Exciton Absorption Spectra Research Articles

Magneto-excitons in Cu2O: theoretical model from weak to high magnetic fields

Recent experimental and theoretical work on hydrogen-like absorption spectra of excitons in external magnetic fields revealed new effects when the Coulomb interaction becomes comparable to the magnetic perturbation. We present a theoretical approach that allows for calculation of absorption spectra for any value of magnetic field. This approach opens the possibility to compute the optical functions i.e. reflectivity, transmission and absorption including the excitonic effects for various strength of external magnetic field.

Exciton states and absorption spectra in freestanding monolayer transition metal dichalcogenides: A variationally optimized diagonalization method

The comprehensive analyses of exciton states and absorption spectra from freestanding monolayer transition metal dichalcogenides such as ${\mathrm{MoS}}_{2}, {\mathrm{MoSe}}_{2}, {\mathrm{MoTe}}_{2}, {\mathrm{WS}}_{2}$, and ${\mathrm{WSe}}_{2}$ are theoretically presented in the Wannier\ensuremath{-}Mott exciton theory. We propose an efficient and simple exact diagonalization method based on a variationally optimized two-dimensional (2D) modified Laguerre basis set, which has been successfully applied to calculate both the ground and excited states. The convergence of the method as a function of the basis set size was analyzed in detail. The modified Laguerre basis functions were very closely concentrated in space, and they led to a rather rapid convergence. Moreover, the convergence rate was faster under variational optimization. Our results regarding the exciton binding energies of a ground state with even a small number of basis states are in excellent agreement with those of the density-function theory calculations in the literature [I. Kyl\anp\a\a and H.-P. Komsa, Phys. Rev. B 92, 205418 (2015)]. The exciton states appeared in an anomalous energy-level ordering of the orbital angular momentum caused by the dielectric screening effect. The exciton absorption spectra exhibited strong absorption lines of the nonhydrogenic exciton Rydberg series, which was dominated by the s-type exciton states. There were two prominent low-energy peaks of the A and B excitons, and the A exciton was slightly higher in intensity than the B exciton, which is in good agreement with the experimental observations. In general, our presented exact diagonalization method based on a variationally optimized 2D modified Laguerre basis set has proven to be applicable to more general cases of screened potentials in 2D materials and atomic physics, as well as providing a simple approach for investigating exciton properties.

Generalized Kasha’s Model: T-Dependent Spectroscopy Reveals Short-Range Structures of 2D Excitonic Systems

Summary Excitonic organic materials owe their tunable optoelectronic properties to intricate microscopic configurations, challenging for conventional characterization methods to resolve. We generalize Kasha’s model by incorporating the temperature (T)-dependent absorption peak shift, in addition to the monomer-aggregate absorption peak shift that defines J- and H-aggregates, to characterize the microscopic structures. We show that the short-range interactions dominate in determining the direction of the T-dependent peak shift, which accounts for previously observed T-dependent blueshifting J-aggregates (BJ-aggregates) that were not explained and predicts the existence of redshifting H-aggregates (RH-aggregates). This defines four types of excitonic aggregates: RJ-, BH-, BJ-, and RH-aggregates, where the latter two unconventional aggregates are possible because of the two dimensionality of excitonic systems and cannot be understood with the original Kasha’s theory. Our conceptual framework is useful for elucidating structure-function relationships in molecular excitonic systems and is fully compatible with existing tools. Possible extensions to other spectroscopic observables and related systems are discussed.

Superlocalization of Excitons in Carbon Nanotubes at Cryogenic Temperature.

At cryogenic temperature and at the single emitter level, the optical properties of single-wall carbon nanotubes depart drastically from that of a one-dimensional (1D) object. In fact, the (usually unintentional) localization of excitons in local potential wells leads to nearly 0D behaviors such as photon antibunching, spectral diffusion, inhomogeneous broadening, etc. Here, we present a hyperspectral imaging of this spontaneous exciton localization effect at the single nanotube level using a super-resolved optical microscopy approach. We report on the statistical distribution of the trap localization, depth, and width. We use a quasi-resonant photoluminescence excitation approach to probe the confined quantum states. Numerical simulations of the quantum states and exciton diffusion show that the excitonic states are deeply modified by the interface disorder inducing a remarkable discretization of the excitonic absorption spectrum and a quenching of the free 1D exciton absorption.

Exciton absorption spectra in narrow armchair graphene nanoribbons in an electric field

We present an analytical investigation of the exciton optical absorption in a narrow armchair graphene nanoribbon (AGNR) in the presence of a longitudinal external electric field directed parallel to the ribbon axis. The two-body 2D Dirac equation for the massless electron and hole subject to the ribbon confinement, Coulomb interaction and electric field is employed. The ribbon confinement is assumed to be much stronger than the internal exciton electric field which in turn considerably exceeds the external electric field. This justifies an adiabatic approximation implying a slow longitudinal and fast transverse electron-hole relative motion governed by the exciton attraction and accompanied by the external electric field and ribbon confinement effects, respectively. In the single subband approximation of the isolated size-quantized subbands induced by the ribbon confinement the exciton electroabsorption coefficient is determined in an explicit form. The pronounced dependencies of the exciton peak positions, widths and intensities on the ribbon width and electric field strength are traced. The electron-hole exciton attraction modifies remarkably the Franz-Keldysh electroabsorption in the frequency region both below and above the edges determined by the size-quantized energy levels. In the double-subband approximation of the interacting ground and first excited subbands the combined effect of the exciton electro- and autoionization caused by the electric field and intersubband coupling, respectively, are explored. Estimates of the expected experimental values for the typically employed AGNR show that for a weak electric field the exciton quasi-discrete states remain sufficiently stable to be observed in optical experiments, while relatively strong fields free the captured carriers to further restore their contribution to the transport.

Longer Cations Increase Energetic Disorder in Excitonic 2D Hybrid Perovskites.

We synthesize and characterize derivatives of the two-dimensional hybrid perovskite (2DHP) phenethylammonium lead iodide ((PEA)2PbI4) in which the para H on the cation is replaced with F, Cl, CH3, or Br. These substitutions increase the length of the cation but leave the cross-sectional area unchanged, resulting in structurally similar PbI42- frameworks with increasing interlayer spacing. Longer cations result in broader, blue-shifted excitonic absorption spectra with reduced or eliminated structure, indicating greater energetic disorder. Photoluminescence spectra are largely invariant and insensitive to cation length, suggesting polaron formation stabilizes a structural and electronic minimum. Temperature-dependent line width analysis reveals excitons couple to a vibration on the organic framework that is weakly sensitive to these cation substitutions, and Raman spectra and electronic structure calculations support the presence of such a cationic mode. Despite carriers being confined to the inorganic framework, the length of the organic cation alters the optical and electronic properties of 2DHPs.

Temperature dependence of the band gap of high optical quality CdS:Dy thin films based on exciton spectra

CdS:Dy films were prepared by CSVS method on the cleaned glass substrates. The influence of Dy doping on the optical properties of CdS thin (500 nm) films was studied. The presence of narrow lines of bound and free excitons in the photoluminescence, reflection and absorption spectra shows a remarkable optical quality of the investigated films. The temperature dependence of the band gap of the films was studied on the basis of measurements of the energy position of the free excitons. A decrease in the anisotropic crystal field and the effect of depolarization of free exciton absorption spectra with increasing temperature are observed. It was concluded that the efficiency of CdS:Dy thin films photovoltaic applications can be further increased.

The exciton absorption spectrum of thin films of ternary compounds in the AgBr–PbBr2 system

Exciton absorption spectra of thin films of complex compounds AgPbBr3, AgPb2Br5, and AgPb3Br7 were studied in the photon energy range 2–6 eV. It was established that the compounds belong to the direct band dielectrics; low-frequency excitons are localized in the structural layers (PbBr8)6– of the crystal lattice and have a quasi-two-dimensional nature.

Magneto-absorption spectra of hydrogen-like yellow exciton series in cuprous oxide: excitons in strong magnetic fields

We study the absorption spectra of the yellow excitons in Cu2O in high magnetic fields using polarization-resolved optical absorption measurements with a high frequency resolution. We show that the symmetry of the yellow exciton results in unusual selection rules for the optical absorption of polarized light and that the mixing of ortho- and para- excitons in magnetic field is important. The calculation of the energies of the yellow exciton series in strong and weak magnetic field limits suggests that a broad n = 2 line is comprized by two closely overlapping lines, gives a good fit to experimental data and allows to interpret the complex structure of excitonic levels.

Exciton Absorption Spectra by Linear Response Methods: Application to Conjugated Polymers.

The theoretical description of the time-evolution of excitons requires, as an initial step, the calculation of their spectra, which has been inaccessible to most users due to the high computational scaling of conventional algorithms and accuracy issues caused by common density functionals. Previously (J. Chem. Phys. 2016, 144, 204105), we developed a simple method that resolves these issues. Our scheme is based on a two-step calculation in which a linear-response TDDFT calculation is used to generate orbitals perturbed by the excitonic state, and then a second linear-response TDDFT calculation is used to determine the spectrum of excitations relative to the excitonic state. Herein, we apply this theory to study near-infrared absorption spectra of excitons in oligomers of the ubiquitous conjugated polymers poly(3-hexylthiophene) (P3HT), poly(2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene) (MEH-PPV), and poly(benzodithiophene-thieno[3,4-b]thiophene) (PTB7). For P3HT and MEH-PPV oligomers, the calculated intense absorption bands converge at the longest wavelengths for 10 monomer units, and show strong consistency with experimental measurements. The calculations confirm that the exciton spectral features in MEH-PPV overlap with those of the bipolaron formation. In addition, our calculations identify the exciton absorption bands in transient absorption spectra measured by our group for oligomers (1, 2, and 3 units) of PTB7. For all of the cases studied, we report the dominant orbital excitations contributing to the optically active excited state-excited state transitions, and suggest a simple rule to identify absorption peaks at the longest wavelengths. We suggest our methodology could be considered for further developments in theoretical transient spectroscopy to include nonadiabatic effects, coherences, and to describe the formation of species such as charge-transfer states and polaron pairs.

Charge-transfer states and optical transitions at the pentacene-TiO2 interface

Pentacene molecules have recently been observed to form a well-ordered monolayer on the (110) surface of rutile TiO2, with the molecules adsorbed lying flat, head to tail. With the geometry favorable for direct optical excitation and given its ordered character, this interface seems to provide an intriguing model to study charge-transfer excitations where the optically excited electrons and holes reside on different sides of the organic–inorganic interface. In this work, we theoretically investigate the structural and electronic properties of this system by means of ab initio calculations and compute its excitonic absorption spectrum. Molecular states appear in the band gap of the clean TiO2 surface, which enables charge-transfer excitations directly from the molecular HOMO to the TiO2 conduction band. The calculated optical spectrum shows a strong polarization dependence and displays excitonic resonances corresponding to the charge-transfer states, which could stimulate new experimental work on the optical response of this interface.

Excitonic absorption spectra in graphene nanoflakes: Tuning of exciton binding energy by dielectric environments.

By solving the Bethe-Salpeter equation within the Hartree-Fock formalism, we study the excitonic absorption spectra of graphene nanoflakes embedded in various dielectric environments. With the excitonic effects fully taken into account, the exciton binding energy as a function of the dielectric constant is found to be well described by a single scaling rule in which the scaling factor is found to vary slowly with the size of the nanoflakes. Furthermore, it is revealed that the exciton binding energy scales almost linearly with the on-site interaction energy and exhibits more sensitive dependence in smaller nanoflakes. Our results are found to agree well with the recent experiment.

Fine structure of the exciton electroabsorption in semiconductor superlattices

Wannier-Mott excitons in a semiconductor layered superlattice (SL) are investigated analytically for the case that the period of the superlattice is much smaller than the 2D exciton Bohr radius. Additionally we assume the presence of a longitudinal external static electric field directed parallel to the SL axis. The exciton states and the optical absorption coefficient are derived in the tight-binding and adiabatic approximations. Strong and weak electric fields providing spatially localized and extended electron and hole states, respectively, are studied. The dependencies of the exciton states and the exciton absorption spectrum on the SL parameters and the electric field strength are presented in an explicit form. We focus on the fine structure of the ground quasi-2D exciton level formed by the series of closely spaced energy levels adjacent from the high frequencies. These levels are related to the adiabatically slow relative exciton longitudinal motion governed by the potential formed by the in-plane exciton state. It is shown that the external electric fields compress the fine structure energy levels, decrease the intensities of the corresponding optical peaks and increase the exciton binding energy. A possible experimental study of the fine structure of the exciton electroabsorption is discussed.

Influence of strong screening effect on the perpendicular- polarized linear excitonic absorption spectra of semiconducting carbon nanotubes

For incident light polarized perpendicular to the tube axis the multi-band semiconductor Bloch equations (MB-SBEs) that involve various screened interband Coulomb interactions (ICIs) are derived. The calculated E 12 peak is very close to the longitudinal excitonic peak E 22. Compared with the previous theoretical peak positions, the blue-shift of the peak in our results is about 0.5 eV. Then, subsequent detailed analyses show that the screening effect on the diagonal ICIs (D-ICIs) plays a key role in this big blue-shift. The valley-degenerate transverse pair excitations holding the same selection rule further enhance the screening effect on D-ICIs. Specially at q = 0 the dielectric function acting on the D-ICIs enhances two times. In our calculation the strong screening effect contributes 90% of the big blue-shift, while the non-diagonal ICIs (ND-ICIs) contribute to 10% of the blue-shift.

Bayesian Analysis of an Excitonic Absorption Spectrum in a Cu2O Thin Film Sandwiched by Paired MgO Plates

We analyzed the absorption spectrum of a Cu2O thin film sandwiched by paired MgO plates with the Metropolis algorithm of Bayesian estimation to estimate the energy shift of a yellow excitonic band gap. In the absorption spectrum, discrete excitonic resonant transitions with homogeneous and inhomogeneous widths are superimposed upon the tail parts of excitonic continuum and band-to-band absorption bands. On the basis of the Metropolis samplings with 2.5 million steps after sufficient burn-in steps, the spectral parameters of the excitonic resonant transitions can be estimated satisfactorily with a high degree of accuracy. In particular, we demonstrated that the yellow excitonic band gap in the Cu2O thin film shifts to the lower energy side than that of Cu2O bulk crystals. This result is consistent with the stress relaxation model for such Cu2O thin films, which was reported in Eur. Phys. J. B 86, 194 (2013).

Features of exciton dynamics in molecular nanoclusters (J-aggregates): Exciton self-trapping (Review Article)

We present thoroughly analyzed experimental results that demonstrate the anomalous manifestation of the exciton self-trapping effect, which is already well-known in bulk crystals, in ordered molecular nanoclusters called J-aggregates. Weakly-coupled one-dimensional (1D) molecular chains are the main structural feature of J-aggregates, wherein the electron excitations are manifested as 1D Frenkel excitons. According to the continuum theory of Rashba-Toyozawa, J-aggregates can have only self-trapped excitons, because 1D excitons must adhere to barrier-free self-trapping at any exciton-phonon coupling constant g = εLR/2β, wherein εLR is the lattice relaxation energy, and 2β is the half-width of the exciton band. In contrast, very often only the luminescence of free, mobile excitons would manifest in experiments involving J-aggregates. Using the Urbach rule in order to analyze the low-frequency region of the low-temperature exciton absorption spectra has shown that J-aggregates can have both a weak (g < 1) and a strong (g > 1) exciton-phonon coupling. Moreover, it is experimentally demonstrated that under certain conditions, the J-aggregate excited state can have both free and self-trapped excitons, i.e., we establish the existence of a self-trapping barrier for 1D Frenkel excitons. We demonstrate and analyze the reasons behind the anomalous existence of both free and self-trapped excitons in J-aggregates, and demonstrate how exciton-self trapping efficiency can be managed in J-aggregates by varying the values of g, which is fundamentally impossible in bulk crystals. We discuss how the exciton-self trapping phenomenon can be used as an alternate interpretation of the wide band emission of some J-aggregates, which has thus far been explained by the strongly localized exciton model.

Light-hole exciton mixing and dynamics in Mn-doped quantum dots

We investigate theoretically the spectral and dynamical effects of the short-range exchange interaction between a single manganese (Mn) atom hosted by cylindrical CdTe quantum dots and its light-hole excitons or biexcitons. Our approach is based on the Kohn-Luttinger KP theory and configuration interaction method, the dynamics of the system in the presence of intraband relaxation being derived from the von Neumann-Lindblad equation. The complex structure of the light-hole exciton absorption spectrum reveals the exchange-induced exciton mixing and depends strongly on the Mn position. In particular, if the Mn atom is closer to the edges of the cylinder the bright and dark light-hole excitons are mixed by the hole-Mn exchange alone. Consequently, their populations exhibit exchange-induced Rabi oscillations which can be viewed as optical signatures of light-hole spin reversal. Similar results are obtained for mixed biexcitons, in this case the exchange-induced Rabi oscillations being damped by the intraband hole relaxation processes. The effect of light-hole heavy-hole mixing is also discussed.

Low driving voltage band-filling-based III-V-on-silicon electroabsorption modulator

In this paper, a method for realizing a low driving voltage electroabsorption modulator based on the band-filling effect is demonstrated. The InP-based electroabsorption modulator is integrated using divinylsiloxane-bis-benzocyclobutene adhesive bonding on a silicon-on-insulator waveguide platform. When the electroabsorption modulator is forward biased, the band-filling effect occurs, which leads to a blue shift of the exciton absorption spectrum, while the absorption strength stays almost constant. In static operation, an extinction ratio of more than 20 dB with 100 mV bias variation is obtained in an 80 μm long device. In dynamic operation, 1.25 Gbps modulation with a 6.3 dB extinction ratio is obtained using only a 50 mV peak-to-peak driving voltage. The band-filling effect provides a method for realizing ultra-low-driving-voltage electroabsorption modulators.

Linewidths in excitonic absorption spectra of cuprous oxide

We present a theoretical calculation of the absorption spectrum of cuprous oxide $\left({\mathrm{Cu}}_{2}\mathrm{O}\right)$ based on the general theory developed by Y. Toyozawa. An inclusion not only of acoustic phonons but also of optical phonons and of specific properties of the excitons in ${\mathrm{Cu}}_{2}\mathrm{O}$ like the central-cell corrections for the $1S$ exciton allows us to calculate the experimentally observed linewidths in experiments by T. Kazimierczuk et al. [T. Kazimierczuk, D. Fr\"ohlich, S. Scheel, H. Stolz, and M. Bayer, Nature (London) 514, 343 (2014)] within the same order of magnitude, which demonstrates a clear improvement in comparison to earlier work on this topic. We also discuss a variety of further effects, which explain the still observable discrepancy between theory and experiment but can hardly be included in theoretical calculations.

Exciton effective mass enhancement in coupled quantum wells in electric and magnetic fields

We present a calculation of exciton states in semiconductor coupled quantum wells in the presence of electric and magnetic fields applied perpendicular to the QW plane. The exciton Schrödinger equation is solved in real space in three-dimensions to obtain the Landau levels of both direct and indirect excitons. Calculation of the exciton energy levels and oscillator strengths enables mapping of the electric and magnetic field dependence of the exciton absorption spectrum. For the ground state of the system, we evaluate the Bohr radius, optical lifetime, binding energy and dipole moment. The exciton mass renormalization due to the magnetic field is calculated using a perturbative approach. We predict a non-monotonous dependence of the exciton ground state effective mass on magnetic field. Such a trend is explained in a classical picture, in terms of the ground state tending from an indirect to a direct exciton with increasing magnetic field.