Excitonic Features Research Articles

First principle calculation of structural, electronic, optical, elastic and thermodynamic properties of group IIA metal iodides: Structure-property correlation

The Structural, Electronic, Optical, Elastic and Thermodynamic Properties of Group IIA Metal Iodides were investigated using DFT calculations employing full potential linearized augmented plane wave plus local orbitals with Perdew Burke Ernzerhof-Generalized Gradient Approximation (PBE-GGA). We have also carried out band structure calculations using some other exchange-correlation functionals such as LSDA, PBEsol-GGA,WC-GGA and TB-mBJ for all the compounds. Among these iodides, MgI2 and CaI2 have same trigonal structure while SrI2 and BaI2 follow same orthorhombic structure with BeI2 having orthorhombic structure of entirely different space group. All the calculated properties show consistently the similarity for the iodides of same structure following the structure-property correlation. Bands are fewer and less dense for MgI2 and CaI2 in contrast with many and denser bands of SrI2 and BaI2 in comparison to altogether different moderately dense bands of BeI2. The band structure reveals an indirect band gap of 4.08 eV, 3.5 eV, 3.58 eV for BeI2, MgI2, CaI2 respectively and a direct band gap of 3.79, 3.35 for SrI2, BaI2 respectively. The optical anisotropy with excitonic features exhibited by BeI2, MgI2 and CaI2 is clearly absent in SrI2 and BaI2. The calculated elastic constants show that all these compounds are quite mechanically stable having the magnitude of elastic anisotropy in the order: BeI2>CaI2>BaI2>MgI2>SrI2. All the thermodynamic properties show bunching according to their structure consistent with structure-property correlation. Debye temperatures were calculated for BeI2, MgI2, CaI2, SrI2 and BaI2 at room temperature and zero pressure as 183.53 K, 188.51 K, 166.98 K, 151.12 K and 135.55 K respectively. Many parameters of these properties are new in the literature. A reasonable agreement between our calculated and available theoretical/experimental band gaps of these iodides in the literature justifies the accuracy of the calculations of other properties. All the properties of these iodides are explained consistently and comprehensively in terms of their structure-property correlation.

Excitonic Effects in the Optical Properties of Scandium and Hafnium MXene Semiconductors from First‐Principles Calculations

The present study uses a full‐potential linearized augmented plane wave method and Bethe–Salpeter equation to calculate and interpret the optical properties of Sc2CT2 (T = O, F, and OH) and Hf2CO2 MXene semiconductors, including real and imaginary parts of the dielectric function along with energy loss function. Excitonic structures are observed below calculated bandgaps in these compounds. Sc2CO2 and Sc2CF2 have three excitonic features, whereas Sc2C(OH)2 and Hf2CO2 show two. As compared to other compounds, Sc2CO2 has a larger exciton binding energy. The energy loss functions display spectral features near the bandgap regions due to the excitonic structures in the imaginary part of the dielectric function.

Dielectric Function of 2D Tungsten Disulfide in Homo‐ and Heterobilayer Stacking

AbstractThe opto‐electronic properties of semiconducting 2D materials can be flexibly manipulated by engineering the atomic‐scale environment. This can be done by including 2D materials in tailored van der Waals (vdW) stacks, whose optical response is a function of the number and the type of adjacent 2D layers. This work reports a systematic investigation of the dielectric function of 2D semiconducting WS2 in various stacking configurations: monolayer, 3R/2H homobilayer, and WS2/MoS2 heterobilayer. Reliable, Kramers–Kronig‐consistent dielectric functions are obtained for WS2 in each configuration by means of spectroscopic ellipsometry (SE) and related parametric optical modeling in a wide spectral range (1.55–3.10 eV). The results of SE are combined with photoluminescence and absorbance spectra to identify the spectral position of the main excitonic features in WS2, which manifest sizable redshifts depending on the stacking configuration. These results represent a consistent reference set for the dielectric function of WS2 in vdW stacking configurations of particular interest for the scientific and technological field, and can be fruitfully exploited for reliable predictions of the optical response of WS2‐containing systems.

Decoupling excitons behavior of two-dimensional Ruddlesden-Popper PEA2PbI4 nanosheets

Two-dimensional (2D) Ruddlesden-Popper hybrid organic-inorganic perovskites are the most promising candidates for highly efficient optoelectronic devices due to their remarkable exciton characteristics, adjustable band structure and long-term environmental stability. However, excitons emission behavior of 2D Ruddlesden-Popper perovskites is still unclear. Here we theoretically-experimentally decoupled the excitons behavior in 2D Ruddlesden-Popper PEA2PbI4 nanosheets. Theoretically, the Elliott theory was used to separate exciton and band edge absorptions of PEA2PbI4 nanosheets and determine an exciton binding energy of about 274 meV. Experimentally, spectral-dependent photoluminescence lifetime and excitation powder density-dependent photoluminescence spectra revealed that a distinct photoluminescence tail emission should be derived from localized excitons with lower emission energy than free excitons. Further, the luminescent component of the free excitons and localized excitons with their corresponding densities of states was theoretically decoupled by line-shape analysis of PEA2PbI4 nanosheets photoluminescence spectra, which is consistent with the experimental results demonstrating the existence of localized excitons. Hence, our work provides understanding on the exciton behavior and luminescence mechanism of 2D Ruddlesden-Popper perovskites, which would benefit the prediction of high-performance excitonic devices based on 2D Ruddlesden-Popper perovskites.

Two‐Dimensional Excitonic Networks Directed by DNA Templates as an Efficient Model Light‐Harvesting and Energy Transfer System

AbstractPhotosynthetic organisms organize discrete light‐harvesting complexes into large‐scale networks to facilitate efficient light collection and utilization. Inspired by nature, herein, synthetic DNA templates were used to direct the formation of dye aggregates with a cyanine dye, K21, into discrete branched photonic complexes, and two‐dimensional (2D) excitonic networks. The DNA templates ranged from four‐arm DNA tiles, ≈10 nm in each arm, to 2D wireframe DNA origami nanostructures with different geometries and varying dimensions up to 100×100 nm. These DNA‐templated dye aggregates presented strongly coupled spectral features and delocalized exciton characteristics, enabling efficient photon collection and energy transfer. Compared to the discrete branched photonic systems templated on individual DNA tiles, the interconnected excitonic networks showed approximately a 2‐fold increase in energy transfer efficiency. This bottom‐up assembly strategy paves the way to create 2D excitonic systems with complex geometries and engineered energy pathways.

Two-Dimensional Excitonic Networks Directed by DNA Templates as an Efficient Model Light-Harvesting and Energy Transfer System.

Photosynthetic organisms organize discrete light-harvesting complexes into large-scale networks to facilitate efficient light collection and utilization. Inspired by nature, herein, synthetic DNA templates were used to direct the formation of dye aggregates with a cyanine dye, K21, into discrete branched photonic complexes, and two-dimensional (2D) excitonic networks. The DNA templates ranged from four-arm DNA tiles, ≈10 nm in each arm, to 2D wireframe DNA origami nanostructures with different geometries and varying dimensions up to 100×100 nm. These DNA-templated dye aggregates presented strongly coupled spectral features and delocalized exciton characteristics, enabling efficient photon collection and energy transfer. Compared to the discrete branched photonic systems templated on individual DNA tiles, the interconnected excitonic networks showed approximately a 2-fold increase in energy transfer efficiency. This bottom-up assembly strategy paves the way to create 2D excitonic systems with complex geometries and engineered energy pathways.

Surface Versus Bulk State Transitions in Inkjet-Printed All-Inorganic Perovskite Quantum Dot Films.

The anion exchange of the halides, Br and I, is demonstrated through the direct mixing of two pure perovskite quantum dot solutions, CsPbBr3 and CsPbI3, and is shown to be both facile and result in a completely alloyed single phase mixed halide perovskite. Anion exchange is also observed in an interlayer printing method utilizing the pure, unalloyed perovskite solutions and a commercial inkjet printer. The halide exchange was confirmed by optical absorption spectroscopy, photoluminescent spectroscopy, X-ray diffraction, and X-ray photoemission spectroscopy characterization and indicates that alloying is thermodynamically favorable, while the formation of a clustered alloy is not favored. Additionally, a surface-to-bulk photoemission core level transition is observed for the Cs 4d photoemission feature, which indicates that the electronic structure of the surface is different from the bulk. Time resolved photoluminescence spectroscopy indicates the presence of multiple excitonic decay features, which is argued to originate from states residing at surface and bulk environments.

Near-Infrared Plasmon-Induced Hot Electron Extraction Evidence in an Indium Tin Oxide Nanoparticle/Monolayer Molybdenum Disulfide Heterostructure.

In this work, we observe plasmon-induced hot electron extraction in a heterojunction between indium tin oxide nanocrystals and monolayer molybdenum disulfide. We study the sample with ultrafast differential transmission, exciting the sample at 1750 nm where the intense localized plasmon surface resonance of the indium tin oxide nanocrystals is and where the monolayer molybdenum disulfide does not absorb light. With the excitation at 1750 nm, we observe the excitonic features of molybdenum disulfide in the visible range, close to the exciton of molybdenum disulfide. Such a phenomenon can be ascribed to a charge transfer between indium tin oxide nanocrystals and monolayer molybdenum disulfide upon plasmon excitation. These results are a first step toward the implementation of near-infrared plasmonic materials for photoconversion.

Tunable magneto-optical properties in MoS2 via defect-induced exciton transitions

The presence of chalcogen vacancies in monolayer transition metal dichalcogenides (TMDs) leads to excitons with mixed localized-delocalized character and to reduced valley selectivity. Recent experimental advances in defect design in TMDs allow for a close examination of such mixed exciton states as a function of their degree of circular polarization under external magnetic fields, revealing strongly varying defect-induced magnetic properties. A theoretical understanding of these observations and their physical origins demands a predictive, structure-sensitive theory. In this work, we study the effect of chalcogen vacancies on the exciton magnetic properties in monolayer ${\mathrm{MoS}}_{2}$. Using many-body perturbation theory, we show how the complex excitonic picture associated with the presence of defects---with reduced valley and spin selectivity due to hybridized electron-hole transitions---leads to a structurally controllable exciton magnetic response. We find a variety of $g$-factors with changing magnitudes and sign depending on the exciton energy and character. Our findings suggest a pathway to tune the nature of the excitons---and by that their magneto-optical properties---through defect architecture.

Moiré exciton condensate: Nonlinear Dirac point, broken-symmetry Bloch waves, and unusual optical selection rules

Moir\'e 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 moir\'e excitons. Here we study the properties of moir\'e 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 moir\'e potential. We find the nonlinear dispersion of the moir\'e exciton condensate exhibits complex loop structure induced by exciton-exciton interaction. A nonlinear Dirac cone emerges at $\boldsymbol{\Gamma}$ point of the Bloch band, with a three-fold degenerate nonlinear Dirac point. Each degenerate Bloch wave at nonlinear Dirac point spontaneously breaks $C3$ rotational symmetry of the moir\'e potential, and themselves differ by $C3$ rotations. Since they reside in the light cone, these nontrivial Bloch band structure and broken-symmetry Bloch waves can be experimentally detected by examining light emission from those states. Symmetry breaking of Bloch states implies unusual optical selection rules compared with single exciton case: moir\'e exciton condensate at $\boldsymbol{\Gamma}$ point emits light with all three components of polarization instead of only left or right circular polarization. We further propose that, by applying in-plane electric field on one layer to drive an initially optically dark exciton condensate towards light cone, the light polarization of final states as well as their dependence on field direction serves as the smoking gun for experimental observation.

Exploring magneto-optic properties of colloidal two-dimensional copper-doped CdSe nanoplatelets

Abstract Transition-metal-doped semiconductor nanocrystals have received significant attention because of their attractive features deeming them invaluable in various technological fields including optoelectronics, bio-photonics, and energy conversion, to name a few. Of particular, these interests are two-dimensional materials with useful optical and magnetic properties combined with their large surface areas opening up new applications in biotechnology. These applications range from multimodal optical and magnetic bioimaging and sensing to measuring the weak magnetic field due to brain waves using their magneto-optic properties stemming from the exchange interaction between the transition metal dopants and the carrier spins. These magnetic 2D materials could also significantly advance the field of spintronics. In this work, we report on a study of the magnetic and magneto-optic properties of colloidal two-dimensional (2D) copper-doped CdSe nanoplatelets (NPLs) that are synthesized using a high-temperature colloidal technique. We carried out optical and circularly polarized magneto-photoluminescence spectrometry to investigate the magnetism in our solution-processed nanostructures doped with copper ion impurities. At cryogenic temperatures, two excitonic features are observed for doped NPLs, which are more prominent compared to the undoped NPLs. Furthermore, the excitonic circular polarization (CP) is recorded as a function of the applied magnetic field (B) and temperature (T). The detailed analysis provides a picture of the magneto-optical behavior of the doped 2D NPLs in the presence of paramagnetic copper ions. This work paves the way for significant advances in bio/nanophotonics where tunable optical and magnetic properties of doped nanoplatelets can be leveraged to make more efficient, flexible, and low-cost devices.

Modulating the intralayer and interlayer valley excitons in WS2 through interaction with AlGaN

The fine-tuning of exciton transition and valley polarization process in two-dimensional materials have drawn tremendous research interest due to their rich valley-contrasting physics. Here, we demonstrate highly tunable exciton and valley characteristics in monolayer and bilayer WS2 through coupling to AlGaN with different doping levels. A notable redshift in exciton energy is observed by interfacing WS2 with n-type AlGaN. More interestingly, an interlayer exciton peak emerges as a result of the formation of type-II band alignment in bilayer WS2. Both the interlayer and intralayer exciton energies are tunable by the twist angle of bilayer WS2. A high valley polarization of 82.2% is achieved in monolayer WS2 at 13 K by coupling with n-type AlGaN, due to the faster exciton decay rate through electron-phonon interaction and the reduced intervalley scattering by doping-induced carrier screening. The valley polarization of interlayer exciton is higher than that of the intralayer exciton, due to the suppressed intervalley scattering resulting from the reduced electron-hole interaction. This work has presented a facile and efficient technique to modulate the excitonic properties of 2D materials. The reported high valley polarization in monolayer WS2 and the discovery of interlayer exciton in bilayer WS2 will trigger innovative study in valley exciton physics and facilitate emerging valleytronic applications.

Heavy-hole–light-hole exciton system in GaAs/AlGaAs quantum wells

Light-hole (lh) excitons (Xlhs) in quantum wells (QWs) are hardly studied compared with heavy-hole (hh) excitons (Xhhs), mainly due to the difficulties of their experimental observation. In this paper, a comprehensive study of both types of excitons in high-quality GaAs/AlGaAs QWs of different widths is performed. We focus on the energy positions of exciton resonances and the exciton-light interaction. The effect of mixing lhs and hhs in GaAs-based structures on these exciton characteristics is investigated. The corrections to the exciton energy due to mixing are only a fraction of millielectronvolts for wide QWs, in which the energy levels of Xhhs and Xlhs are close to each other. It is also experimentally found that the oscillator strength of Xlhs is $\ensuremath{\sim}2.5$ times less than that of Xhhs. This value noticeably deviates from the 3:1 oscillator strength ratio known for optical transitions between free electron and hole states. This deviation originates from the different squeezing of the Xlh and Xhh wave functions due to distinct values of the effective masses of the Xlh and Xhh in the heterostructure. Mixing of hh and lh valence bands is not so important.

Theory of the dark state of polyenes and carotenoids

A theory is developed to describe the singlet dark state (usually labeled S1 or 2Ag) of polyenes and carotenoids. The theory assumes that in principle this state is a linear combination of a singlet triplet-pair and an odd-parity charge-transfer exciton. Crucially, these components only couple when the triplet-pair occupies neighboring dimers, such that an electron transfer between the triplets creates a nearest-neighbor charge-transfer excitation. This local coupling stabilises the 2Ag state and induces a nearest neighbor attraction between the triplets. In addition, because of the electron-hole attraction in the exciton, the increased probability that the electron-hole pair occupies neighboring dimers enhances the triplet-triplet attraction: the triplet pair is `slaved' to the charge-transfer exciton. The theory also predicts that as the Coulomb interaction is increased, the 2Ag state evolves from a predominately odd-parity charge-transfer exciton state with a small component of triplet-pair character to a state predominately composed of a triplet-pair with some exciton character. Above a critical Coulomb interaction there is a decoupling of the triplet-pair and charge-transfer exciton subspaces, such that the 2Ag state becomes entirely composed of an unbound spin-correlated triplet pair. The predictions of this theory are qualitatively consistent with high-level density matrix renormalization group calculations of the Pariser-Parr-Pople (or extended Hubbard) model.

Signatures of bright-to-dark exciton conversion in corrugated MoS2 monolayers

In this study, we investigated the effect of periodic uniaxial strains on electron and phonon transports of polycrystalline and single-crystal molybdenum disulphide (MoS2) monolayers on a periodically corrugated sapphire surface. Analysis of micro-Raman, polarized photoluminescence and second harmonic generation results shows the anisotropy of the corrugation-induced strain in both single- and polycrystalline MoS2 monolayers. AFM topography measurements show periodically-rippled surfaces of the MoS2 in the nanometre scale. Our results show that the application of the periodic strain produces two major effects on the band structure of MoS2 monolayers: modulations on the band gap anisotropy and reduction of out-of-plane spin-relaxation time due to substrate-induced bending of MoS2. Spin memory loss, in other words, shortening the spin relaxation time, enables an electron spin-flip scattering process that can convert a formerly bright exciton to a dark exciton. Such conversion is reflected in decreasing intensity of photoluminescence and in the light intensity collected by scanning near-field microscope. Our results demonstrate the ability to control both the bandgap and exciton character in monolayer MoS2 via periodic strains imposed by corrugated sapphire substrates. This approach offers an effective means in designing novel electronic devices for photovoltaic applications. The bright-to-dark excitons conversion in photovoltaic devices can boast longer lifetimes than their bright exciton counterparts so they can be more efficiently collected by external electrodes. The strain-induced conversion of the bright-to-dark excitons makes the hybrid MoS2/corrugated sapphire structure an interesting platform for future photovoltaic applications.

Narrow electroluminescence in bromide ligand-capped cadmium chalcogenide nanoplatelets

Colloidal zinc blende II–VI semiconductor nanoplatelets (NPLs) demonstrate as a promising class of materials for optoelectronic devices due to their unique excitonic characteristics, narrow emission linewidth, and quantum well-structure. Adopting heterostructures for these nanocrystals allows tuning of their optical features and enhances their photostability, photoluminescence (PL), quantum yield (QY), and color purity for further device integration. Exchanging of carboxylate capping ligands on top and bottom [001] facets of CdSe NPLs with halide ligands is an alternative to achieve the aims of spectral tunability and improve surface passivation, but to date there have been no reports on integrating the advantages of halide ligand exchanged CdSe NPLs for device fabrication. In this work, we demonstrate green electroluminescence (EL) of bromide ligand-capped CdSe NPLs as active emitters in an electrically driven light emitting diode (LED) with a low turn-on voltage of 3.0 V. We observed EL emission at 533.1 nm with a narrow linewidth of 19.4 nm, a maximum luminance of 1276 cd/m2, and the highest external quantum efficiency (EQE) of 0.803%. These results highlight the ability of halide ligand exchange in tuning the EL properties of CdSe NPL-LEDs and potential of bromide ligand-capped CdSe NPLs in contributing to the green emission region of NPL-LEDs, demonstrating its potential for future device integration and contribution to a high color rendering index of future NPL displays.

Recombination dynamics of indirect excitons in hexagonal BN epilayers containing polytypic segments grown by chemical vapor deposition using carbon-free precursors

Hexagonal (h) BN is a semiconductor that crystallizes in layers of a two-dimensional honeycomb structure. Since hBN exhibits high quantum efficiency (QE) near-band edge emission at around 5.8 eV in spite of the indirect bandgap, hBN has a potential for the use in deep-ultraviolet light emitters. For elucidating the emission dynamics of indirect excitons (iXs) in hBN, spatially and temporally resolved luminescence measurements were carried out on hBN epilayers grown using carbon-free precursors. In addition to major μm-side flat-topped (0001) hBN columnar grains, sub-μm-scale polytypic segments were identified, which were likely formed by certain growth instabilities. The hBN domains exhibited predominant emissions of phonon-assisted fundamental iXs at 5.7–5.9 eV and a less-pronounced 4.0-eV emission band. The photoluminescence lifetime (τPL) for the iX emissions was 54 ps, which most likely represents the midgap recombination lifetime (τMGR) for an iX reservoir. Because τPL did not change while the cathodoluminescence (CL) intensity increased with temperature above 100 K, both the immobile character of iXs and strong exciton–phonon interaction seem significant for procreating the high QE. The CL intensity and τPL of the 5.5 eV band monotonically decreased with temperature, indicating that τPL represents τMGR, most probably a nonradiative lifetime, around the real states. Equally significant emissions at 6.035 eV at 12 K and 6.0–6.1 eV at 300 K were observed from the polytypic segments, most probably graphitic bernal BN, which also exhibited negligible thermal quenching property.

Nanotubes from Ternary WS2(1-x)Se2x Alloys: Stoichiometry Modulated Tunable Optical Properties.

Nanotubes of transition metal dichalcogenides such as WS2 and MoS2 offer unique quasi-1D properties and numerous potential applications. Replacing sulfur by selenium would yield ternary WS2(1–x)Se2x (0 ≤ x ≤ 1; WSSe) nanotubes, which are expected to reveal strong modulation in their absorption edge as a function of selenium content, xSe. Solid WO2.72 oxide nanowhiskers were employed as a sacrificial template to gain a high yield of the nanotubes with a rather uniform size distribution. Though sulfur and selenium belong to the same period, their chemical reactivity with oxide nanowhiskers differed appreciably. Here, the closed ampoule technique was utilized to achieve the completion of the solid–vapor reaction in short time scales instead of the conventional flow reactor method. The structure and chemical composition of the nanotubes were analyzed in detail. X-ray and electron diffractions indicated a systematic modulation of the WSSe lattice upon increasing the selenium content. Detailed chemical mapping showed that the sulfur and selenium atoms are distributed in random positions on the anion lattice site of the nanotubes. The optical excitonic features and absorption edges of the WSSe nanotubes do not vary linearly with the composition xSe, which was further confirmed by density functional theory calculations. The WSSe nanotubes were shown to exhibit strong light–matter interactions forming exciton–polariton quasiparticles, which was corroborated by finite-difference time-domain simulations. Transient absorption analysis permitted following the excited state dynamics and elucidating the mechanism of the strong coupling. Thus, nanotubes of the ternary WSSe alloys offer strong band gap tunability, which would be useful for multispectral vision devices and other optoelectronic applications.

Efficient treatment of low-frequency response and decoherence in a real-time evolution scheme.

In this paper, we present an improved real-time current-based approach for calculating the frequency-dependent dielectric function of a bulk periodic system, which can achieve a unified treatment of longitudinal and transverse macroscopic geometries on the same footing, and an improvement to make the approach of calculating dielectric function more robust for the avoidance of numerical divergencies at low frequency near zero in some specific cases. The validity of the improved approach implementation is verified by calculating the dielectric function of bulk periodic system in the ground in the longitudinal geometry, enabling the improved approach to be extended to excited bulk periodic systems in the transverse geometry. Further, a phenomenological description of decoherence has been incorporated within the framework of time-dependent density-functional theory (TDDFT). It is concluded that the decoherence model can suppress the numerical divergence of low frequency and grows the excitonic feature of silicon, although it adopts the approximate time-dependent exchange-correlation potential. Thus, the use of the decoherence TDDFT model opens pathways for handling the decoherence effects within the framework of TDDFT.

Excitonic fine structure of epitaxial Cd(Se,Te) on ZnTe type-II quantum dots

The structure of the ground-state exciton of Cd(Se,Te) quantum dots embedded in ZnTe matrix is studied experimentally using photoluminescence spectroscopy and theoretically using $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ and configuration interaction methods. The experiments reveal a considerable reduction of fine-structure splitting energy of the exciton with an increase of Se content in the dots. That effect is interpreted by theoretical calculations to originate due to the transition from spatially direct (type-I) to indirect (type-II) transition between electrons and holes in the dot induced by an increase of Se. The trends predicted by the theory match those of the experimental results very well. The theory identifies that the main mechanism causing elevated fine-structure energy, in particular in type-I dots, is due to the multipole expansion of the exchange interaction. Moreover, the theory reveals that for Se contents in the dot $>0.3$, there also exists a peculiar type of confinement showing signatures of both type I and type II and which exhibits extraordinary properties, such as an almost purely light hole character of exciton and toroidal shapes of hole states.