A systematic microscopic approach combining ab-initio density functional theory with the Dirac-Bloch equations is applied to investigate the intra-excitonic transitions of magneto-excitons in transition metal dichalcogenide monolayers. For the example of hBN-encapsulated $\mathrm{Mo}{\mathrm{S}}_{2}$, the linear optical response and mid-infrared spectra of the pre-excited system are numerically evaluated. It is shown that the transition probability between a subset of the magneto-excitons can be inverted under suitable conditions to display negative absorption, i.e., gain. With the help of an applied magnetic field, the absorption and gain spectra can be tuned over a wide spectral range. Evaluating the Zeeman shift of the excitonic states, effective $g$ factors are deduced that depend on the dielectric environment of the sample under consideration.

Electron–hole plasma‐induced dephasing and its influence on the excitonic absorption and the degenerate four‐wave mixing spectra in monolayer transition metal dichalcogenides are investigated. A systematic microscopic theory is presented that combines density functional calculations for the linear material properties with a many‐body equation of motion approach for the optical response. Numerical results are obtained for the example of an hBN‐encapsulated layer of . It is shown that the influence of the excitation‐induced dephasing depends only weakly on the exact shape of the carrier distribution for small densities, whereas distribution details become more important with increasing density.

The dynamics of band-gap renormalization and gain build-up in monolayer MoTe$_2$ is investigated by evaluating the non-equilibrium Dirac-Bloch equations with the incoherent carrier-carrier and carrier-phonon scattering treated via quantum-Boltzmann type scattering equations. For the case where an approximately $300$ fs-long high intensity optical pulse generates charge-carrier densities in the gain regime, the strong Coulomb coupling leads to a relaxation of excited carriers on a few fs time scale. The pump-pulse generation of excited carriers induces a large band-gap renormalization during the time scale of the pulse. Efficient phonon coupling leads to a subsequent carrier thermalization within a few ps, which defines the time scale for the optical gain build-up energetically close to the low-density exciton resonance.

The quasi-two dimensional Coulomb interaction potential in transition metal dichalcogenides is determined using the Kohn-Sham wave functions obtained from ab initio calculations. An effective form factor is derived that accounts for the finite extension of the wave functions in the direction perpendicular to the material layer. The resulting Coulomb matrix elements are used in microscopic calculations based on the Dirac Bloch equations yielding an efficient method to calculate the band gap and the opto-electronic material properties in different environments and under various excitation conditions.

It is shown that the three-fold rotational symmetry in transition metal dichalcogenides leads to a Coulomb induced renormalization of the effective electron and hole masses near the $K$-points of the Brillouin zone. The magnitude of the renormalization depends on the dielectric configuration. The effective exciton mass $m=0.4 m_0$ of a freely suspended MoS$_2$ monolayer changes to $m= 0.35 m_0$ with hBN encapsulation. The mass renormalization increases the excitonic binding energy and reduces the exciton diamagnetic shift and cyclotron frequency. Detailed comparisons with high field measurements of the excitonic diamagnetic shift show excellent agreement.

Valley-selective optical selection rules and a spin-valley locking in transition-metal dichalcogenide (TMDC) monolayers are at the heart of "valleytronic physics", which exploits the valley degree of freedom and has been a major research topic in recent years. In contrast, valleytronic properties of TMDC bilayers have not been in the focus so much by now. Here, we report on the valleytronic properties and optical characterization of bilayers of WS2 as a representative TMDC material. In particular, we study the influence of the relative layer alignment in TMDC homo-bilayer samples on their polarization-dependent optical properties. Therefore, CVD-grown WS2 bilayer samples have been prepared that favor either the inversion symmetric AA' stacking or AB stacking without inversion symmetry during synthesis. Subsequently, a detailed analysis of reflection contrast and photoluminescence spectra under different polarization conditions has been performed. We observe circular and linear dichroism of the photoluminescence that is more pronounced for the AB stacking configuration. Our experimental findings are supported by theoretical calculations showing that the observed dichroism can be linked to optical selection rules, that maintain the spin-valley locking in the AB-stacked WS2 bilayer, whereas a spin-layer-locking is present the inversion symmetric AA' bilayer instead. Furthermore, our theoretical calculations predict a small relative shift of the excitonic resonances in both stacking configurations, which is also experimentally observed.

The coupling of the spin and valley degrees of freedom and valley-selective optical selection rules in transition-metal dichalcogenides (TMDCs) monolayers (ML) has been a major research topic in recent years [1]. In contrast, valleytronic properties of TMDC bilayers have not been in the focus so much by now. In our contribution, we study the effect of the relative layer alignment in TMDC homo-bilayer samples on their polarization-dependent optical properties. To this end, CVD-grown WS 2 bilayer samples have been prepared that during synthesis favour either the inversion symmetric AA' or AB stacking without inversion symmetry. For the optical studies, the bilayer samples were transferred either onto a bare SiO 2 (cf. fig. 1 a,b) or a few-layer h-BN buffer (fig. 1 c,d). To verify the difference in symmetry for these bilayer configurations, second-harmonic-generation (SHG) raster-scans have been performed (cf. fig. 1 e-h), confirming inversion symmetry for the AA' configuration. Subsequently, a detailed analysis of reflection contrast and photoluminescence (PL) spectra under different polarization conditions has been performed.

Fully microscopic many-body models based on the Dirac-Bloch equations and quantum-Boltzmann type scattering equations are used to study the carrier dynamics in monolayer transition metal dichalcogenides (TMDCs) under conditions as typical for applications as lasers, diodes or saturable absorbers. The carrier-carrier scattering is shown to be happening on an ultra-fast few-femtosecond timescale for excitations high above the bandgap. Once the carriers have relaxed into quasi-equilibrium distributions near the bandgap, the scattering is slowed dramatically by phase-space filling and screening of the Coulomb interaction. Here, the scatterings and resulting dephasing of the optical polarizations happen on a 100fs timescale and lead to similar broadenings as found in conventional III-V semiconductor materials. Also like the case in III-V materials, the carrier phonon scattering times are found to be in the picosecond range. The scatterings are shown to allow for gain spectra as needed for good lasing operation. It is shown that the weak interaction between the two bands associated with the two different sub-lattices can potentially allow for simultaneous lasing at two different frequencies. Strong absorption and ultrafast carrier relaxation could allow for TMDCs to be used in saturable absorption applications.

A self-consistent scheme for the calculations of the interacting groundstate and the near bandgap optical spectra of mono- and multilayer transition-metal-dichalcogenide systems is presented. The approach combines a dielectric model for the Coulomb interaction potential in a multilayer environment, gap equations for the renormalized groundstate, and the Dirac-Wannier-equation to determine the excitonic properties. To account for the extension of the individual monolayers perpendicular to their basic plane, an effective thickness parameter in the Coulomb interaction potential is introduced. Numerical evaluations for the example of MoS$_2$ show that the resulting finite size effects lead to significant modifications in the optical spectra, reproducing the experimentally observed non hydrogenic features of the excitonic resonance series. Applying the theory for multi-layer configurations, a consistent description of the near bandgap optical properties is obtained all the way from monolayer to bulk. In addition to the well-known in-plane excitons, also interlayer excitons occur in multilayer systems suggesting a reinterpretation of experimental results obtained for bulk material.

So far, spatially indirect or charge transfer excitons are only known to exist in certain heterostructures. Here, via confocal reflection spectroscopy and quantitative comparison with theoretical analysis using the Dirac-Bloch equations, the authors identify a previously unknown species of spatially indirect exciton in bilayer to multilayer MoSe${}_{2}$ single crystals. They coexist with spatially direct ones at a lower energy, stable only because of the two-dimensional nature of electrons in layered materials. The interlayer exciton binding energy and oscillator strength are comparatively large, enabling convenient optical access to dipolar systems and potentially powerful cavity effects.

Combining ab initio density functional theory with the Dirac–Bloch and gap equations, excitonic properties of transition-metal dichalcogenide hetero-bilayers with type-II band alignment are computed. The existence of interlayer excitons is predicted, whose binding energies are as large as 350 meV, only roughly 100 meV less than those of the coexisting intralayer excitons. The oscillator strength of the interlayer excitons reaches a few percent of the intralayer exciton resonances and their radiative lifetime is two orders of magnitude larger than that of the intralayer excitons.

Cooperative effects allow for fascinating characteristics in light-matter interacting systems. Here, we study naturally occurring superradiant coupling in a class of quasi-two-dimensional, layered semiconductor systems. We perform optical absorption experiments of the lowest exciton for transition-metal dichalcogenides with different numbers of atomic layers. We examine two representative materials, MoSe$_2$ and WSe$_2$, using incoherent broadband white light. The measured transmission at the A exciton resonance does not saturate for optically thick samples consisting of hundreds of atomic layers, and the transmission varies nonmonotonously with the layer number. A self-consistent microscopic calculation reproduces the experimental observations, clearly identifying superradiant coupling effects as the origin of this unexpected behavior.

Optical absorption and gain spectra in MoS2 monolayers with thermal carrier distributions are calculated from the combined gap and Dirac-Bloch equations. It is shown that the excited carriers lead to a bandgap renormalization as large as 800 meV for a suspended monolayer MoS2. Above the critical density, optical gain is obtained over an approx. 400 meV broad spectral range above the gap. Whereas the absorption spectra in the low density regime are very sensitive to the dielectric environment, the spectra become purely intrinsic at elevated carrier densities.

Optical Properties of Graphene, pp. 43-84 (2017) No AccessChapter 2: Microscopic Theory for the Groundstate and Linear Optical Response of Novel Two-Dimensional Materials with Hexagonal SymmetryTineke Stroucken and Stephan W. KochTineke StrouckenDepartment of Physics and Scientific Center for Material Sciences, Philipps University Marburg, Renthof 5, 35032 Marburg, Germany and Stephan W. KochDepartment of Physics and Scientific Center for Material Sciences, Philipps University Marburg, Renthof 5, 35032 Marburg, Germanyhttps://doi.org/10.1142/9789813148758_0002Cited by:2 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: This chapter summarizes recent theoretical work to determine the groundstate and the linear optical properties of quasi-two-dimensional materials with hexagonal lattice symmetry. The main ingredients of the fully relativistic tight-binding model analysis for graphene and transition metal dichalcogenites are summarized. Dirac-Bloch equations are derived and solved in the regimes of weak and strong Coulomb coupling. Whereas single-layer graphene always seems to be in the weak Coulomb-coupling regime, realistic parameter analysis of WSe2 and WS2 identifies these materials to be in the regime of strong Coulomb coupling. Consequently, they are predicted to exhibit an excitonic insulator groundstate with optically active p-excitons. On this basis, a unified understanding and excellent agreement of the theoretical predictions with a large variety of systematic experiments is obtained. FiguresReferencesRelatedDetailsCited By 2Interlayer excitons in transition-metal dichalcogenide heterostructures with type-II band alignmentL Meckbach, U Huttner, L C Bannow, T Stroucken and S W Koch24 August 2018 | Journal of Physics: Condensed Matter, Vol. 30, No. 37Giant excitation induced bandgap renormalization in TMDC monolayersL. Meckbach, T. Stroucken and S. W. Koch5 Feb 2018 | Applied Physics Letters, Vol. 112, No. 6 Optical Properties of GrapheneMetrics History PDF download

It is shown that the strong Coulomb coupling in intrinsic suspended semiconducting transition metal dichalcogenides can exceed the critical value needed for an excitonic ground state. The dipole-allowed optical excitations then correspond to intra-excitonic transitions such that the optically bright excitonic transitions near the Dirac points have a p-like symmetry, whereas the s-like states are dipole forbidden. The large intrinsic coupling strength seems to be a generic property of the semiconducting transition metal dichalcogenides and strong Coulomb-coupling signatures in the form of the optical selection rules can be observed even in samples grown on typical substrates like SiO2. For the examples of WS2 and WSe2, excellent agreement of the computed excitonic resonance energies with recent experiments is demonstrated.

It is shown that the strong Coulomb coupling in intrinsic suspended semiconducting transition metal dichalcogenides can exceed the critical value needed for an excitonic ground state. The dipole-allowed optical excitations then correspond to intra-excitonic transitions such that the optically bright excitonic transitions near the Dirac points have a $p$-like symmetry whereas the $s$-like states are dipole forbidden. The large intrinsic coupling strength seems to be a generic property of the semiconducting transition metal dichalcogenides and strong Coulomb-coupling signatures in the form of the optical selection rules can be observed even in samples grown on typical substrates like SiO$_2$. For the examples of WS$_2$ and WSe$_2$, excellent agreement of the computed excitonic resonance energies with recent experiments is demonstrated.

A self-consistent microscopic theory is applied to analyze the influence of many-body effects on the energy spectrum of biased bilayer graphene. The results show a monotonic increase of the quasiparticle gap with the applied external field and a significant enhancement of the gap due to the many-body interactions.

A fully selfconsistent treatment for gap generation and Coulomb screening in excitonic insulators is presented. The method is based on the equations of motion for the relevant dynamical variables combined with a variational approach. Applying the theory for a model system of bilayer graphene, an excitonic groundstate with a gap exceeding 10 meV is predicted.

Radiative coupling between oscillators is one of the most fundamental subjects of research in optics, where particularly a Bragg-type arrangement is of interest and has already been applied to atoms and excitons in quantum wells. Here we explore this arrangement in a plasmonic structure. We observe the emergence of an octave-wide photonic band gap in the optical regime. Compared with atomic or excitonic systems, the coupling efficiency of the particle plasmons utilized here is several orders of magnitude larger and widely tunable by changing the size and geometry of the plasmonic nanowires. We are thus able to explore the regime where the coupling distance is even limited by the large radiative decay rate of the oscillators. This Bragg-stacked coupling scheme will open a new route for future plasmonic applications such as far-field coupling to quantum emitters without quenching, plasmonic cavity structures and plasmonic distributed gain schemes for spasers.

The Wannier equation for quasiparticles with a linear dispersion is investigated. It is shown that Coulomb bound compounds of mass less electron-hole pairs can only exist if the effective coupling strength exceeds the critical value of approximately 0.46. At the critical value, a second-order transition to a weak Coulomb regime is found. It is shown that the existence of bound excitons indicates an instability of the noninteracting ground state.