskedasticity. In such a model, restrictions that are just-identifying in the homoskedastic case, become over-identifying and can be tested. A set of parametric restrictions is derived under which the structural matrix is globally or partially identified and a Savage-Dickey density ratio is used to assess the validity of the identification conditions. The latter is facilitated by analytical derivations that make the computations fast and numerical standard errors small. As an empirical example, monetary models are compared using heteroskedasticity as an additional device for identification. The empirical results support models with money in the interest rate reaction function., Comment: Keywords: Identification Through Heteroskedasticity, Bayesian Hypotheses Assessment, Markov-switching Models, Mixture Models, Regime Change

We propose a new marginal data density estimator (MDDE) that uses the variational Bayes posterior density as a weighting density of the reciprocal importance sampling (RIS) MDDE. This computationally convenient estimator is based on variational Bayes posterior densities that are available for many models and requires simulated draws only from the posterior distribution. It provides accurate estimates with a moderate number of posterior draws, has a finite variance, and provides a minimum variance candidate for the class of RIS MDDEs. Its reciprocal is consistent, asymptotically normally distributed, and unbiased. These properties are obtained without truncating the weighting density, which is typical for other such estimators. Our proposed estimators outperform many existing MDDEs in terms of bias and numerical standard errors. In particular, our RIS MDDE performs uniformly better than other estimators from this class.

By combining experimental photoluminescence excitation spectroscopy and calculations based on density functional theory and many-body Green's functions, the most efficient excitation channels of infra-red (IR) emission from Mn-Mg$_{k}$ paramagnetic complexes stabilized in GaN:(Mn,Mg) are here identified. Moreover, a Tanabe-Sugano energy diagram for 3$d^{2}$Mn$ ^{5+}$ is reconstructed and Mn-Mg$_{3}$ are singled out as the predominant configurations responsible for the IR emission. The correlation of intensity of the individual emission lines as a function of temperature and excitation energy, allows assigning them to well defined and specific optical transitions., Comment: 17 pages, 6 figures, 45 references