Exciton Series Research Articles

Critical dependence of the excitonic absorption in cuprous oxide on experimental parameters

AbstractWe study the modification of the exciton absorption in cuprous oxide by the presence of free carriers excited through above band gap excitation. Without this pumping, the absorption spectrum below the band gap consists of the yellow exciton series with principal quantum numbers up to more than n = 20, depending on the temperature, changing over to an about constant, only slowly varying absorption above the gap. Careful injection of free carriers, starting from densities well below 1 μm^–3, leads to a reduction of the band gap through correlation effects. The excitons in the Rydberg regime above n = 10 remain unaffected until the band gap approaches them. Then they lose oscillator strength and ultimately vanish upon crossing with the band gap.

Landau-level quantization of the yellow excitons in cuprous oxide

AbstractLately, the yellow series of P -excitons in cuprous oxide could be resolved up to the principal quantum number n = 25. Adding a magnetic field, leads to additional confinement normal to the field. Thereby, the transition associated with the exciton n is transformed into the transition between the electron and hole Landau levels with quantum number n , once the associated magnetic length becomes smaller than the related exciton Bohr radius. The magnetic field of this transition scales roughly as n ^–3. As a consequence of the extended exciton series, we are able to observe Landau level transitions with unprecedented high quantum numbers of more than 75.

Экситонные линии поглощения PbS в композите CdS-PbS

AbstractThe spectral dependences of transmission, absorption, and reflection in CdS−PbS semiconductor layers, which are promising for the development of photodetectors and emitters in the region of an atmospheric- transparency window, were studied. It has been established that a series of thin lines are observed in the infrared spectrum on an absorption edge of the narrow-gap phase (PbS). A method for identification of exciton series was used, and exciton-binding energy E _ ex , exciton concentration N , and value of valence-band splitting Δ E _ v were determined.

Dielectric environment and/or random disorder effects on free, charged and localized excitonic states in monolayer WS2

Excitonic effects play an important role on the optoelectronic behavior of atomically thin two-dimensional (2D) crystals of the WS2 transition metal dichalcogenide. In this paper, neutral and charged exciton behaviors in monolayer WS2 are handled within effective-mass approximation for which the critical parameters are ensured from our ab initio calculations. Firstly, we reveal an exciton series with a novel energy dependence on the orbital angular momentum. Considerable control of the dielectric environment on neutral and charged excitons binding energies is elucidated. We demonstrate that for accepted values of effective masses, the negative and positive trion binding energies should be identical. Secondly, localization of neutral exciton center of mass motion by random potential arising from monolayer defects is also studied. The results obtained are in agreement with available experimental work.

Even exciton series in Cu2O

In $\mathrm{Cu_{2}O}$ parity is a good quantum number and thus the exciton spectrum falls into two parts: The dipole-active exciton states of negative parity and odd angular momentum, which can be observed in one-photon absorption ($\Gamma_4^-$ symmetry) and the exciton states of positive parity and even angular momentum, which can be observed in two-photon absorption ($\Gamma_5^+$ symmetry). The unexpected observation of $D$ excitons in two-photon absorption and of $F$ excitons in one-photon absorption has given evidence that the dispersion properties of the $\Gamma_5^+$ orbital valence band is giving rise to a coupling of the yellow and green exciton series. In this paper we show that the even and odd parity exciton system can be consistently described within the same theoretical approach. However, the Hamiltonian of the even parity system needs, in comparison to the odd exciton case, modifications to account for the very small radius of the $1S$ exciton. In the presented treatment we take special care of the central-cell corrections, which comprise a reduced screening of the Coulomb potential at distances comparable to the polaron radius, the exchange interaction being responsible for the exciton splitting into ortho and para states, and the inclusion of terms in the fourth power of $p$ in the kinetic energy. Since the yellow $1S$ exciton state is coupled to all other states of positive parity, we show how the central-cell corrections affect the whole even exciton series. The close resonance of the $1S$ green exciton with states of the yellow exciton series has a strong impact on the energies and oscillator strengths of all implied states. The consistency between theory and experiment with respect to energies and oscillator strengths for the even and odd exciton system in $\mathrm{Cu_{2}O}$ is a convincing proof for the validity of the applied theory.

Optical selection rules for excitonic Rydberg series in the massive Dirac cones of hexagonal two-dimensional materials

We investigate the optical transition selection rules for excitonic Rydberg series formed in massive Dirac cones. The entanglement of the exciton envelop function with the pseudospin texture leads to anomalous selection rules for one-photon generation of excitons, where $d$-orbitals can be excited with the opposite helicity selection rule from the $s$-orbitals in a given valley. The trigonal warping effects in realistic hexagonal lattices further renders more excited states bright, where $p$-orbitals can also be accessed by one-photon excitation with the opposite valley selection rules to the $s$-orbitals. The one-photon generation of exciton in the various states and the intra-excitonic transition between these states are both dictated by the discrete in-plane rotational symmetry of the lattices, and our results show that in hexagonal 2D materials the symmetry allowed transitions are enabled when trigonal warping effects are included in the massive Dirac fermion model. In monolayer transition metal dichalcogenides where excitons can be generated by visible light and intra-excitonic transitions can be induced by infrared light, we give the strength of these optical transitions, estimated using modified hydrogen-like envelope functions combined with the optical transition matrix elements between the Bloch states calculated at various $k$ points.

Excitonic polaritons of zinc diarsenide single crystals

Excitonic polaritons of ZnAs2 single crystals had been investigated. Parameters of singlet excitons with Г2¯(z) symmetry and orthoexcitons 2Г1¯(y)+Г2¯(x) had been determined. Spectral dependencies of ordinary and extraordinary dispersion of refractive index had been calculated using interferential reflection and transmittance spectra. It was shown, that A excitonic series were due to hole (V1) and electron (C1) bands. The values of effective masses of electrons (mc*=0.10m0) and holes (mv1*=0.89m0) had been estimated. It was revealed that the hole mass mv1* changes from 1.03m0 to 0.55m0 at temperature increasing from 10K up to 230K and that the electron mass mc* does not depend on temperature. The integral absorption A (eVcm−1) of the states n=1, 2 and 3 of Г2¯(z) excitons depends on the An≈n−3 equality, which it is characteristic for S-type excitonic functions. Temperature dependences of the integral absorption of ground states for Г2¯(z) and Г2¯(х) excitons differ. The ground states of B and C excitons formed by V3 – C1 and V4 – C1 bands and its parameters had been determined.

Coupled valence band dispersions and the quantum defect of excitons in Cu2O

Recent high-resolution absorption spectroscopy on highly excited excitons in cuprous oxide (Kazimierczuk et al 2014 Nature 514 343–347) have revealed significant deviations of their spectrum from the ideal hydrogen-like series. In atomic physics, the influence of the ionic core and the resulting modifications of the Coulomb interaction are accounted for by the introduction of a quantum defect. Here we translate this concept to the realm of semiconductor physics and show how the complex band dispersion of a crystal is mirrored in a set of empirical parameters similar to the quantum defect in atoms. Experimental data collected from high-resolution absorption spectroscopy in electric fields allow us to compare results for multiple angular momentum states of the yellow and even the green exciton series of . The agreement between theory and experiment validates our assignment of the quantum defect to the nonparabolicity of the band dispersion.

Excitonic spectra and energy band structure of ZnAl2Se4 crystals

Absorption, reflection and wavelength modulated reflection spectra were investigated in ZnAl2Se4 crystals. The energy positions of ground and excited states for three excitonic series (А, В and С) were determined. The main parameters of excitons and more precise values of energy intervals V1(Γ7)–C1(Γ6), V2(Γ6)–C1(Γ6), and V3(Γ7)–C1(Γ6) were estimated. Values of splitting due to crystal field and spin–orbital interaction were calculated. Effective masses of electrons (mC1∗) and holes (mV1∗, mV2∗, mV3∗) were estimated. Reflection spectra contours in excitonic region were calculated using dispersion equations. Optical functions for E>Eg from measured reflection spectra were assigned on the base of Kramers–Kronig relations.

Dielectric Genome of van der Waals Heterostructures.

Vertical stacking of two-dimensional (2D) crystals, such as graphene and hexagonal boron nitride, has recently lead to a new class of materials known as van der Waals heterostructures (vdWHs) with unique and highly tunable electronic properties. Ab initio calculations should in principle provide a powerful tool for modeling and guiding the design of vdWHs, but in their traditional form such calculations are only feasible for commensurable structures with a few layers. Here we show that the dielectric properties of realistic, incommensurable vdWHs comprising hundreds of layers can be efficiently calculated using a multiscale approach where the dielectric functions of the individual layers (the dielectric building blocks) are computed ab initio and coupled together via the long-range Coulomb interaction. We use the method to illustrate the 2D-3D transition of the dielectric function of multilayer MoS2 crystals, the hybridization of quantum plasmons in thick graphene/hBN heterostructures, and to demonstrate the intricate effect of substrate screening on the non-Rydberg exciton series in supported WS2. The dielectric building blocks for a variety of 2D crystals are available in an open database together with the software for solving the coupled electrodynamic equations.

Diversity of electronic transitions and photoluminescence properties of p-type cuprous oxide films: A temperature-dependent spectral transmittance study

Cuprous oxide films have been deposited on quartz substrates by a sol-gel method under various annealing temperatures. The X-ray diffraction analysis and Raman scattering show that all the films are of pure Cu2O phase. From comparison of photoluminescence with 488 and 325 nm laser excitations, the electronic transition energies and intensities present the annealing-temperature dependent behavior. The electronic band structures of the Cu2O film annealed at 800 °C, especially for the contribution of exciton series and high energy transitions, have been investigated by temperature dependent transmittance. The extracted refraction index and the high frequency dielectric constant both abruptly decrease until the temperature rises up to 100 K. Six transitions can be clearly identified and the red shift trend of Eo3-Eo5 transition energies with increasing the temperature can be found. Moreover, the anomalous behavior takes place at about 200 K from the Eo6 transition. The singularities indicate that the change in the crystalline and electronic band structure occurs as the temperature near 100 K and 200 K for the film.

Probing excitonic dark states in single-layer tungsten disulphide.

Transition metal dichalcogenide (TMDC) monolayers have recently emerged as an important class of two-dimensional semiconductors with potential for electronic and optoelectronic devices. Unlike semi-metallic graphene, layered TMDCs have a sizeable bandgap. More interestingly, when thinned down to a monolayer, TMDCs transform from indirect-bandgap to direct-bandgap semiconductors, exhibiting a number of intriguing optical phenomena such as valley-selective circular dichroism, doping-dependent charged excitons and strong photocurrent responses. However, the fundamental mechanism underlying such a strong light-matter interaction is still under intensive investigation. First-principles calculations have predicted a quasiparticle bandgap much larger than the measured optical gap, and an optical response dominated by excitonic effects. In particular, a recent study based on a GW plus Bethe-Salpeter equation (GW-BSE) approach, which employed many-body Green's-function methodology to address electron-electron and electron-hole interactions, theoretically predicted a diversity of strongly bound excitons. Here we report experimental evidence of a series of excitonic dark states in single-layer WS2 using two-photon excitation spectroscopy. In combination with GW-BSE theory, we prove that the excitons are of Wannier type, meaning that each exciton wavefunction extends over multiple unit cells, but with extraordinarily large binding energy (∼0.7electronvolts), leading to a quasiparticle bandgap of 2.7electronvolts. These strongly bound exciton states are observed to be stable even at room temperature. We reveal an exciton series that deviates substantially from hydrogen models, with a novel energy dependence on the orbital angular momentum. These excitonic energy levels are experimentally found to be robust against environmental perturbations. The discovery of excitonic dark states and exceptionally large binding energy not only sheds light on the importance of many-electron effects in this two-dimensional gapped system, but also holds potential for the device application of TMDC monolayers and their heterostructures in computing, communication and bio-sensing.

Optical transmittance of thin GaAs wafers upon laser pumping in the region of exciton resonances and the continuum of states: Exciton-exciton interaction

The transmittance spectra of thin “pure” GaAs bulk wafers upon optical pumping corresponding to the band of the ground state of the exciton series are recorded at a temperature of T = 1.7 K. The wafers were grown by molecular-beam epitaxy and vapor-phase epitaxy. An increase in the line amplitude and width upon pumping is observed, with no noticeable changes in the spectral position of the line peak. The increase is similar to that observed upon pumping in the continuum of states, but occurs at a somewhat lower rate. Estimation of the concentration of excitons created by pumping provides a means for determining the exciton-exciton interaction constant and comparing the result with known data. The integrated absorption method makes it possible to refine the exciton polariton-free charge carrier and exciton polariton-impurity interaction constants. The differential photoabsorption of the samples at the pumping modulation frequency is measured. The resultant modulated absorption spectra demonstrate the connection between induced absorption and the formation of differential spectra.

Excitonic spectra and band structure of CdGa2Se4 birefractive crystals

We report on the intersection of spectral dependences of refractive indices no and ne at the wavelengths 546nm (λ0) and 450nm (λ01) in CdGa2Se4 single crystals. The value of difference Δn=ne−no is equal to zero at the wavelengths involved. When placed between two crossed polarizers, the crystals of CdGa2Se4 exhibit a transmission band at the wavelength of λ0=546nm (300K). The ground and excited states of three excitonic series (A, B and C) were found out at 13K in CdGa2Se4 crystals, and other parameters of excitons and bands were determined. In the Г point of Brillouin zone the effective mass of electrons mc is equal to 0.14m0, and the effective masses of holes mv2 and mv3 are equal to 0.76m0 and 0.94m0, respectively. The hole mass mv1 depends upon the direction of wave vector k: at polarization E∥c, k∥a the mass mv1=1.15m0, and at polarization E∥c, k∥b mv1=0.84m0. The values of valence bands splitting in the center of Brillouin zone by the crystal field (Δcf=49meV) and spin–orbital interaction (Δso=351meV) were determined. The optical functions n, k, ε1 and ε2 in polarizations E⊥c and E∥c for the energy diapason from 3 to 6eV were calculated from the reflectivity spectra by Kramers–Kronig analysis. The evidenced features are discussed on the basis of recent theoretical calculations of the band structure of CdGa2Se4 crystals.

The band structure of birefractive CdGa2S4 crystals

In this paper, we report on the spectral dependence of Δn=no−ne for CdGa2S4 single crystals for shorter and longer wavelengths than the isotropic wavelength λ0=485.7nm (300K). It was established that Δn is positive at λ>λ0 and it is negative in the spectral range λ<λ0. The isotropic wavelength λ0 exhibits blue spectral shift with temperature decreasing. The ground and excited states of three excitonic series A, B and C with binding energies of 53meV, 52meV and 46meV, respectively, were found out at 10K. The effective masses of electrons for k=0 were derived from the calculation of excitonic spectra: mc∥(Е∥с)=0.21m0 and mc⊥(Е⊥с)=0.19m0. The holes masses are equal to 0.59m0 and 0.71m0 for Е∥с and Е⊥с, respectively. The value of valence bands splitting, V1−V2, by crystalline field equals 24meV, and V2−V3 splitting due to the spin–orbital interaction equals to 130meV. The optical functions n, k, ε1 and ε2 for Е⊥с and Е∥с polarizations were calculated by means of Kramers–Kronig analyses in the energy interval 3–6eV. The evidenced features are discussed taking into account the results of new theoretical calculations of CdGa2S4 band structure.

Wavelength‐modulated excitonic spectra in green series of Cu2O thin films sandwiched by MgO plates

AbstractIn order to clarify uniaxial stress effects on a green excitonic series in Cu2O, we measured temperature dependence of wavelength modulated (WM) absorption spectra of a Cu2O thin film sandwiched by MgO plates. In these spectra, excitonic resonances of 2P∼4P states are clearly observed even at 180 K. From these resonance spectral structures at each temperature, it is found that the band gap of the green series shifts to lower energy side than that of bulk crystals and the red shift becomes obvious with cooling down to 7 K. These results indicate that the trapping potential for the green excitons is formed by the uniaxial stress due to a lattice mismatch between the Cu2O and MgO (© 2012 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Optical spectra and energy band structure of AgAsS2 crystals

Ground and excited states of three exciton series are observed in the region of fundamental absorption edge of AgAsS2 crystals. The contours of exciton reflection spectra are calculated and the main parameters of excitons and energy bands are determined in the center of Brillouin zone. The optical reflection spectra are investigated at 30K in Eǁc and E⊥c polarizations in AgAsS2 crystals in the region of 2–6eV. The optical functions are calculated from the reflection spectra and a scheme of electronic transitions responsible for peculiarities of reflection spectra deep into the absorption band is proposed.

Direct Optical Observation of Band-Edge Excitons, Band Gap, and Fermi Level in Degenerate Semiconducting Oxide Nanowires In2O3

Direct optical evidence of Burstein–Moss shift (BMS) in conduction band of cubic c-In2O3 nanowires is reported herein. The optical property of degenerate semiconducting oxide c-In2O3 has been investigated by thermoreflectance (TR) spectroscopy. Low-temperature TR spectra clearly show a series of band-edge excitons for c-In2O3. The threshold energy for the exciton series was determined. One transition feature of direct gap caused by BMS was detected in all TR spectra from 20 to 300 K. The Femi-level (EF) energy above conduction-band edge (EC) is determined to be EF – EC ≈ 92 meV. The energy value causes a calculated electron density of ∼2.1 × 1019 cm–3. The direct gap of c-In2O3 with BMS is 3.43 eV at 300 K. Free exciton, bound exciton complexes, donor–acceptor pair transition, and defect emissions have been evaluated by photoluminescence (PL) measurements from 10 to 300 K. Photoresistivity change (i.e., 5.71 × 10–2 → 4.85 × 10–2 Ω-cm) under the illumination of halogen lamp (5 mW·cm–2) for c-In2O3 thin-film nanorods was detected. The experimental results show In2O3 nanocrystals an appropriate candidate applied not only for light-emitting devices but also for photoelectric-conversion cells.

Hexagonal Boron Nitride as a New Ultraviolet Luminescent Material and Its Application

Hexagonal boron nitride (hBN), which is conventionally used as one of the best-known heat-resistant materials due to its high thermal and chemical stability, has recently been found as a highly luminous material in the far-ultraviolet (FUV) region. This paper reviews the recent studies of hBN growth, optical properties, and device application development. In the case of highly pure crystals of hBN grown by the solvent growth method, the electronic excitation states near the band gap are governed by optically allowed exciton effects, which originate from the Jahn–Teller effect on the exciton series. The excitonic luminescence bands are utilized for an FUV plane light-emitting device excited by field emitters to take advantage of the highly luminous character.

Variational discrete variable representation for excitons on a lattice

We construct numerical basis function sets on a lattice, whose spatial extension is scalable from single lattice sites to the continuum limit. They allow us to compute small and large bound states with comparable, moderate effort. Adopting concepts of discrete variable representations, a diagonal form of the potential term is achieved through a unitary transformation to Gaussian quadrature points. Thereby the computational effort in three dimensions scales as the fourth instead of the sixth power of the number of basis functions along each axis, such that it is reduced by two orders of magnitude in realistic examples. As an improvement over standard discrete variable representations, our construction preserves the variational principle. It allows for the calculation of binding energies, wave functions, and excitation spectra. We use this technique to study central-cell corrections for excitons beyond the continuum approximation. A discussion of the mass and spectrum of the yellow exciton series in the cuprous oxide, which does not follow the hydrogenic Rydberg series of Mott-Wannier excitons, is given on the basis of a simple lattice model.