Excited Exciton States Research Articles

Role of excited states in the dynamics of excitons and their spins in diluted magnetic semiconductors

We theoretically investigate the impact of excited states on the dynamics of the exciton ground state in diluted magnetic semiconductor quantum wells. Exploiting the giant Zeeman shift in these materials, an external magnetic field is used to bring transitions between the exciton ground state and excited states close to resonance. It turns out that, when treating the exciton dynamics in terms of a quantum kinetic theory beyond the Markov approximation, higher exciton states are populated already well below the critical magnetic field required to bring the exciton ground state in resonance to an excited state. This behavior is explained by exciton-impurity correlations that can bridge energy differences on the order of a few meV and require a quantum kinetic description beyond the independent-particle picture. Of particular interest is the significant spin transfer toward states on the optically dark $2p$ exciton parabola which are protected against radiative decay.

Energy spectrum of excitons in square quantum wells

Energies of the ground and excited states of excitons in GaAs/AlGaAs and InGaAs/GaAs finite square quantum wells (QWs) of various widths are calculated. This is achieved by studying the three-dimensional Schrödinger equation for the exciton in a QW and, in particular, by determining the lower energy boundary of the continuous spectrum of the corresponding differential operator. The eigenvalue problem for the Schrödinger equation is solved numerically by the finite-difference method properly taking into account discontinuities of the material parameters at the interfaces of the QW. The calculated bound states of electron-hole pairs are classified based on the types of their dominant in-plane and quantum-confinement one-dimensional functions of the wave function factorized form. A dependence of energy levels on a QW width as a parameter is thoroughly studied for widths up to 100 nm. The accurate radiative decay rates for calculated s-like exciton states are also obtained. Calculated energy spectra are confronted with the experimental reflectance spectra measured for high-quality InGaAs/GaAs heterostructures with QWs. The ground and, at least, a few excited states of the heavy-hole exciton in QW are identified in the experimental spectra.

Spectrum of exciton states in monolayer transition metal dichalcogenides: Angular momentum and Landau levels

A four-band exciton Hamiltonian is constructed starting from the single-particle Dirac Hamiltonian for charge carriers in monolayer transition metal dichalcogenides (TMDs). The angular part of the exciton wave function can be separated from the radial part, in the case of zero center of mass momentum excitons, by exploiting the eigenstates of the total exciton angular momentum operator with which the Hamiltonian commutes. We explain why this approach fails for excitons with finite center of mass momentum or in the presence of a perpendicular magnetic field and present an approximation to resolve this issue. We calculate the (binding) energy and average interparticle distance of different excited exciton states in different TMDs and compare these with results available in the literature. Remarkably, we find that the intervalley exciton ground state in the $\mp K$ valley has angular momentum $j=\pm1$, which is due to the pseudospin of the separate particles. The exciton mass and the exciton Landau levels are calculated and we find that the degeneracy of exciton states with opposite relative angular momentum is altered by a magnetic field.

Coherent excitonic quantum beats in time-resolved photoemission measurements

Coherent excitation of materials via ultrafast laser pulses can have interesting, observable dynamics in time-resolved photoemission measurements. The broad spectral width of ultrafast pump pulses can coherently excite multiple exciton energy levels. When such coherently excited states are probed by means of photoemission spectroscopy, interference between the polarization of different exciton levels can lead to observable coherent exciton beats. Here, we present the theoretical formalism for evaluating the Time- and Angle- Resolved Photoemission Spectra (tr-ARPES) arising from the coherently excited exciton states. We subsequently apply our formalism to a simple model example of hydrogenic exciton energy levels to identify the dependencies that control the quantum beats. Our findings indicate that the most pronounced effect of coherent quantum excitonic beats is seen midway between the excited exciton energy levels and the central energy of the pump pulse provides tunability of this effect.

Probing the exciton k-space dynamics in monolayer tungsten diselenides

Monolayer transition metal dichalcogenides (TMDs) provide 2D semiconductors with a rich interplay of electron spin and valley degrees of freedom. Along with strong optical coupling strength, it provides an ideal platform to study exciton-related physics in the 2D limit. Intensive experimental approaches on exciton dynamics in monolayer TMDs have been focusing on the lifetime of the exciton, exciton valley/spin polarization, and coherence, whereas the ‘hot’ exciton relaxation is rarely addressed. Here we probe the dynamics of bright excitons in monolayer tungsten diselenides, by pumping at exciton ground state and probing at higher energy, where excitonic excited states can be identified from the pump-probe spectroscopy. Remarkably, the rise time of the differential reflection signal increases significantly with the index of the excited states, which we attribute to the phase-space filling effect that probes the momentum distribution of ground state exciton. Our results reveal fast exciton momentum relaxation as a signature of the strong Coulomb interaction in 2D TMDs.

Luminescent Emission of Excited Rydberg Excitons from Monolayer WSe2.

We report the experimental observation of radiative recombination from Rydberg excitons in a two-dimensional semiconductor, monolayer WSe2, encapsulated in hexagonal boron nitride. Excitonic emission up to the 4 s excited state is directly observed in photoluminescence spectroscopy in an out-of-plane magnetic field up to 31 T. We confirm the progressively larger exciton size for higher energy excited states through diamagnetic shift measurements. This also enables us to estimate the 1 s exciton binding energy to be about 170 meV, which is significantly smaller than most previous reports. The Zeeman shift of the 1 s to 3 s states, from both luminescence and absorption measurements, exhibits a monotonic increase of the g-factor, reflecting nontrivial magnetic-dipole-moment differences between ground and excited exciton states. This systematic evolution of magnetic dipole moments is theoretically explained from the spreading of the Rydberg states in momentum space.

Evidence for moiré excitons in van der Waals heterostructures.

Recent advances in the isolation and stacking of monolayers of van der Waals materials have provided approaches for the preparation of quantum materials in the ultimate two-dimensional limit1,2. In van der Waals heterostructures formed by stacking two monolayer semiconductors, lattice mismatch or rotational misalignment introduces an in-plane moiré superlattice3. It is widely recognized that the moiré superlattice can modulate the electronic band structure of the material and lead to transport properties such as unconventional superconductivity4 and insulating behaviour driven by correlations5-7; however, the influence of the moiré superlattice on optical properties has not been investigated experimentally. Here we report the observation of multiple interlayer exciton resonances with either positive or negative circularly polarized emission in a molybdenum diselenide/tungsten diselenide (MoSe2/WSe2) heterobilayer with a small twist angle. We attribute these resonances to excitonic ground and excited states confined within the moiré potential. This interpretation is supported by recombination dynamics and by the dependence of these interlayer exciton resonances on twist angle and temperature. These results suggest the feasibility of engineering artificial excitonic crystals using van der Waals heterostructures for nanophotonics and quantum information applications.

Exciton binding energy and hydrogenic Rydberg series in layered ReS2

Unlike monolayers of transition metal dichalcogenides such as MoS2, which possess high in-plane symmetry, layered ReS2 exhibits reduced in-plane crystal symmetry with a distorted 1 T structure. This unique symmetry leads to anisotropic optical properties, very promising for light polarization devices. Here, we report on low temperature polarization-resolved emission and absorption measurements of excitons in ReS2 from bulk to monolayer. In photoluminescence and reflectivity contrast spectra we distinguish two strongly polarized excitons X1 and X2 with dipole vectors along different crystal directions, which persist from bulk down to monolayer. Basing on the PL and RC spectra of bulk crystals we determine the energy of the ground and first four excited states of both excitons, which follow the usual hydrogenic Rydberg series of energy levels of 3D excitonic states (En = Ry*/n2). From the numerical fit we estimate that the energy gap is direct and equal to 1671.7 meV and binding energy of X1 and X2 is equal to 117.5 and 86.6 meV, respectively. In magneto-PL spectra of bulk ReS2 up to B = 10 T, the energy shift of all the states is below 2 meV. On reducing the crystal thickness from bulk to monolayer the ground state experience a strong blue shift.

Excitons without effective mass: Biased bilayer graphene

Understanding the dynamics of excitons in two dimensional semiconductors requires a theory that incorporates the essential physics distinct from their three-dimensional counterparts. In addition to the modified dielectric environment, single-particle states with strongly non-parabolic dispersion appear in many two-dimensional band structures, so that "effective mass" is ill-defined. Focusing on electrostatically-biased bilayer graphene as an example where quartic (and higher) dispersion terms are necessary, we present a semi-analytic theory used to investigate the properties of ground and excited excitonic states. This includes determination of relative oscillator strengths and magnetic moments (g-factors) which can be directly compared to recent experimental measurements.

Radiative decay time as a function of temperature in double GaAs quantum rings

This study examined the temperature-dependent, time-integrated/-resolved photoluminescence of the exciton states in double GaAs quantum rings. The density of states was analyzed from the temperature-dependent radiative decay time of exciton states to better understand the intra-relaxation process from thermally excited exciton states. To distinguish the radiative decay time from a non-radiative process, the decay time from the exciton states was calibrated by a comparison with the photoluminescence intensity at low temperatures, where the non-radiative process can be negligible. In ideal quantum ring structures, the ring width becomes almost zero. Therefore, one-dimensional nature would be expected. On the other hand, this assumption is not valid because widthless ring structures cannot be grown using current growth techniques. In other words, the quasi-one-dimensional nature (power order of the temperature dependence from radiative decay times ∼0.8 between 1.0 (two-dimensional nature) and 0.5 (one-dimensional nature)) was observed in quantum ring structures when the ring width was comparable to the radius of the ring structures. In the case of double quantum rings, however, the power order of the temperature dependence was obtained from the radiative decay times, which gave rise to 1.0, corresponding to a two-dimensional nature. This increased dimensional nature can be attributed to the appreciable ring width and ring size, extended wave function due to optical coupling, and the presence of dark exciton states.

Electron-Hole Correlations Govern Auger Recombination in Nanostructures.

The fast nonradiative decay of multiexcitonic states via Auger recombination is a fundamental process affecting a variety of applications based on semiconductor nanostructures. From a theoretical perspective, the description of Auger recombination in confined semiconductor nanostructures is a challenging task due to the large number of valence electrons and exponentially growing number of excited excitonic and biexcitonic states that are coupled by the Coulomb interaction. These challenges have restricted the treatment of Auger recombination to simple, noninteracting electron-hole models. Herein we present a novel approach for calculating Auger recombination lifetimes in confined nanostructures having thousands to tens of thousands of electrons, explicitly including electron-hole interactions. We demonstrate that the inclusion of electron-hole correlations are imperative to capture the correct scaling of the Auger recombination lifetime with the size and shape of the nanostructure. In addition, correlation effects are required to obtain quantitatively accurate lifetimes even for systems smaller than the exciton Bohr radius. Neglecting such correlations can result in lifetimes that are two orders of magnitude too long. We establish the utility of the new approach for CdSe quantum dots of varying sizes and for CdSe nanorods of varying diameters and lengths. Our new approach is the first theoretical method to postdict the experimentally known "universal volume scaling law" for quantum dots and makes novel predictions for the scaling of the Auger recombination lifetimes in nanorods.

Exciton States in Monolayer MoSe2 and MoTe2 Probed by Upconversion Spectroscopy

Transitions metal dichalcogenides (TMDs) are direct semiconductors in the atomic monolayer (ML) limit with fascinating optical and spin-valley properties. The strong optical absorption of up to 20 % for a single ML is governed by excitons, electron-hole pairs bound by Coulomb attraction. Excited exciton states in MoSe$_2$ and MoTe$_2$ monolayers have so far been elusive due to their low oscillator strength and strong inhomogeneous broadening. Here we show that encapsulation in hexagonal boron nitride results in emission line width of the A:1$s$ exciton below 1.5 meV and 3 meV in our MoSe$_2$ and MoTe$_2$ monolayer samples, respectively. This allows us to investigate the excited exciton states by photoluminescence upconversion spectroscopy for both monolayer materials. The excitation laser is tuned into resonance with the A:1$s$ transition and we observe emission of excited exciton states up to 200 meV above the laser energy. We demonstrate bias control of the efficiency of this non-linear optical process. At the origin of upconversion our model calculations suggest an exciton-exciton (Auger) scattering mechanism specific to TMD MLs involving an excited conduction band thus generating high energy excitons with small wave-vectors. The optical transitions are further investigated by white light reflectivity, photoluminescence excitation and resonant Raman scattering confirming their origin as excited excitonic states in monolayer thin semiconductors.

Unraveling biexciton and excitonic excited states from defect bound states in monolayer MoS2

Being direct band gap semiconductor, two-dimensional monolayer (ML) MoS2 has remarkable optical transitions arising from excitons, trions, biexciton and defects mediated bound states. However, experimental realization of biexciton in ML MoS2 has been challenging due to broad spectral feature of exciton. Here, we report on systematic observation of biexciton (AXX ∼ 1.90 eV) along with A- trion ∼ 1.92 eV and ground state exciton A1s ∼ 1.96 eV in ML MoS2 at 4 K, by laser-power and temperature-dependent non-resonant photoluminescence (PL) spectroscopy. At low temperatures the excited state of A exciton has also been observed, A2s ∼ 2.13 eV, which consequently merges in thermal broadening of B excitons, with rise in temperature. With excitation energy and power dependent PL, emission arising from exciton bound to sulfur vacancy (∼1.82 eV) have been distinguished from biexciton. Thus understanding of such excitonic states and biexcitons is useful for future quantum information processing, optoelectronic, photonics and THz applications.

Fine Structure of Rydberg Excitons in Cuprous Oxide

In 1952, E.F. Gross and N.A. Karryev discovered excitons of big radius also called the Wannier–Mott excitons. Their energy spectrum, response to external electric and magnetic fields, and also elastic deformations of a crystal were extensively studied in the 1960s–1970s. The second wave of interest to excitons in Cu2O crystals appeared comparatively recent, in 2014, after the “giant” highly excited exciton states had been observed in this material. A theoretical description of highly excited exciton states needs, as a rule, new approaches, because, for such states, a deviation from the exactly solved hydrogen-like model becomes substantial and a numerical solution of the Schrodinger equation with allowance made for the features of the crystal energy band structure becomes extremely resource consuming. This report is a brief review of recent theoretical and experimental studies of the fine structure of the exciton energy spectrum in copper protoxide.

Proposal of tunable Rydberg exciton maser.

We propose a continuous-mode solid-state maser based on Cu2O, where ensemble of highly excited Rydberg exciton states serves as a gain medium. We show that the system is highly tunable with an external electric field, allowing for a wide range of emission frequencies within terahertz range. Numerical simulations of the system dynamics are performed to optimize the conditions for efficient masing and estimate the emission power.

Temperature dependence of the radiative recombination time in laterally coupled GaAs quantum dots

We performed temperature dependent photoluminescence measurements of exciton states in GaAs laterally coupled quantum dots. The temperature dependence of the radiative decay time was used to investigate the density of states to study the intra-relaxation of thermally excited exciton states. We analyzed the density of states in laterally coupled quantum dots by observing the radiative decay time of exciton states as a function of temperature, where the decay time of exciton photoluminescence was calibrated with respect to photoluminescence intensity to extract the radiative decay time. In the case of laterally coupled quantum dots, a one-dimensional structure can be formed by elongation along the direction of coupling between two quantum dots. However, this assumption is not valid when the size in the uncoupled direction is comparable to that in the coupled direction. From experimental measurements, the power order of the temperature dependence was found to be 0.8, which corresponds to a quasi-one-dimensional system (∼Tα=0.8), which is in between a two-dimensional (α = 1) and a one-dimensional (α = 0.5) density of states. This is due to several factors including a large size along the uncoupled direction, an extended wave function owing to optical coupling, and the presence of dark states.

Optical spectroscopy of excited exciton states in MoS2 monolayers in van der Waals heterostructures

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 excited states of the A-exciton in MoS2 monolayers encapsulated in hBN layers of calibrated thickness, allowing to extrapolate an exciton binding energy of about 220 meV. We theoretically reproduce the energy separations and oscillator strengths measured in reflectivity by combining the exciton resonances calculated for a screened two-dimensional Coulomb potential with transfer matrix calculations of the reflectivity for the van der Waals structure. Our analysis shows a very different evolution of the exciton oscillator strength with principal quantum number for the screened Coulomb potential as compared to the ideal two-dimensional hydrogen model.

Тонкая структура ридберговских экситонов в закиси меди

AbstractIn 1952, E.F. Gross and N.A. Karryev discovered excitons of big radius also called the Wannier–Mott excitons. Their energy spectrum, response to external electric and magnetic fields, and also elastic deformations of a crystal were extensively studied in the 1960s–1970s. The second wave of interest to excitons in Cu_2O crystals appeared comparatively recent, in 2014, after the “giant” highly excited exciton states had been observed in this material. A theoretical description of highly excited exciton states needs, as a rule, new approaches, because, for such states, a deviation from the exactly solved hydrogen-like model becomes substantial and a numerical solution of the Schrödinger equation with allowance made for the features of the crystal energy band structure becomes extremely resource consuming. This report is a brief review of recent theoretical and experimental studies of the fine structure of the exciton energy spectrum in copper protoxide.

Origin of luminescence quenching in structures containing CdSe/ZnSe quantum dots with a few Mn2+ ions

We present a detailed spectroscopic study of the photoluminescence quenching in an epitaxial structures containing CdSe/ZnSe quantum dots doped with low concentration of Mn$^{2+}$ ions. Our time-resolved and time-integrated experiments reveal the origin of the quenching observed in macro-photoluminescence studies of ensembles of such dots. We show that incorporation of even a few ions to an individual dot does not quench its luminescence effectively, although some fingerprints of expected spin-dependent quenching are visible. At the same time, the presence of Mn$^{2+}$ ions in the sample significantly affects the luminescence intensity of the wetting layer, resulting in a quenching of the global luminescence from studied structure. On the other hand, the luminescence decay dynamics is found to be independent of the presence of Mn$^{2+}$ ions, which suggests that the observed quenching occurs for the excited excitonic states.

Temporal dynamics of the frequency non-degenerate transient photoluminescence enhancement observed following excitation of inter-configurational [formula omitted] transitions in CaF2:Yb2+

We present a detailed investigation of the dynamics of impurity-trapped excitons in CaF2:Yb2+ using transient photoluminescence enhancement induced via a two-frequency, sequential excitation process employing a UV optical parametric amplifier (OPA) synchronized to an infrared free electron laser (FEL). The temporal behaviour is well approximated by a multi-level rate equation model as relaxation between excited states of the exciton as well as a small contribution from local lattice heating by the FEL which becomes evident due to the 40cm−1 splitting of the exciton excited states giving rise to the transient photoluminescence enhancement itself.