Exciton Ground State Research Articles

Exciton Ground State Fine Structure and Excited States Landscape in Layered Halide Perovskites from Combined BSE Simulations and Symmetry Analysis

AbstractLayered halide perovskites are solution‐processed natural heterostructures where quantum and dielectric confinement down to the nanoscale strongly influence the optical properties, leading to stabilization of bound excitons. Detailed understanding of the exciton properties is crucial to boost the exploitation of these materials in energy conversion and light emission applications, with on‐going debate related to the energy order of the four components of the most stable exciton. To provide theoretical feedback and solve among contrasting literature reports, this work performs ab initio solution of the Bethe–Salpeter equation (BSE) for symmetrized reference Cs2PbX4 (X = I and Br) models, with detailed interpretation of the spectroscopic observables based on group‐theory analysis. Simulations predict the following Edark < Ein‐plane < Eout‐of‐plane fine‐structure assignment, consistent with recent magneto‐absorption experiments and obtain similar increase in dark/bright splitting when going from lead‐iodide to a lead‐bromide composition as found experimentally. The authors further suggest that polar distortions may lead to stabilization of the in‐plane component and end‐up in a bright lowest exciton component, discuss exciton landscape over a broad energy range and clarify the exciton spin‐character, when large spin‐orbit coupling is in play, to rationalize the potential of halide perovskites as triplet sensitizers in combination with organic dyes.

Chester Supersolid of Spatially Indirect Excitons in Double-Layer Semiconductor Heterostructures.

A supersolid, a counterintuitive quantum state in which a rigid lattice of particles flows without resistance, has to date not been unambiguously realized. Here we reveal a supersolid ground state of excitons in a double-layer semiconductor heterostructure over a wide range of layer separations outside the focus of recent experiments. This supersolid conforms to the original Chester supersolid with one exciton per supersolid site, as distinct from the alternative version reported in cold-atom systems of a periodic density modulation or clustering of the superfluid. We provide the phase diagram augmented by the supersolid. This new phase appears at layer separations much smaller than the predicted exciton normal solid, and it persists up to a solid-solid transition where the quantum phase coherence collapses. The ranges of layer separations and exciton densities in our phase diagram are well within reach of the current experimental capabilities.

Universal scaling laws for charge-carrier interactions with quantum confinement in lead-halide perovskites

Lead halide perovskites open great prospects for optoelectronics and a wealth of potential applications in quantum optical and spin-based technologies. Precise knowledge of the fundamental optical and spin properties of charge-carrier complexes at the origin of their luminescence is crucial in view of the development of these applications. On nearly bulk Cesium-Lead-Bromide single perovskite nanocrystals, which are the test bench materials for next-generation devices as well as theoretical modeling, we perform low temperature magneto-optical spectroscopy to reveal their entire band-edge exciton fine structure and charge-complex binding energies. We demonstrate that the ground exciton state is dark and lays several millielectronvolts below the lowest bright exciton sublevels, which settles the debate on the bright-dark exciton level ordering in these materials. More importantly, combining these results with spectroscopic measurements on various perovskite nanocrystal compounds, we show evidence for universal scaling laws relating the exciton fine structure splitting, the trion and biexciton binding energies to the band-edge exciton energy in lead-halide perovskite nanostructures, regardless of their chemical composition. These scaling laws solely based on quantum confinement effects and dimensionless energies offer a general predictive picture for the interaction energies within charge-carrier complexes photo-generated in these emerging semiconductor nanostructures.

Optical classification of excitonic phases in molecular functionalized atomically-thin semiconductors

The excitonic insulator is an elusive electronic phase exhibiting a correlated excitonic ground state. Materials with such a phase are expected to have intriguing properties such as excitonic high-temperature superconductivity. However, compelling evidence on the experimental realization is still missing. Here, we theoretically propose hybrids of two-dimensional semiconductors functionalized by organic molecules as prototypes of excitonic insulators, with the exemplary candidate ${\mathrm{WS}}_{2}$-F6TCNNQ. This material system exhibits an excitonic insulating phase at room temperature with a ground state formed by a condensate of interlayer excitons. To address an experimentally relevant situation, we calculate the corresponding phase diagram for the important parameters: temperature, gap energy, and dielectric environment. Further, to guide future experimental detection, we show how to optically characterize the different excitonic phases via far-infrared to terahertz spectroscopy valid also for monolayer materials.

Experimental progress of topological exciton insulators

Under Coulomb interactions, electrons and holes have a phase transition from a semi-metal state into an excitonic ground state, with a gap spontaneously opening at the Fermi level. The excitonic ground state is called excitonic insulator. The excitonic insulator has attracted extensive attention in condensed matter physics, but the experimental evidence of such a quantum state is still under search. Until recent years, optical spectral and transport evidence of the excitonic insulator has first been observed in shallowly inverted InAs/GaSb quantum wells, which confirms the existence of the exciton insulator in a two-dimensional system. Surprisingly, one-dimensional helical-like topological edge states, which are not sensitive to temperature nor magnetic field, have been observed in the excitonic insulator state by transport measurements. This new quantum phase cannot be well explained by existing single-particle theories, which is called a topological excitonic insulator. In this paper, we systematically review the experimental studies on the topological excitonic insulator in the InAs quantum well and GaAs quantum well, including magneto transport, terahertz transmission, capacitance, and Coulomb drag measurements. These experimental results comprehensively characterize the bulk properties and edge properties of the topological excitonic insulator. Furthermore, as a ground state consisting of bosons, the topological excitonic insulator is expected to have a quantum phase transition into Bose-Einstein condensate with macroscopic coherence under extreme conditions, which provides a new platform for studying the quantum phenomena of Coulomb interactions in low dimensions.

Excitonic ground states in phosphorene nanoflakes.

By using a configuration-interaction approach beyond the framework of independent multiexcitons, we predict that an excitonic ground state may exist in phosphorene nanoflakes when an in-plain electric field is applied. The ground state of the system is shown to undergo a transition from purely electronic to almost fully biexcitonic with the increasing strength of the electric field. As the field exceeds 0.25 V nm-1, a biexcitonic ground state is revealed to be energetically more favorable by a few hundred meV than the system without excitons. A similar transformation of the ground state is also found as the screening effect varies from strong to weak. The enhanced electron-hole correlation, mostly caused by the applied electric field as well as the lack of strong screening in low-dimensional nanostructures, is believed to account for such an extraordinary transition. Furthermore, the system with a biexcitonic ground state is found to exhibit an absorption spectrum where many transitions are polarized along the zigzag direction, which breaks the optical anisotropy well-known for bulk phosphorene.

Excitons and trions in WSSe monolayers

The possibility of almost linear tuning of the band gap and of the electrical and optical properties in monolayers (MLs) of semiconducting transition metal dichalcogenide (S-TMD) alloys opens up the way to fabricate materials with on-demand characteristics. By making use of photoluminescence spectroscopy, we investigate optical properties of WSSe MLs with a S/Se ratio of 57/43 deposited on SiO2/Si substrate and encapsulated in hexagonal BN flakes. Similarly to the ‘parent’ WS2 and WSe2 MLs, we assign the WSSe MLs to the ML family with the dark ground exciton state. We find that, in addition to the neutral bright A exciton line, three observed emission lines are associated with negatively charged excitons. The application of in-plane and out-of-plane magnetic fields allows us to assign undeniably the bright and dark (spin- and momentum-forbidden) negative trions as well as the phonon replica of the dark spin-forbidden complex. Furthermore, the existence of the single photon emitters in the WSSe ML is also demonstrated, thus prompting the opportunity to enlarge the wavelength range for potential future quantum applications of S-TMDs.

ZnPSe3 as ultrabright indirect band-gap system with microsecond excitonic lifetimes.

ZnPSe3 was identified as a two-dimensional material wherein valley and spin can be optically controlled in technologically relevant timescales. We report an optical characterization of ZnPSe3 crystals that show indirect band-gap characteristics in combination with unusually strong photoluminescence. We found evidence of interband recombination from photoexcited electron-hole states with lifetimes in a microsecond timescale. Through a comparative analysis of photoluminescence and photoluminescence excitation spectra, we reconstructed the electronic band scheme relevant to fundamental processes of light absorption, carrier relaxation, and radiative recombination through interband pathways and annihilation of defect-bound excitons. The investigation of the radiative processes in the presence of a magnetic field revealed spin splitting of electronic states contributing to the ground excitonic states. Consequently, the magnetic field induces an imbalance in the number of excitons with the opposite angular momentum according to the thermal equilibrium as seen in the photoluminescence decay profiles resolved by circular polarization.

Rydberg exciton-polaritons in a magnetic field

We theoretically investigate exciton-polaritons in a two-dimensional (2D) semiconductor heterostructure, where a static magnetic field is applied perpendicular to the plane. To explore the interplay between magnetic field and a strong light-matter coupling, we employ a fully microscopic theory that explicitly incorporates electrons, holes and photons in a semiconductor microcavity. Furthermore, we exploit a mapping between the 2D harmonic oscillator and the 2D hydrogen atom that allows us to efficiently solve the problem numerically for the entire Rydberg series as well as for the ground-state exciton. In contrast to previous approaches, we can readily obtain the real-space exciton wave functions and we show how they shrink in size with increasing magnetic field, which mirrors their increasing interaction energy and oscillator strength. We compare our theory with recent experiments on exciton-polaritons in GaAs heterostructures in an external magnetic field and we find excellent agreement with the measured polariton energies. Crucially, we are able to capture the observed light-induced changes to the exciton in the regime of very strong light-matter coupling where a perturbative coupled oscillator description breaks down. Our work can guide future experimental efforts to engineer and control Rydberg excitons and exciton-polaritons in a range of 2D materials.

Strain-Induced Exciton Hybridization in WS2 Monolayers Unveiled by Zeeman-Splitting Measurements

Mechanical deformations and ensuing strain are routinely exploited to tune the band gap energy and to enhance the functionalities of two-dimensional crystals. In this Letter, we show that strain leads also to a strong modification of the exciton magnetic moment in WS_{2} monolayers. Zeeman-splitting measurements under magnetic fields up to 28.5 T were performed on single, one-layer-thick WS_{2} microbubbles. The strain of the bubbles causes a hybridization of k-space direct and indirect excitons resulting in a sizable decrease in the modulus of the g factor of the ground-state exciton. These findings indicate that strain may have major effects on the way the valley number of excitons can be used to process binary information in two-dimensional crystals.

Temperature-Dependent Exciton Dynamics in a Single GaAs Quantum Ring and a Quantum Dot.

Micro-photoluminescence was observed while increasing the excitation power in a single GaAs quantum ring (QR) at 4 K. Fine structures at the energy levels of the ground (N = 1) and excited (N = 2) state excitons exhibited a blue shift when excitation power increased. The excited state exciton had a strong polarization dependence that stemmed from the asymmetric localized state. According to temperature-dependence measurements, strong exciton–phonon interaction (48 meV) was observed from an excited exciton state in comparison with the weak exciton–phonon interaction (27 meV) from the ground exciton state, resulting from enhanced confinement in the excited exciton state. In addition, higher activation energy (by 20 meV) was observed for the confined electrons in a single GaAs QR, where the confinement effect was enhanced by the asymmetric ring structure.

Temperature dependent activation energies of exciton states on a single GaAs laterally coupled-quantum-dot molecule and quantum dot

The objective of this study was to perform spectroscopy measurements of a single GaAs laterally coupled quantum dot molecule and quantum dot. Compared to photoluminescence spectra between a single GaAs laterally coupled quantum dot molecule and a single quantum dot, the presence of optical coupling was confirmed through dipole-dipole interactions in a single coupled quantum dot molecule. Based on temperature dependence measurements, weak exciton-phonon interactions (25 meV) were observed from the ground exciton state of a single GaAs laterally coupled quantum dot molecule in comparison with a strong exciton-phonon interaction (49 meV) from the ground exciton state of a single GaAs QD. Such weak interactions were due to reduced confinement at exciton states in a single laterally coupled quantum dot molecule. In addition, weaker activation energy (∼15 meV) was observed in terms of confined electrons in a single laterally coupled quantum dot molecule, where a confinement effect became reduced due to enlarged dimensional area in one direction along [1 1‾ 0].

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.

All-order correlation of single excitons in nanocrystals using ak·penvelope-function approach: Application to lead halide perovskites

We discuss a variety of many-body approaches, within effective-mass and $\mathbf{k}\cdot\mathbf{p}$ envelope-function formalisms, for calculating correlated single excitons in semiconductor nanocrystals (NCs) to all orders in the electron-hole Coulomb interaction. These approaches are applied to NCs of the lead-halide perovskite CsPbBr$_{3}$, which typically present excitons in intermediate confinement with physical observables often strongly renormalized by correlation (e.g., radiative decay rate enhanced by a factor of about 7 relative to a mean-field approach, for a NC of edge length 11 nm). The many-body methods considered include the particle-hole Bethe-Salpeter equation, configuration interaction with single excitations, and the random-phase approximation with exchange (RPAE), which are shown to be closely related to each other but to treat $\mathbf{k}\cdot\mathbf{p}$ corrections differently, with RPAE being the most complete method. The methods are applied to calculate the correlation energy, the radiative lifetime, and the long-range Coulomb contribution to the fine structure of the ground-state exciton. In the limit of large NC sizes, the numerical results are shown to agree well with analytical results for this limit, where these are known. Correlated excited states of the single exciton are used to calculate the one-photon absorption cross section; the shape of the resulting cross-section curve (versus laser wavelength) at threshold and up to an excitation energy of about 1 eV is in good agreement with experimental cross sections. The equations for the methods are explicitly adapted to spherical symmetry (involving radial integrals and angular factors) and in this form permit a rapid computation for systems in intermediate confinement.

Ultranarrow lines in Raman spectra of quantum wells due to effective acoustic phonon selection by in-plane wave vector

An unusual fine spectrum of very narrow lines ($<1\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ overall) is observed in resonance Raman scattering from a CdTe quantum well under normal light incidence, when the laser excitation is about one longitudinal optical (LO) phonon energy higher than the quantum well exciton ground state. The visibility of this fine spectrum is improved by sample doping which reduces the quantum yield of the exciton photoluminescence. The appearance of the four sideway lines of the fine spectrum is explained by the Raman scattering on the combination of LO and longitudinal acoustic (LA) [transverse acoustic (TA)] phonons with the $e1hh1(2s)$ exciton serving as an intermediate state. The central line is due to elastic scattering of the $2s$ exciton to the hot $1s$-exciton state on a static random potential of the heterostructure followed by emission of a LO phonon.

Exciton absorption, band structure, and optical emission in biased bilayer graphene

Biased bilayer graphene (BBG) is a variable band gap semiconductor, with a strongly field-dependent band gap of up to $300 \, \text{meV}$, making it of particular interest for graphene-based nano-electronic and -photonic devices. The optical properties of BBG are dominated by strongly bound excitons. We perform ab initio density-functional-theory+Bethe-Salpeter-equation modelling of excitons in BBG and calculate the exciton band structures and optical matrix elements for field strengths in the range $30-300 \, \text{mV}/{\unicode{x212B}}$. The exciton properties prove to have a strong field dependence, with both energy ordering and dipole alignment varying significantly between the low and high field regions. Namely, at low fields we find a mostly dark ground state exciton, as opposed to high fields, where the lowest exciton is bright. Also, excitons preferentially align with a dipole moment opposite the field, due to the field-induced charge transfer in the ground state of BBG. However, in stronger fields, this alignment becomes energetically less favorable. Additionally, the bright excitons show particle- and light-like bands similar to monolayer transition metal dichalchogenides. Finally, we model the radiative lifetimes and emission properties of BBG, which prove to be strongly dependent on temperature in addition to field strength.

Interplay between multipole expansion of exchange interaction and Coulomb correlation of exciton in colloidal II–VI quantum dots

We study the effect of Coulomb correlation on the emission properties of the ground state exciton in zincblende CdSe/ZnS core–shell and in wurtzite ZnO quantum dots (QDs). We validate our theory model by comparing results of computed exciton energies of CdSe/ZnS QDs to photoluminescence and scanning near-field optical microscopy measurements. We use that to estimate the diameter of the QDs using a simple model based on infinitely deep quantum well and compare the results with the statistics of the atomic force microscopy scans of CdSe/ZnS dots, obtaining excellent agreement. Thereafter, we compute the energy fine structure of exciton, finding striking difference between properties of zincblende CdSe/ZnS and wurtzite ZnO dots. While in the former the fine structure is dominated by the dipole terms of the multipole expansion of the exchange interaction, in the latter system that is mostly influenced by Coulomb correlation. Furthermore, the correlation sizeably influences also the exciton binding energy and emission radiative rate in ZnO dots.

Nonclassical light from finite-range interactions in a two-dimensional quantum mirror

Excitons in a semiconductor monolayer form a collective resonance that can reflect resonant light with extraordinarily high efficiency. Here, we investigate the nonlinear optical properties of such atomistically thin mirrors and show that finite-range interactions between excitons can lead to the generation of highly non-classical light. We describe two scenarios, in which optical nonlinearities arise either from direct photon coupling to excitons in excited Rydberg states or from resonant two-photon excitation of Rydberg excitons with finite-range interactions. The latter case yields conditions of electromagnetically induced transparency and thereby provides an efficient mechanism for single-photon switching between high transmission and reflectance of the monolayer, with a tunable dynamical timescale of the emerging photon-photon interactions. Remarkably, it turns out that the resulting high degree of photon correlations remains virtually unaffected by Rydberg-state decoherence, in excess of non-radiative decoherence observed for ground-state excitons in two-dimensional semiconductors. This robustness to imperfections suggests a promising new approach to quantum photonics at the level of individual photons.

Transition from metal to semiconductor by semi-hydrogenation of borophene

Borophene has triggered a surge of interest due to its outstanding properties including mechanical flexibility, polymorphism, and optoelectrical anisotropy. Very recently, a novel semi-hydrogenated borophene, called ${\ensuremath{\alpha}}^{\ensuremath{'}}$-4H, was synthesized in large-scale freestanding samples, exhibiting excellent air-stability and semiconducting nature. Herein, using the density functional theory (DFT) and many-body perturbation theory (MBPT), we investigate the electronic and excitonic optical properties of ${\ensuremath{\alpha}}^{\ensuremath{'}}$-4H borophene. The DFT results reveal that hydrogenation breaks the mirror symmetry and increases the buckling height of pure ${\ensuremath{\alpha}}^{\ensuremath{'}}$ borophene, which results in an orbital hybridization and indirect band gap of 1.49 eV in ${\ensuremath{\alpha}}^{\ensuremath{'}}$-4H borophene. Moreover, the optical spectrum achieved from solving the Bethe-Salpeter equation (i.e., $\mathrm{GW}+\mathrm{BSE}$) shows an optical band gap of 2.40 eV, which corresponds to a strongly bound and stable bright exciton with a binding energy of 1.18 eV. The mean value of absorption within the visible area is 1.68 (1.13)$\ifmmode\times\else\texttimes\fi{}{10}^{7}\phantom{\rule{4pt}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}$ for $E\ensuremath{\parallel}x$ ($E\ensuremath{\parallel}y$) polarization, which shows a linear dichroism for visible light. The effective mass and Bohr radius of the ground-state exciton are 0.78 ${m}_{0}$ and 2.03 \AA{}, respectively, which demonstrates the characteristics of Frenkel exciton. The excitonic states are robust against tension up to 10%, under which the monolayer is dynamically stable. We also study the bilayer ${\ensuremath{\alpha}}^{\ensuremath{'}}$-4H borophene with different stackings. For the weak van der Waals interactions between the layers, the bilayer preserves most of the structural and electronic properties of the monolayer. Our study exposes the underlying physics behind the structural, electronic, and optical properties of ${\ensuremath{\alpha}}^{\ensuremath{'}}$-4H borophene and suggests it as a very promising candidate for flexible optoelectronic applications.

Atypical dependence of excited exciton energy levels and electron-hole correlation on emission energy in pyramidal InP-based quantum dots

We calculate the spectrum of excited exciton states in application-relevant self-assembled pyramidal quantum dots grown in InAs/InP and InAs/AlGaInAs material systems. These types of dots have been recently shown to combine the emission in the third optical fiber window with low surface density and a reasonable level of in-plane symmetry of emitters, which predestines them for studies on single- and entangled-photon emission and for corresponding applications. The spectrum of optically active excited states is crucial for successful resonant and quasi-resonant excitation of emitters, allowing for conservation of angular momentum and addressing individual selected quantum states. Here, we show that in both types of studied dots, due to their specific morphology of truncated pyramid, the density of excited-state ladder, especially the s–p shell splitting may follow an unconventional dependence on emission energy, opposite to the one typically met in regular quantum dots. We obtain this result via modeling based on available morphological data and calculation within the multi-band {{varvec{k}} {cdot } {varvec{p}}} envelope-function theory combined with the configuration-interaction method used to calculate exciton states. Then, we explain this observation in purely geometric terms, as a result of an increasing effective quantum confinement width in a pyramid that is progressively cut from the top. Additionally, we show that the inverted trend is also manifested in the amount of electron-hole correlation in the exciton ground state, which also shows an anomalous dependence on emission energy and quantum dot volume.