Exciton problem is solved in the two-dimensional Dirac model with allowance for strong electron-hole attraction. The exciton binding energy is assumed smaller than but comparable to the band gap. The exciton wavefunction is found in the momentum space as a superposition of all four two-particle states including electron and hole states with both positive and negative energies. The matrix element of exciton generation is shown to depend on the additional components of the exciton wavefunction. Both the Coulomb and the Rytova-Keldysh potentials are considered. The dependence of the binding energy on the coupling constant is analyzed for the ground and first excited exciton states. The binding energy and the oscillator strength are studied as functions of the environmental-dependent dielectric constant for real transition metal dichalcogenide monolayers. We demonstrate that the multicomponent nature of the exciton wavefunction is crucial for description of resonant optical properties of two-dimensional Dirac systems.
In this work, we provide a detailed derivation of Foldy-Wouthuysen (FW) transformation for two-dimensional (2D) gapped Dirac fermions under external fields and apply the formalism to study valley excitons in 2D semiconducting materials. Similar to relativistic quantum few-body problem, the gapped Dirac equation can be transformed into a Schrödinger equation with "relativistic" correction terms. In this 2D materials system, the correction terms can be interpreted as the Berry-curvature effect. The Hamiltonian for a valley exciton in external fields can be written based on the FW transformed Dir…
Coulomb bound electron-hole pairs, excitons, govern the optical properties of semi-conducting transition metal dichalcogenides like MoS$_2$ and WSe$_2$. We study optical transitions at the K-point for 2H homobilayer MoS$_2$ in Density Functional Theory (DFT) including excitonic effects and compare with reflectivity measurements in high quality samples encapsulated in hexagonal BN. In both calculated and measured spectra we find a strong interlayer exciton transition in energy between A and B intralayer excitons, observable for T$=4 -300$ K, whereas no such transition is observed for the monola…
Driven and non-equilibrium quantum states of matter have attracted growing interest in both theoretical and experimental studies in condensed matter physics. We review recent progress in realizing transient collective states in driven or pumped Dirac materials (DMs). In particular, we focus on optically-pumped DMs which have been theoretically proposed as a promising platform for observation of a transient excitonic instability. Optical pumping combined with the linear (Dirac) dispersion of the electronic spectrum offers a knob for tuning the effective interaction between the photoexcited elec…
Moiré exciton features tunable Dirac dispersion and spatially dependent optical selection rules. With the long lifetime due to its interlayer nature, it is promising to realize a Bose-Einstein condensation of moiré excitons. Here we study the properties of moiré exciton condensate within the mean-field theory, with special focus on exciton-exciton interaction effect on the nonlinear Bloch band and Bloch waves of exciton condensate in moiré potential. We find the nonlinear dispersion of the moiré exciton condensate exhibits complex loop structure induced by exciton-exciton interaction. A nonlin…
The optical properties of MoS2 monolayers are dominated by excitons, but for spectrally broad optical transitions in monolayers exfoliated directly onto SiO2 substrates detailed information on excited exciton states is inaccessible. Encapsulation in hexagonal boron nitride (hBN) allows approaching the homogenous exciton linewidth, but interferences in the van der Waals heterostructures make direct comparison between transitions in optical spectra with different oscillator strength more challenging. Here we reveal in reflectivity and in photoluminescence excitation spectroscopy the presence of …
We present a description of vacuum polarization in a circular Dirac quantum dot in two spatial dimensions assuming $α$ - the relative strength of the Coulomb interaction small enough to render an approximation with a single electron (hole) lowest energy level relevant. Applying this approximation, we find that for $ α_c \approx 1.05$ the lowest level is half-filled irrespective of the number of flavors that are present. The ground state can be represented as a superposition of particular (even number) excitonic states which constitute an excitonic cloud that evolves in a crossover manner. The …
Two-dimensional Dirac fermions are subjected to two types of interactions, namely the long-range Coulomb interaction and the short-range on-site interaction. The former induces excitonic pairing if its strength $α$ is larger than some critical value $α_c$, whereas the latter drives an antiferromagnetic Mott transition when its strength $U$ exceeds a threshold $U_c$. Here, we study the impacts of the interplay of these two interactions on excitonic pairing with the Dyson-Schwinger equation approach. We find that the critical value $α_c$ is increased by weak short-range interaction. As $U$ incre…
The properties of energy spectrum of excitons in monolayer transition metal dichalcogenides are investigated using a multiband model. In the multiband model we use the excitonic Hamiltonian in the product base of the Dirac single-particle states at the conduction and valence band edges. Following the separation of variables we decouple the corresponding energy eigenvalue system of the first order ODE radial equations rigorously and solve the resulting the second order ODE self-consistently, using the finite difference method, thus we determine the energy eigenvalues of the discrete excitonic s…
The way nuclear motion affects electronic responses has become a very hot topic in materials science. Coherent acoustic phonons can dynamically modify optical, magnetic and mechanical properties at ultrasonic frequencies, with promising applications as sensors and transducers. Here, by means of ultrafast broadband deep-ultraviolet spectroscopy, we demonstrate that coherent acoustic phonons confined in anatase TiO$_2$ nanoparticles can selectively modulate the oscillator strength of the two-dimensional bound excitons supported by the material. We use many-body perturbation-theory calculations t…
Strain in two-dimensional (2D) transition metal dichalcogenide (TMD) has led to localized states with exciting optical properties, in particular in view of designing one photon sources. The naturally formed of the MoS2 monolayer deposed on hBN substrate leads to a reduction of the bandgap in the strained region creating a nanobubble. The photogenerated particles are thus confined in the strain-induced potential. Using numerical diagonalization, we simulate the spectra of the confined exciton states, their oscillator strengths and radiative lifetimes. We show that a single state of the confined…
Interlayer valley excitons in bilayer MoS2 feature concurrently large oscillator strength and long lifetime, and hence represent an advantageous scenario for valleytronic applications. However, control of valley pseudospin of interlayer excitons in pristine bilayer MoS2, which lies at the heart of valleytronics, has remained elusive. Here we report the observation of highly circularly polarized photoluminescence from interlayer excitons of bilayer MoS2 with both optical and magnetic addressability. Under excitation of circularly polarized light near exciton resonance, interlayer excitons of bi…
Using the quasiclassical concept of Berry curvature we demonstrate that a Dirac exciton - a pair of Dirac quasiparticles bound by Coulomb interactions - inevitably possesses an intrinsic angular momentum making the exciton effectively self-rotating. The model is applied to excitons in two-dimensional transition metal dichalcogenides, in which the charge carriers are known to be described by a Dirac-like Hamiltonian. We show that the topological self-rotation strongly modifies the exciton spectrum and, as a consequence, resolves the puzzle of the overestimated two-dimensional polarizability emp…
The 1T-phase layered PtX2 chalcogenides has attracted widespread interest due to its thickness dependent metal-semiconductor transition driven by strong interlayer coupling. While the ground state properties of this paradigmatic material system have been widely explored, its fundamental excitation spectrum remains poorly understood. Here we combine first principles calculations with momentum (q) resolved electron energy loss spectroscopy (q-EELS) to study the collective excitations in 1T-PtSe2 from the monolayer limit to the bulk. At finite momentum transfer all the spectra are dominated by tw…
In this paper a theoretical studies of the space separation of electron and hole wave functions in the quantum well ZnO/Mg0.27Zn0.73O are presented. For this aim the self-consistent solution of the Schrödinger equations for electrons and holes and the Poisson equations at the presence of spatially varying quantum well potential due to the piezoelectric effect and local exchange-correlation potential is found. The one-dimensional Poisson equation contains the Hartree potential which includes the one-dimensional charge density for electrons and holes along the polarization field distribution. Th…
Transition metal dichalcogenides have a rich exciton landscape consisting of a variety of bright and dark excitonic states. We consider the lowest-energy dark states in $\hbox{MoS}_2$, which can be referred to as hybrid excitons, as they are formed by a Dirac electron and a Schrödinger hole. The chiral nature of the Dirac electron introduces asymmetry to the excited exciton state spectrum and entangles the relative motion of the electron and hole with the center-of-mass motion. We demonstrate that the entanglement generates an additional contribution to the Berry curvature of hybrid excitons. …
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-l…
The optoelectronic properties of metal chalcogenide colloidal nanoplatelets are often interpreted in terms of excitonic states. However, recent spectroscopic experiments evidence the presence of trion states, enabled by the slow Auger recombination in these structures. We analyze how the presence of an additional charge in trions modifies the emission energy and oscillator strength as compared to neutral excitons. These properties are very sensitive to dielectric confinement and electronic correlations, which we describe accurately using image-charge and variational Quantum Monte Carlo methods…
Van der Waals heterostructures composed of transition metal dichalcogenide monolayers (TMDs) are characterized by their truly rich excitonic properties which are determined by their structural, geometric and electronic properties: In contrast to pure monolayers, electrons and holes can be hosted in different materials, resulting in highly tunable dipolar manyparticle complexes. However, for genuine spatially indirect excitons, the dipolar nature is usually accompanied by a notable quenching of the exciton oscillator strength. Via electric and magnetic field dependent measurements, we demonstra…
