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Semiconducting transition metal dichalcogenides of group VI are well-known for their prominent excitonic effects and the transition from an indirect to a direct band gap when reduced to monolayers. While considerable efforts have elucidated the Rydberg series of excitons in monolayers, understanding their properties in multilayers remains incomplete. In these structures, despite an indirect band gap, momentum-direct excitons largely shape the optical response. In this work, we combine magneto-reflectance experiments with theoretical modeling based on the $\mathbf {k\cdot p}$ approach to investigate the origin of excitonic resonances in WSe$_2$ bi-, tri-, and quadlayers. For all investigated thicknesses, we observe a series of excitonic resonances in the reflectance spectra, initiated by a ground state with an amplitude comparable to the ground state of the 1$s$ exciton in the monolayer. Higher energy states exhibit a decrease in intensity with increasing energy, as expected for the excited states of the Rydberg series, although a significant increase in the diamagnetic shift is missing in tri- and quadlayers. By comparing the experimental observations with theoretical predictions, we discover that the excitonic resonances observed in trilayers originate from two Rydberg series, while quadlayers exhibit four such series, and bilayers host a single Rydberg series similar to that found in monolayers., Comment: 31 pages, 16 figures, published in Phys. Rev. B

The optically dark states play an important role in the electronic and optical properties of monolayers (MLs) of semiconducting transition metal dichalcogenides. The effect of temperature on the in-plane-field activation of the neutral and charged dark excitons is investigated in a WSe$_2$ ML encapsulated in hexagonal BN flakes. The brightening rates of the neutral dark (X$^D$) and grey (X$^G$) excitons and the negative dark trion (T$^D$) differ substantially at a particular temperature. More importantly, they vanish considerably by about 3 -- 4 orders of magnitude with the temperature increased from 4.2 K to 100 K. The quenching of the dark-related emissions is accompanied by the two-order-of-magnitude increase in the emissions of their neutral bright counterparts, $i.e.$ neutral bright exciton (X$^B$) and spin-singlet (T$^S$) and spin-triplet (T$^T$) negative trions, due to the thermal activations of dark states. Furthermore, the energy splittings between the dark X$^D$ and T$^D$ complexes and the corresponding bright X$^B$, T$^S$, and T$^T$ ones vary with temperature rises from 4.2 K to 100 K. This can be explained in terms of the different exciton-phonon couplings for the bright and dark excitons stemming from their distinct symmetry properties., Comment: Main text: 6 pages, 4 figures. Supplementary: 5 pages, 4 figures

The interaction between light and matter in condensed matter excitations and electromagnetic resonators serves as a rich playground for fundamental research and lies at the core of photonic and quantum technologies. Herein, we present comprehensive experimental and theoretical studies of the photon-mediated hybridization of magnons and phonons in the terahertz (THz) range. We demonstrate the intriguing concept of composite states formed by distinct electric and magnetic quasiparticles strongly coupled to the same optical cavity modes. Specifically, we explore magnons excited in a slab of an antiferromagnetic crystal and phonons excited in a distinct specimen of an insulating material. The crystal slabs form an optical cavity with Fabry-P\'erot oscillations in the THz range. We demonstrate hybridized phonon-magnon polariton modes and their tunability by adjusting the distance between the slabs, showing that hybridization persists even at separations up to several millimeters. The experimental results are interpreted using both classical and quantum electrodynamical models. The quantum description allows us to quantify the degree of hybridization that is linked to a topological behavior of the electric field phasor, in agreement with the classical electrodynamics expectations. Importantly, the presented results refer to temperature conditions and cavities of millimeter size, paving the way for engineering realistic, frequency-tunable THz devices through the hybridization of electric (phononics) and magnetic (spintronics) elementary excitations of matter.

Raman scattering excitation (RSE) is an experimental technique in which the spectrum is made up by sweeping the excitation energy when the detection energy is fixed. We study the low-temperature ($T$=5~K) RSE spectra measured on four high quality monolayers (ML) of semiconducting transition metal dichalcogenides (S-TMDs), $i.e.$ MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$, encapsulated in hexagonal BN. The outgoing resonant conditions of Raman scattering reveal an extraordinary intensity enhancement of the phonon modes, which results in extremely rich RSE spectra. The obtained spectra are composed not only of Raman-active peaks, $i.e.$ in-plane E$'$ and out-of-plane A$'_1$, but the appearance of 1$^{st}$, 2$^{nd}$, and higher-order phonon modes is recognised. The intensity profiles of the A$'_1$ modes in the investigated MLs resemble the emissions due to neutral excitons measured in the corresponding PL spectra for the outgoing type of resonant Raman scattering conditions. Furthermore, for the WSe$_2$ ML, the A$'_1$ mode was observed when the incoming light was in resonance with the neutral exciton line. The strength of the exciton-phonon coupling (EPC) in S-TMD MLs strongly depends on the type of their ground excitonic state, $i.e.$ bright or dark, resulting in different shapes of the RSE spectra. Our results demonstrate that RSE spectroscopy is a powerful technique for studying EPC in S-TMD MLs., Comment: 9 pages, 6 figures, ESI

Magnon gap excitations selectively coupled to phonon modes have been studied in FePSe$_3$ layered antiferromagnet with magneto-Raman scattering experiments performed at different temperatures. The bare magnon excitation in this material has been found to be split (by $\approx~1.2$ cm$^{-1}$) into two components each being selectively coupled to one of the two degenerated, nearby phonon modes. Lifting the degeneracy of the fundamental magnon mode points out toward the biaxial character of the FePS$_3$ antiferromagnet, with an additional in-plane anisotropy complementing much stronger, out-of-plane anisotropy. Moreover, the tunability, with temperature, of the phonon- versus the magnon-like character of the observed coupled modes has been demonstrated., Comment: 7 pages, 5 figures

Optical magneto-spectroscopy methods (Raman scattering, far-infrared transmission, and photoluminescence) have been applied to investigate the properties of the NiPS3 semiconducting antiferromagnet. The fundamental magnon gap excitation in this van der Waals material has been found to be split into two components, in support of the biaxial character of the NiPS3 antiferromagnet. Photoluminescence measurements in the near-infrared spectral range show that the intriguing 1.475 eV-excitation unique to the NiPS3 antiferromagnetic phase splits upon the application of the in-plane magnetic field. The observed splitting patterns are correlated with properties of magnon excitations and reproduced with the simple model proposed. Possible routes toward a firm identification of the spin-entangled 1.475 eV-optical excitation in NiPS3, which can hardly be recognized as a coherent Zhang-Rice exciton, are discussed., Comment: 8 pages, 8 figures

Employing the original, all-optical method, we quantify the magnetic susceptibility of a two-dimensional electron gas (2DEG) confined in the MoSe$_2$ monolayer in the range of low and moderate carrier densities. The impact of electron-electron interactions on the 2DEG magnetic susceptibility is found to be particularly strong in the limit of, studied in detail, low carrier densities. Following the existing models, we derive the value of $g_0 = 2.5 \pm 0.4$ for the bare (in the absence of the interaction effects) $g$-factor of the ground state electronic band in the MoSe$_2$ monolayer. The derived value of this parameter is discussed in the context of estimations from other experimental approaches. Surprisingly, the conclusions drawn differ from theoretical ab-initio studies.

Competition between exchange interactions and magnetocrystalline anisotropy may bring new magnetic states that are of great current interest. An applied hydrostatic pressure can further be used to tune their balance. In this work we investigate the magnetization process of a biaxial antiferromagnet in an external magnetic field applied along the easy axis. We find that the single metamagnetic transition of the Ising type observed in this material under ambient pressure transforms under hydrostatic pressure into two transitions, a first-order spin flop transition followed by a second order transition towards a polarized ferromagnetic state near saturation. This reversible tuning into a new magnetic phase is obtained in layered bulk CrSBr at low temperature by varying the interlayer distance using high hydrostatic pressure, which efficiently acts on the interlayer magnetic exchange, and is probed by magneto-optical spectroscopy., Comment: 3 Figures, 6 pages. To appear in ACS NanoLetters

Quantifying and controlling the coherent dynamics and couplings of optically active excitations in solids is of paramount importance in fundamental research in condensed matter optics and for their prospective optoelectronic applications in quantum technologies. Here, we perform ultrafast coherent nonlinear spectroscopy of a charge-tunable MoSe$_2$ monolayer. The experiments show that the homogeneous and inhomogeneous line width and the population decay of exciton complexes hosted by this material can be directly tuned by an applied gate bias, which governs the Fermi level and therefore the free carrier density. By performing two-dimensional spectroscopy, we also show that the same bias-tuning approach permits us to control the coherent coupling strength between charged and neutral exciton complexes.

We report on magneto-optical studies of the quasi-two-dimensional van der Waals antiferromagnet FePS$_3$. Our measurements reveal an excitation that closely resembles the antiferromagnetic resonance mode typical of easy-axis antiferromagnets, nevertheless, it displays an unusual, four-times larger Zeeman splitting in an applied magnetic field. We identify this excitation with an $|S_z|=4$ multipolar magnon -- a single-ion 4-magnon bound state -- that corresponds to a full reversal of a single magnetic moment of the Fe$^{2+}$ ion. We argue that condensation of multipolar magnons in large-spin materials with a strong magnetic anisotropy can produce new exotic states., Comment: 7 pages, 3 figures + supplement

The possibility of almost linear tuning of the band gap and of the electrical and optical properties in monolayers (MLs) of semiconducting transition metal dichalcogenide (S-TMD) alloys opens up the way to fabricate materials with on-demand characteristics. By making use of photoluminescence spectroscopy, we investigate optical properties of WSSe MLs with a S/Se ratio of 57/43 deposited on SiO$_2$/Si substrate and encapsulated in hexagonal BN flakes. Similarly to the $"parent"$ WS$_2$ and WSe$_2$ MLs, we assign the WSSe MLs to the ML family with the dark ground exciton state. We find that, in addition to the neutral bright A exciton line, three observed emission lines are associated with negatively charged excitons. The application of in-plane and out-of-plane magnetic fields allows us to assign undeniably the bright and dark (spin- and momentum-forbidden) negative trions as well as the phonon replica of the dark spin-forbidden complex. Furthermore, the existence of the single photon emitters in the WSSe ML is also demonstrated, thus prompting the opportunity to enlarge the wavelength range for potential future quantum applications of S-TMDs., Comment: 6 pages, 5 figures, +ESI

We perform a polarization-resolved magnetoluminescence study of excitons in ReS$_2$. We observe that two linearly polarized Rydberg series of excitons are accompanied by two other Rydberg series of dark excitons, brightened by an in-plane magnetic field. All series extrapolate to the same single-electron bandgap, indicating that the observed excitons originate either from the same valley or from two valleys related by the inversion symmetry, and are split by exchange interaction. To interpret our observations of the magnetic brightening, we have to assume the dominant spin-orbit coupling to be Ising-like, which hints at an approximate symmetry of the electronic states in ReS$_2$ which is higher than the crystal symmetry $C_i$., Comment: 16 pages, 8 figures

Magnetic layered materials have emerged recently as promising systems to introduce magnetism in structures based on two-dimensional (2D) materials and to investigate exotic magnetic ground states in the 2D limit. In this work, we apply high hydrostatic pressures up to P = 8.7 GPa to the bulk layered antiferromagnet FePS$_3$ to tune the collective lattice excitations (phonons) in resonance with magnetic excitations (magnons). Close to P = 4 GPa, the magnon-phonon resonance is achieved and the strong coupling between these collective modes leads to the formation of new quasi-particles, the magnon-polarons, evidenced in our low temperature Raman scattering experiments by a particular avoided crossing behavior between the phonon and the doubly degenerate antiferromagnetic magnon. At the pressure-induced magnon-phonon resonance, three distinct coupled modes emerge. As it is mainly defined by intralayer properties, we show that the energy of the magnon is nearly pressure independent. We additionally apply high magnetic fields up to B = 30 T to fully identify and characterize the magnon excitations, and to explore the different magnon-polaron regimes for which the phonon has an energy lower-, equal to-, or higher- than the magnon energy. The description of our experimental data requires introducing a phonon-phonon coupling not taken into account in actual calculations., Comment: 11 pages + 6 pages of supplementary materials

We demonstrate a novel electro-luminescence device in which GaN-based $\mu$-LEDs are used to trigger the emission spectra of monolayers of transition metal dichalcogenides, which are deposited directly on the $\mu$-LED surface. A special $\mu$-LED design enables the operation of our structures even in the limit of low temperatures. A device equipped with a selected WSe$_2$ monolayer flake is shown to act as a stand-alone, electrically-driven single-photon source., Comment: 6 pages, 4 figures

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

We present an experimental set-up developed to perform optical spectroscopy experiments (Raman scattering and photoluminescence measurements) with a micrometer spatial resolution, in an extreme environment of low temperature, high magnetic field and high pressure. This unique experimental setup, to the best of our knowledge, allows us to explore deeply the phase diagram of condensed matter systems by tuning independently these three thermodynamic parameters, while monitoring the low-energy excitations (electronic, phononic or magnetic excitations), to spatially map the Raman scattering response or to investigate objects with low dimensions. We apply this technique to bulk FePS3, a layered antiferromagnet with a Neel temperature of T = 120 K., Comment: 5 pages, 5 figures

Optical response of crystalline solids is to a large extent driven by excitations that promote electrons among individual bands. This allows one to apply optical and magneto-optical methods to determine experimentally the energy band gap - a fundamental property crucial to our understanding of any solid - with a great precision. Here we show that such conventional methods, applied with great success to many materials in the past, do not work in topological Dirac semimetals with a dispersive nodal line. There, the optically deduced band gap depends on how the magnetic field is oriented with respect to the crystal axes. Such highly unusual behaviour is explained in terms of band-gap renormalization driven by Lorentz boosts., Comment: 9 pages, 3 figures + supplementary materials

Monolayers of transition metal dichalcogenides display a strong excitonic optical response. Additionally encapsulating the monolayer with hexagonal boron nitride allows to reach the limit of a purely homogeneously broadened exciton system. On such a MoSe$_{2}$-based system we perform ultrafast six-wave mixing spectroscopy and find a novel destructive photon echo effect. This process manifests as a characteristic depression of the nonlinear signal dynamics when scanning the delay between the applied laser pulses. By theoretically describing the process within a local field model we reach an excellent agreement with the experiment. We develop an effective Bloch vector representation and thereby demonstrate that the destructive photon echo stems from a destructive interference of successive repetitions of the heterodyning experiment.

We report magneto-photoluminescence spectroscopy of gated MoS$_2$ monolayers in high magnetic fields to 28 T. At B = 0T and electron density $n_s\sim 10^{12}cm^-2$, we observe three trion resonances that cannot be explained within a single-particle picture. Employing ab initio calculations that take into account three-particle correlation effects as well as local and non-local electron-hole exchange interaction, we identify those features as quantum superpositions of inter- and intravalley spin states. We experimentally investigate the mixed character of the trion wave function via the filling factor dependent valley Zeeman shift in positive and negative magnetic fields. Our results highlight the importance of exchange interactions for exciton physics in monolayer MoS$_2$ and provide new insights into the microscopic understanding of trion physics in 2D multi-valley semiconductors for low excess carrier densities., Comment: Main manuscript: 7 pages, 3 figures ; Supplemental material: 16 pages, 4 figures

The hybridization of magnons (spin waves) with phonons, if sufficiently strong and comprising long wavelength excitations, may offer a new playground when manipulating the magnetically ordered systems with light. Applying a magnetic field to a quasi-2D antiferromagnet, FePS3, we tune the magnon-gap excitation towards coincidence with the initially lower-in-energy phonon modes. Hybrid magnon-phonon modes, the magnon polarons are unveiled with demonstration of a pronounced avoided crossing between the otherwise bare magnon and phonon excitations. The magnon polarons in FePS3 are primary traced with Raman scattering experiments, but, as we show, they also couple directly to terahertz photons, what evokes their further explorations in the domain of antiferromagnetic optospintronics., Comment: 10 pages, 4 figures and Supplementary Materials, to be published in Phys. Rev. B

Two-dimensional layered materials offer the possibility to create artificial vertically stacked structures possessing an additional degree of freedom - $the$ $interlayer$ $twist$. We present a comprehensive optical study of artificially stacked bilayers (BLs) MoS$_2$ encapsulated in hexagonal BN with interlayer twist angle ranging from 0 to 60 degrees using Raman scattering and photoluminescence spectroscopies. It is found that the strength of the interlayer coupling in the studied BLs can be estimated using the energy dependence of indirect emission versus the A$_\textrm{1g}$-E$_\textrm{2g}^1$ energy separation. Due to the hybridization of electronic states in the valence band, the emission line related to the interlayer exciton is apparent in both the natural (2H) and artificial (62$^\circ$) MoS$_2$ BLs, while it is absent in the structures with other twist angles. The interlayer coupling energy is estimated to be of about 50 meV. The effect of temperature on energies and intensities of the direct and indirect emission lines in MoS$_2$ bilayers is also quantified., Comment: 15 pages including Appendices

Using a novel approach to ultrafast resonant pump-probe spectroscopy we investigate the spectral shape and dynamics of absorption features related to the A exciton in an hBN/MoSe$_2$/hBN van der Waals heterostructure. While in a pure two-level system a pump-probe experiment measures the occupation or the polarization dynamics, depending on the time ordering of the pulse pair, in the transition metal dichalcogenide (TMD) system both quantities get thoroughly mixed by strong exciton-exciton interaction. We find that for short positive delays the spectral lines experience pronounced changes in their shape and energy and they relax to the original situation on a picosecond time scale. For negative delays distinctive spectral oscillations appear indicating the first-time observation of perturbed free induction decay for a TMD system. The comparison between co-circular and cross-circular excitation schemes further allows us to investigate the rapid inter-valley scattering. By considering a three-level system as a minimal model including the local field effect, excitation induced dephasing and scattering between the excited states we explain all phenomena observed in the experiment with excellent consistency. Our handy model can be even further reduced to two levels in the case of a co-circular excitation, for which we derive analytic expressions to describe the detected signals. This allows us to trace back the spectral shapes and shifts to the impact of local field effect and excitation induced dephasing thus fully reproducing the complex behavior of the observed effects.

Strong Coulomb correlations together with multi-valley electronic bands in the presence of spin-orbit interaction and possible new optoelectronic applications are at the heart of studies of the rich physics of excitons in semiconductor structures made of monolayers of transition metal dichalcogenides (TMD). In intrinsic TMD monolayers the basic, intravalley excitons are formed by a hole from the top of the valence band and an electron either from the lower or upper spin-orbit-split conduction band subbands: one of these excitons is optically active, the second one is "dark", although possibly observed under special conditions. Here we demonstrate the s-series of Rydberg dark exciton states in monolayer WSe$_2$, which appears in addition to a conventional bright exciton series in photoluminescence spectra measured in high in-plane magnetic fields. The comparison of energy ladders of bright and dark Rydberg excitons is shown to be a method to experimentally evaluate one of the missing band parameters in TMD monolayers: the amplitude of the spin-orbit splitting of the conduction band., Comment: Manuscript: 9 pages, 4 figures; SM: 3 pages, 2 figures

We investigate the origin of emission lines apparent in the low-temperature photoluminescence spectra of $n$-doped WS$_2$ monolayer embedded in hexagonal BN layers using external magnetic fields and first-principles calculations. Apart from the neutral A exciton line, all observed emission lines are related to the negatively charged excitons. Consequently, we identify emissions due to both the bright (singlet and triplet) and dark (spin- and momentum-forbidden) negative trions as well as the phonon replicas of the latter optically-inactive complexes. The semi-dark trions and negative biexcitons are distinguished. Based on their experimentally extracted and theoretically calculated $g$-factors, we identify three distinct families of emissions due to exciton complexes in WS$_2$: bright, intravalley and intervalley dark. The $g$-factors of the spin-split subbands in both the conduction and valence bands are also determined., Comment: Manuscript: 7 pages, 5 figures; SI: 5 pages, 3 figures

We report magneto-optical spectroscopy of gated monolayer MoS$_2$ in high magnetic fields up to 28T and obtain new insights on the many-body interaction of neutral and charged excitons with the resident charges of distinct spin and valley texture. For neutral excitons at low electron doping, we observe a nonlinear valley Zeeman shift due to dipolar spin-interactions that depends sensitively on the local carrier concentration. As the Fermi energy increases to dominate over the other relevant energy scales in the system, the magneto-optical response depends on the occupation of the fully spin-polarized Landau levels in both $K/K^{\prime}$ valleys. This manifests itself in a many-body state. Our experiments demonstrate that the exciton in monolayer semiconductors is only a single particle boson close to charge neutrality. We find that away from charge neutrality it smoothly transitions into polaronic states with a distinct spin-valley flavour that is defined by the Landau level quantized spin and valley texture., Comment: Main manuscript: 7 pages, 4 figures ; Supplemental material: 20 pages, 8 figures

We make use of micro-magneto Raman scattering spectroscopy to probe magneto-phonon resonances (MPR) in suspended mono- to penta-layer graphene. MPR correspond to avoided crossings between zone-center optical phonons (G-mode) and optically-active inter Landau level (LL) transitions and provide a tool to perform LL spectroscopy at a fixed energy ($\approx 197~\rm{meV}$) set by the G-mode phonon. Using a single-particle effective bilayer model, we readily extract the velocity parameter associated with each MPR. A single velocity parameter slightly above the bulk graphite value suffices to fit all MPR for $N\geq2$ layer systems. In contrast, in monolayer graphene, we find that the velocity parameter increases significantly from $(1.23\pm 0.01) \times 10^6~\mathrm{m.s^{-1}}$ up to $(1.45\pm0.02) \times 10^6~\mathrm{m.s^{-1}}$ as the first to third optically-active inter LL transition couple to the G-mode phonon. This result is understood as a signature of enhanced many-body effects in unscreened graphene., Comment: 8 pages, 5 figures

Low temperature and polarization resolved magneto-photoluminescence experiments are used to investigate the properties of dark excitons and dark trions in a monolayer of WS$_2$ encapsulated in hexagonal BN (hBN). We find that this system is an $n$-type doped semiconductor and that dark trions dominate the emission spectrum. In line with previous studies on WSe$_2$, we identify the Coulomb exchange interaction coupled neutral dark and grey excitons through their polarization properties, while an analogous effect is not observed for dark trions. Applying the magnetic field in both perpendicular and parallel configurations with respect to the monolayer plane, we determine the g-factor of dark trions to be $g\sim$-8.6. Their decay rate is close to 0.5 ns, more than 2 orders of magnitude longer than that of bright excitons., Comment: 6 pages, 6 figures, supplemental material

Zeeman effect induced by the magnetic field introduces a splitting between the two valleys at K$^+$ and K$^-$ points of the Brillouin zone in monolayer semiconducting transition metal dichalcogenides. In consequence, the photoluminescence signal exhibits a field dependent degree of circular polarization. We present a comprehensive study of this effect in the case of a trion in monolayer MoTe$_2$, showing that although time integrated data allows us to deduce a g-factor of the trion state, such an analysis cannot be substantiated by the timescales revealed in the time-resolved experiments.

We report experimental and theoretical studies on the magnetoelastic interactions in MnPS$_3$. Raman scattering response measured as a function of temperature shows a blue shift of the Raman active modes at 120.2 and 155.1 cm$^{-1}$, when the temperature is raised across the antiferromagnetic-paramagnetic transition. Density functional theory (DFT) calculations have been performed to estimate the effective exchange interactions and calculate the Raman active phonon modes. The calculations lead to the conclusion that the peculiar behavior with temperature of the two low energy phonon modes can be explained by the symmetry of their corresponding normal coordinates which involve the virtual modification of the super-exchange angles associated with the leading antiferromagnetic (AFM) interactions., Comment: Main: 9 pages, 7 figures. Supplementary : 5 pages, 4 figures

The spectral signatures associated with different negatively charged exciton complexes (trions) in a WS$_2$ monolayer encapsulated in hBN, are analyzed from low temperature and polarization resolved reflectance contrast (RC) and photoluminescence (PL) experiments, with an applied magnetic field. Based on results obtained from the RC experiment, we show that the valley Zeeman effect affects the optical response of both the singlet and the triplet trion species through the evolution of their energy and of their relative intensity, when applying an external magnetic field. Our analysis allows us to estimate a free electron concentration of $\sim 1.3 \cdot 10^{11}$ cm$^{-2}$. The observed evolutions based on PL experiments on the same sample are different and can hardly be understood within the same simple frame highlighting the complexity of relaxation processes involved in the PL response., Comment: 7 pages, 4 figures; source file corrected

Identifying quantum numbers to label elementary excitations is essential for the correct description of light-matter interaction in solids. In monolayer semiconducting transition metal dichalcogenides (TMDs) such as MoSe$_2$ or WSe$_2$, most optoelectronic phenomena are described well by labelling electron and hole states with the spin projection along the normal to the layer (S$_z$). In contrast, for WSe$_2$/MoSe$_2$ interfaces recent experiments show that taking S$_z$ as quantum number is not a good approximation, and spin mixing needs to be always considered. Here we argue that the correct quantum number for these systems is not S$_z$, but the $z$-component of the total angular momentum -- J$_z$ = L$_z$ + S$_z$ -- associated to the C$_3$ rotational lattice symmetry, which assumes half-integer values corresponding modulo 3 to distinct states. We validate this conclusion experimentally through the observation of strong intervalley scattering mediated by chiral optical phonons that -- despite carrying angular momentum 1 -- cause resonant intervalley transitions of excitons, with an angular momentum difference of 2., Comment: are welcome

Excitons with binding energies of a few hundreds of meV control the optical properties of transition metal dichalcogenide monolayers. Knowledge of the fine structure of these excitons is therefore essential to understand the optoelectronic properties of these 2D materials. Here we measure the exciton fine structure of MoS2 and MoSe2 monolayers encapsulated in boron nitride by magneto-photoluminescence spectroscopy in magnetic fields up to 30 T. The experiments performed in transverse magnetic field reveal a brightening of the spin-forbidden dark excitons in MoS2 monolayer: we find that the dark excitons appear at 14 meV below the bright ones. Measurements performed in tilted magnetic field provide a conceivable description of the neutral exciton fine structure. The experimental results are in agreement with a model taking into account the effect of the exchange interaction on both the bright and dark exciton states as well as the interaction with the magnetic field.

We investigate dynamics of resonantly excited excitons in single-layers of MoSe$_2$ and WS$_2$ down to 4.5 K. To this end, we measure the delay dependence of the heterodyne four-wave mixing (FWM) amplitude induced by three, short laser pulses. This signal depends not only on the population of optically active excitons, which affects the absorption of the probe, but also on the population of optically inactive states, by interaction-induced energy shift, influencing the refractive index experienced by the probe. As such, it offers insight into density dynamics of excitons which do not directly couple to photons. Reproducing the coherent signal detected in amplitude and phase, the FWM delay dependence is modeled by a coherent superposition of several exponential decay components, with characteristic time constants from 0.1 picosecond up to 1 nanosecond. With increasing excitation intensity and/or temperature, we observe strong interference effects in the FWM field amplitude, resulting in progressively more complex and nonintuitive signal dynamics. We attribute this behaviour to increasingly populated exciton dark states, which change the FWM field phase by the relative effect on absorption and refractive index. We observe that exciton recombination occurs on a significantly longer timescale in WS$_2$ with respect to MoSe$_2$, which is attributed to the dark character of exciton ground state in the former and the bright in the latter.

We perform coherent nonlinear spectroscopy of excitons in single-layers of MoSe$_2$ and WSe$_2$ encapsulated between thin films of hexagonal boron nitride. Employing four-wave mixing microscopy we identify virtually disorder free areas, generating exciton optical response at the homogeneous limit. Focussing on such areas, we measure exciton homogeneous broadening as a function of environmental factors, namely temperature and exciton density. Exploiting FWM imaging, we find that at such locations, nonlinear absorption of the exciton excited states and their coherent couplings can be observed. Using the WSe$_2$ heterostructure, we infer coherence and density dynamics of the exciton 2S state. Owing to its increased radiative lifetime, at low temperatures, the dephasing of the 2S state is longer than of the 1S transition. While scanning various heterostructures across tens of micrometers, we conclude that the disorder, principally induced by strain variations, remain to be present creating spatially varying inhomogeneous broadening.

At cryogenic temperatures, the photoluminescence spectrum of monolayer WSe2features a num-ber of lines related to the recombination of so-called localized excitons. The intensity of these lines strongly decreases with increasing temperature. In order to understand the mechanism behind this phenomenon, we carried out a time-resolved experiment, which revealed a similar trend in the photoluminescence decay time. Our results identify the opening of additional nonradiative relaxation channels as a primary cause of the observed temperature quenching of the localized excitons' photoluminescence.

We perform absorption and photoluminescence spectroscopy of trions in hBN-encapsulated WSe$_2$, WS$_2$, MoSe$_2$, and MoS$_2$ monolayers, depending on temperature. The different trends for W- and Mo-based materials are excellently reproduced considering a Fermi-Dirac distribution of bright and dark trions. We find a dark trion, $\rm{X_D^-}$ 19 meV $\textit{below}$ the lowest bright trion, $\rm{X}_1^-$ in WSe$_2$ and WS$_2$. In MoSe$_2$, $\rm{X_D^-}$ lies 6 meV $\textit{above}$ $\rm{X}_1^-$, while $\rm{X_D^-}$ and $\rm{X}_1^-$ almost coincide in MoS$_2$. Our results agree with GW-BSE $\textit{ab-initio}$ calculations and quantitatively explain the optical response of doped monolayers with temperature., Comment: 16 pages including supporting information, 4 figures in the main text, 10 figures in the supporting information

Atomically thin materials, like semiconducting transition metal dichalcogenides (S-TMDs), are highly sensitive to the environment. This opens up an opportunity to externally control their properties by changing their surroundings. We investigate the effect of several metallic substrates on the optical properties of MoSe$_2$ monolayer (ML) deposited on top of them with photoluminescence and reflectance contrast techniques. The optical spectra of MoSe$_{2}$ MLs deposited on Pt, Au, Mo and Zr have distinctive metal-related lineshapes. In particular, a substantial variation in the intensity ratio and the energy separation between a negative trion and a neutral exciton is observed. It is shown that using metals as substrates affects the doping of S-TMD MLs. The explanation of the effect involves the Schottky barrier formation at the interface between the MoSe$_{2}$ ML and the metallic substrates. The alignment of energy levels at the metal/semiconductor junction allows for the transfer of charge carriers between them. We argue that a proper selection of metallic substrates can be a way to inject appropriate types of carriers into the respective bands of S-TMDs., Comment: 7 pages, 5 figures

The encapsulation of few-layer transition metal dichalcogenides (TMDs) in hexagonal boron nitride (h-BN) is known to improve significantly their optical and electronic properties. However, it may be expected that the h-BN encapsulation may affect also vibration properties of TMDs due to an atomically flat surface of h-BN layers. In order to study its effect on interlayer interactions in few-layer TMDs, we investigate low-energy Raman scattering spectra of bi- and trilayer MoTe$_2$. Surprisingly, three breathing modes are observed in the Raman spectra of the structures deposited on or encapsulated in h-BN as compared to a single breathing mode for the flakes deposited on a SiO$_2$/Si substrate. The shear mode is not affected by changing the MoTe$_2$ environment. The emerged structure of breathing modes is ascribed to the apparent interaction between the MoTe$_2$ layer and the bottom h-BN flake. The structure becomes visible due to a high-quality surface of the former flake. Consequently, the observed triple structure of breathing modes originates from the combination modes due to interlayer and layer-substrate interactions. Our results confirm that the h-BN encapsulation affects substantially vibration properties of layered materials., Comment: 10 pages, 9 figures

Due to high binding energy and oscillator strength, excitons in thin flakes of transition metal dichalcogenides constitute a perfect foundation for realizing a strongly coupled light-matter system. In this paper we investigate mono- and few-layer WSe$_2$ flakes encapsulated in hexagonal boron nitride and incorporated into a planar dielectric cavity. We use an open cavity design which provides tunability of the cavity mode energy by as much as 150 meV. We observe a strong coupling regime between the cavity photons and the neutral excitons in direct-bandgap monolayer WSe$_2$, as well as in few-layer WSe$_2$ flakes exhibiting indirect bandgap. We discuss the dependence of the exciton's oscillator strength and resonance linewidth on the number of layers and predict the exciton-photon coupling strength.

The Landau level laser has been proposed a long time ago as a unique source of monochromatic radiation, widely tunable in the THz and infrared spectral ranges using an externally applied magnetic field. In spite of decades of efforts, this appealing concept never resulted in the design of a reliable device. This is due to efficient Auger scattering of Landau-quantized electrons, which is an intrinsic non-radiative recombination channel that eventually gains over cyclotron emission in all materials studied so far: in conventional semiconductors with parabolic bands, but also in graphene with massless electrons. The Auger processes are favored in these systems by Landau levels (or their subsets) equally spaced in energy. Here we show that this scheme does not apply to massless Kane electrons in gapless HgCdTe alloy, in which undesirable Auger scattering is strongly suppressed and the sizeable cyclotron emission observed, for the first time in the case of massless particles. The gapless HgCdTe thus appears as a material of choice for future technology of Landau level lasers., Comment: 11 pages, 7 figures including Supplementary materials

The intriguing physics of carrier-carrier interactions, which likewise affect the operation of light emitting devices, stimulate the research on semiconductor structures at high densities of excited carriers, a limit reachable at large pumping rates or in systems with long-lived electron-hole pairs. By electrically injecting carriers into WSe$_2$/MoS$_2$ type-II heterostructures which are indirect in real and k-space, we establish a large population of typical optically silent interlayer excitons. Here, we reveal their emission spectra and show that the emission energy is tunable by an applied electric field. When the population is further increased by suppressing the radiative recombination rate with the introduction of an hBN spacer between WSe$_2$ and MoS$_2$, Auger-type and exciton-exciton annihilation processes become important. These processes are traced by the observation of an up-converted emission demonstrating that excitons gaining energy in non-radiative Auger processes can be recovered and recombine radiatively., Comment: accepted for publication in Nature Communications

We demonstrate that, in monolayers (MLs) of semiconducting transition metal dichalcogenides, the $s$-type Rydberg series of excitonic states follows a simple energy ladder: $\epsilon_n=-Ry^*/(n+\delta)^2$, $n$=1,2,\ldots, in which $Ry^*$ is very close to the Rydberg energy scaled by the dielectric constant of the medium surrounding the ML and by the reduced effective electron-hole mass, whereas the ML polarizability is only accounted for by $\delta$. This is justified by the analysis of experimental data on excitonic resonances, as extracted from magneto-optical measurements of a high-quality WSe$_2$ ML encapsulated in hexagonal boron nitride (hBN), and well reproduced with an analytically solvable Schr\"odinger equation when approximating the electron-hole potential in the form of a modified Kratzer potential. Applying our convention to other, MoSe$_2$, WS$_2$, MoS$_2$ MLs encapsulated in hBN, we estimate an apparent magnitude of $\delta$ for each of the studied structures. Intriguingly, $\delta$ is found to be close to zero for WSe$_2$ as well as for MoS$_2$ monolayers, what implies that the energy ladder of excitonic states in these two-dimensional structures resembles that of Rydberg states of a three-dimensional hydrogen atom., Comment: Manuscript: 6 pages, 4 figures; SM: 11 pages, 12 figures

Monolayers of semiconducting transition metal dichalcogenides are two-dimensional direct-gap systems which host tightly-bound excitons with an internal degree of freedom corresponding to the valley of the constituting carriers. Strong spin-orbit interaction and the resulting ordering of the spin-split subbands in the valence and conduction bands makes the lowest-lying excitons in WX$_2$ (X~being S or Se) spin-forbidden and optically dark. With polarization-resolved photoluminescence experiments performed on a WSe$_2$ monolayer encapsulated in a hexagonal boron nitride, we show how the intrinsic exchange interaction in combination with the applied in-plane and/or out-of-plane magnetic fields enables one to probe and manipulate the valley degree of freedom of the dark excitons., Comment: Manuscript: 6 pages, 3 figures; SM: 6 pages, 5 figures

Monolayers and multilayers of semiconducting transition metal dichalcogenides (TMDCs) offer an ideal platform to explore valley-selective physics with promising applications in valleytronics and information processing. Here we manipulate the energetic degeneracy of the $\mathrm{K}^+$ and $\mathrm{K}^-$ valleys in few-layer TMDCs. We perform high-field magneto-reflectance spectroscopy on WSe$_2$, MoSe$_2$, and MoTe$_2$ crystals of thickness from monolayer to the bulk limit under magnetic fields up to 30 T applied perpendicular to the sample plane. Because of a strong spin-layer locking, the ground state A excitons exhibit a monolayer-like valley Zeeman splitting with a negative $g$-factor, whose magnitude increases monotonically when thinning the crystal down from bulk to a monolayer. Using the $\mathbf{k\cdot p}$ calculation, we demonstrate that the observed evolution of $g$-factors for different materials is well accounted for by hybridization of electronic states in the $\mathrm{K}^+$ and $\mathrm{K}^-$ valleys. The mixing of the valence and conduction band states induced by the interlayer interaction decreases the $g$-factor magnitude with an increasing layer number. The effect is the largest for MoTe$_2$, followed by MoSe$_2$, and smallest for WSe$_2$. Keywords: MoSe$_2$, WSe$_2$, MoTe$_2$, valley Zeeman splitting, transition metal dichalcogenides, excitons, magneto optics., Comment: 14 pages, 5 figures

We study the relaxation dynamics of the electron system in graphene flakes under Landau quantization regime using a novel approach of time-resolved Raman scattering. The non-resonant character of the experiment allows us to analyze the field dependence of the relaxation rate. Our results clearly evidence sharp increase in the relaxation rate upon the resonance between the energy of the Landau transition and the G-band and shed new light on relaxation mechanism of the Landau-quantized electrons in graphene beyond the previously studied Auger scattering.

A time-resolved observation of coherent interlayer longitudinal acoustic phonons in 2$H$-MoSe$_2$ is reported. A femtosecond pump-probe technique is used to investigate the evolution of the energy loss of these vibrational modes in a wide selection of MoSe$_2$ flakes with different thicknesses ranging from bilayer up to the bulk limit. By directly analysing the temporal decay of the modes, we can clearly distinguish an abrupt crossover related to the acoustic mean free path of the phonons in a layered system, and the constraints imposed to the acoustic decay channels when reducing the dimensionality. Loses intrinsic to the low dimensionality of single or few layer materials impose critical limitations for their use in optomechanical and optoelectronic devices., Comment: 21 pages, 16 figures, submitted material

Reflectance and magneto-reflectance experiments together with theoretical modelling based on the $\mathbf{k\cdot p}$ approach have been employed to study the evolution of direct bandgap excitons in MoS$_2$ layers with a thickness ranging from mono- to trilayer. The extra excitonic resonances observed in MoS$_2$ multilayers emerge as a result of the hybridization of Bloch states of each sub-layer due to the interlayer coupling. The properties of such excitons in bi- and trilayers are classified by the symmetry of corresponding crystals. The inter- and intralayer character of the reported excitonic resonances is fingerprinted with the magneto-optical measurements: the excitonic $g$-factors of opposite sign and of different amplitude are revealed for these two types of resonances. The parameters describing the strength of the spin-orbit interaction are estimated for bi- and trilayer MoS$_2$., Comment: 14 pages, 10 figures

Monolayer transition metal dichalcogenides, known for exhibiting strong excitonic resonances, constitute a very interesting and versatile platform for investigation of light-matter interactions. In this work we report on a strong coupling regime between excitons in monolayer WSe2 and photons confined in an open, voltage-tunable dielectric microcavity. The tunability of our system allows us to extend the exciton-polariton state over a wide energy range and, in particular, to bring the excitonic component of the lower polariton mode into resonance with other excitonic transitions in monolayer WSe2. With selective excitation of spin-polarized exciton-polaritons we demonstrate the valley polarization when the polaritons from the lower branch come into resonance with a bright trion state in monolayer WSe2 and valley depolarization when they are in resonance with a dark trion state., Comment: 7 pages, 7 figures

The effect of bis(trifluoromethane) sulfonimide (TFSI, superacid) treatment on the optical properties of MoS$_2$ monolayers is investigated by means of photoluminescence, reflectance contrast and Raman scattering spectroscopy employed in a broad temperature range. It is shown that when applied multiple times, the treatment results in progressive quenching of the trion emission/absorption and in the redshift of the neutral exciton emission/absorption associated with both the A and B excitonic resonances. Based on this evolution, a trion complex related to the B exciton in monolayer MoS$_2$ is unambiguously identified. A defect-related emission observed at low temperatures also disappears from the spectrum as a result of the treatment. Our observations are attributed to effective passivation of defects on the MoS$_{2}$ monolayer surface. The passivation reduces the carrier density, which in turn affects the out-of-plane electric field in the sample. The observed tuning of the carrier concentration strongly influences also the Raman scattering in the MoS$_2$ monolayer. An enhancement of Raman scattering at resonant excitation in the vicinity of the A neutral exciton is clearly seen for both the out-of-plane A$_1^{'}$ and in-plane E$^{'}$ modes. On the contrary, when the excitation is in resonance with a corresponding trion, the Raman scattering features become hardly visible. These results confirm the role of the excitonic charge state plays in the resonance effect of the excitation energy on the Raman scattering in transition metal dichalcogenides., Comment: 8 pages, 4 figures

Cadmium arsenide (Cd3As2) has recently became conspicuous in solid-state physics due to several reports proposing that it hosts a pair of symmetry-protected 3D Dirac cones. Despite vast investigations, a solid experimental insight into the band structure of this material is still missing. Here we fill one of the existing gaps in our understanding of Cd3As2, and based on our Landau level spectroscopy study, we provide an estimate for the energy scale of 3D Dirac electrons in this system. We find that the appearance of such charge carriers is limited - contrary to a widespread belief in the solid-state community - to a relatively small energy scale (below 40 meV)., Comment: to be published in Phys. Rev. B