Two-dimensional Excitons Research Articles

Motion of Two-Dimensional Excitons in Momentum Space Leads to Pseudospin Distribution Narrowing on the Bloch Sphere.

Motional narrowing implies narrowing induced by motion; for example, in nuclear magnetic resonance, the thermally induced random motion of the nuclei in an inhomogeneous environment leads to a counterintuitive narrowing of the resonance line. Similarly, the excitons in monolayer semiconductors experience magnetic inhomogeneity: the electron-hole spin-exchange interaction manifests as an in-plane pseudomagnetic field with a periodically varying orientation inside the exciton band. The excitons undergo random momentum scattering and pseudospin precession repeatedly in this inhomogeneous magnetic environment, typically resulting in fast exciton depolarization. On the contrary, we show that such magnetic inhomogeneity averages out at high scattering rates due to motional narrowing. Physically, a faster exciton scattering leads to a narrower pseudospin distribution on the Bloch sphere, implying a nontrivial improvement in exciton polarization. The in-plane nature of the pseudomagnetic field enforces a contrasting scattering dependence between the circularly and linearly polarized excitons, providing a spectroscopic way to gauge the sample quality.

Gain enhancement of perovskite nanosheets by a patterned waveguide: excitation and temperature dependence of gain saturation

Optical gain enhancement of two-dimensional CsPbBr3 nanosheets was studied when the amplified spontaneous emission is guided by a patterned structure of polyurethane-acrylate. Given the uncertainties and pitfalls in retrieving a gain coefficient from the variable stripe length method, a gain contour g(hslash omega ,x) was obtained in the plane of spectrum energy (ℏω) and stripe length (x), whereby an average gain was obtained, and gain saturation was analysed. Excitation and temperature dependence of the gain contour show that the waveguide enhances both gain and thermal stability due to the increased optical confinement and heat dissipation, and the gain origins were attributed to the two-dimensional excitons and the localized states.

Edge-Confined Excitons in Monolayer Black Phosphorus.

Quantum confinement of two-dimensional excitons in van der Waals materials via electrostatic trapping, lithographic patterning, Moiré potentials, and chemical implantation has enabled significant advances in tailoring light emission from nanostructures. While such approaches rely on complex preparation of materials, natural edges are a ubiquitous feature in layered materials and provide a different approach for investigating quantum-confined excitons. Here, we observe that certain edge sites of monolayer black phosphorus (BP) strongly localize the intrinsic quasi-one-dimensional excitons, yielding sharp spectral lines in photoluminescence, with nearly an order of magnitude line width reduction. Through structural characterization of BP edges using transmission electron microscopy and first-principles GW plus Bethe-Salpeter equation (GW-BSE) calculations of exemplary BP nanoribbons, we find that certain atomic reconstructions can strongly quantum-confine excitons resulting in distinct emission features, mediated by local strain and screening. We observe linearly polarized luminescence emission from edge reconstructions that preserve the mirror symmetry of the parent BP lattice, in agreement with calculations. Furthermore, we demonstrate efficient electrical switching of localized edge excitonic luminescence, whose sites act as excitonic transistors for emission. Localized emission from BP edges motivates exploration of nanoribbons and quantum dots as hosts for tunable narrowband light generation, with future potential to create atomic-like structures for quantum information processing applications as well as exploration of exotic phases that may reside in atomic edge structures.

Two- and three-particle complexes with logarithmic interaction: Compact wave functions for two-dimensional excitons and trions

Two- and three-particle complexes with logarithmic interaction: Compact wave functions for two-dimensional excitons and trions

Possibility of Exciton Bose-Einstein Condensation in CdSe Nanoplatelets.

The quasi-two-dimensional exciton subsystem in CdSe nanoplatelets is considered. It is theoretically shown that Bose-Einstein condensation (BEC) of excitons is possible at a nonzero temperature in the approximation of an ideal Bose gas and in the presence of an "energy gap" between the ground and the first excited states of the two-dimensional exciton center of inertia of the translational motion. The condensation temperature (Tc) increases with the width of the "gap" between the ground and the first excited levels of size quantization. It is shown that when the screening effect of free electrons and holes on bound excitons is considered, the BEC temperature of the exciton subsystem increases as compared to the case where this effect is absent. The energy spectrum of the exciton condensate in a CdSe nanoplate is calculated within the framework of the weakly nonideal Bose gas approximation, considering the specifics of two-dimensional Born scattering.

Two-dimensional Wannier-Mott exciton diamagnetic shift

We present a model of diamagnetic shifts for two-dimensional Wannier-Mott excitons in out-of-plane magnetic fields, including environmental dielectric effects. We indicate the reasons for the magnetic-field-induced increase of exciton mass and size. In the weak-field limit, we deduce the diamagnetic coefficient and explain why its value is significantly different between excitonic states. Our results agree well with experimental data.

Enhanced Two-Dimensional Exciton Propagation via Strong Light–Matter Coupling with Surface Lattice Plasmons

Exciton–polaritons─hybrid exciton–photon quasi-particles─have enabled exciting long-range coherent transport by taking advantage of the properties of their photonic component. However, most experimental demonstrations of strong coupling have been based on semiconductor Fabry–Pérot microcavities. Here, we report an open and versatile exciton–polariton platform by integrating two-dimensional lead halide perovskites with plasmonic nanoparticle arrays, which support hybridization between excitons and surface lattice resonances in the strong coupling regime. Benefitting from the open architecture, we directly visualized polariton-enhanced exciton transport via angle-dependent transient absorption microscopy measurements. The observed transport enhancement extends into the picosecond timescale, leading to more than 1 order of magnitude improvement of exciton migration, from ∼10 nm to 100s of nanometers. We proposed a polariton-mediated exciton transport model and obtained an average polariton velocity of ∼1 × 106 m/s for states with an ∼40% photonic fraction. These results demonstrate plasmonic particle arrays as a versatile and adaptable cavity to enhance exciton transport.

Tunable Couplings of Photons with Bright and Dark Excitons in Monolayer Semiconductors on Plasmonic-Nanosphere-on-Mirror Cavities

Tunable exciton–photon couplings are of great importance for cavity quantum electrodynamics (QED), polariton chemistry, optical computing, and bosonic lasing. In this regard, two-dimensional (2D) excitons in transition metal dichalcogenides (TMDs) have attracted tremendous interest─the huge oscillator strengths endow sensitive responses to optical modes, and their excitonic properties can be actively tuned by external stimuli. However, tunable coupling with spin-forbidden dark excitons in monolayer TMDs has rarely been demonstrated, and how the bright/dark-exciton–photon couplings coexist in one system is still a mystery. Herein, we utilize waveguide and antenna modes in a gold nanosphere-on-mirror cavity to match the in-plane and out-of-plane dipole moments of bright and dark excitons in monolayer WS2, respectively, and simultaneously. Strong bright-exciton–photon couplings with a coupling strength of up to 60 meV are observed at room temperature. We show that the waveguide mode can be tuned in wavelengths by controlling the spacer thickness and demonstrate the anti-crossing feature of polaritons. Next, by increasing the excitation angle, we dynamically enlarge the relative contribution from the antenna mode coupled with dark excitons and suppress the waveguide mode coupled with bright states. Moreover, a tunable bright exciton linewidth is achieved as a result of suppressed homogeneous broadening caused by the dominant dark exciton decays under strong dark-exciton–photon couplings. This is not only proof of tunable couplings with dark excitons but also an insightful finding that reveals the novel interactions between bright- and dark-exciton–photon hybrids in a single optical cavity, opening new possibilities in tunable QED.

Customizing Radiative Decay Dynamics of Two-Dimensional Excitons via Position- and Polarization-Dependent Vacuum-Field Interference.

Embodying bosonic and interactive characteristics in two-dimensional space, excitons in transition metal dichalcogenides (TMDCs) have garnered considerable attention. The utilization of the strong-correlation effects, long-range transport, and valley-dependent properties requires customizing exciton decay dynamics. Vacuum-field manipulation allows radiative decay engineering without disturbing intrinsic material properties. However, conventional flat mirrors cannot customize the radiative decay landscape in TMDC's plane or support vacuum-field interference with desired spectrum and polarization properties. Here, we present a meta-mirror platform resolving the issues with more optical degrees of freedom. For neutral excitons of the monolayer MoSe2, the optical layout formed by meta-mirrors manipulated the radiative decay rate in space by 2 orders of magnitude and revealed the statistical correlation between emission intensity and spectral line width. Moreover, the anisotropic meta-mirror demonstrated polarization-dependent radiative decay control. Our platform would be promising to tailor two-dimensional distributions of lifetime, density, diffusion, and polarization of TMDC excitons in advanced opto-excitonic applications.

Coherent spin dynamics of excitons in strained monolayer semiconductors

Back in 1958 E.I. Rashba predicted the so-called resonant (long-range exchange) interaction between an electron and a hole in Wannier-Mott excitons. This interaction underlies exciton fine structure and its spin dynamics. Here, the author develops a model of the coherent exciton spin-valley dynamics in two-dimensional transition metal dichalcogenides caused by the interplay of the wave-vector dependent exchange interaction ($L\phantom{\rule{0}{0ex}}T$ splitting) and wave-vector independent anisotropic splitting induced by elastic strain. The author uncoversdifferent regimes of coherent spin dynamics of two-dimensional excitons and outlines the possibilities to disentangle the strain-induced from the $L\phantom{\rule{0}{0ex}}T$ splitting.

Electroreflectance spectroscopy of few-layer MoS2 : Issues related to A1s exciton subspecies, exciton binding energy, and inter-layer exciton

Optical spectra of few-layer transition metal dichalcogenide semiconductors reveal several transitions whose character and origins continue to be debated. We have studied hBN encapsulated few-layer MoS2 films using electroreflectance (ER) spectroscopy. Two strong features are seen in the reflectance spectrum of trilayer MoS2 around the ground state A–exciton transition. In ER, the corresponding features show opposite phase response to the applied voltage. Evidence from first principles ER line shape simulation and photoluminescence spectroscopy suggests that these two features are likely to be A1s exciton subspecies proposed earlier, whose energy depends on which layer the electron–hole pair is located in. The first excited state A2s exciton transition is also identifiable in ER. Through the two-dimensional hydrogenic exciton model, it enables an approximate estimation of the exciton binding energy Eb. The increase in Eb with decreasing film thickness, which originates from reduced dielectric screening, is phenomenologically analyzed through a film thickness and capping material dependent effective dielectric constant. Extending this idea, we show that the A1s exciton is mostly confined to a single S–Mo–S layer, as predicted by theory. An inter-layer (IL) exciton is expected in bilayer and thicker 2H-MoS2 films. However, we show that there can be bilayer films where the IL exciton is absent, which may be related to increased carrier concentration.

Area-Independence of the Biexciton Oscillator Strength in CdSe Colloidal Nanoplatelets.

Colloidal CdSe nanoplatelets (NPLs) are unique systems to study two-dimensional excitons and excitonic complexes. However, while absorption and emission of photons through exciton formation and recombination have been extensively quantified, few studies have addressed the exciton-biexciton transition. Here, we use cross-polarized pump-probe spectroscopy to measure the absorption coefficient spectrum of this transition and determine the biexciton oscillator strength (fBX). We show that fBX is independent of the NPL area and that the concomitant biexciton area (SBX) agrees with predictions of a short-range interaction model. Moreover, we show that fBX is comparable to the oscillator strength of forming localized excitons at room temperature while being unaffected itself by center-of-mass localization. These results confirm the relevance of biexcitons for light-matter interaction in NPLs. Moreover, the quantification of the exciton-biexciton transition introduced here will enable researchers to rank 2D materials by the strength of this transition and to compare experimental results with theoretical predictions.

Theoretical quantum model of two-dimensional propagating plexcitons.

When plasmonic excitations of metallic interfaces and nanostructures interact with electronic excitations in semiconductors, new states emerge that hybridize the characteristics of the uncoupled states. The engendered properties make these hybrid states appealing for a broad range of applications, ranging from photovoltaic devices to integrated circuitry for quantum devices. Here, through quantum modeling, the coupling of surface plasmon polaritons and mobile two-dimensional excitons such as those in atomically thin semiconductors is examined with emphasis on the case of strong coupling. Our model shows that at around the energy crossing of the dispersion relationships of the uncoupled species, they strongly interact and polariton states-propagating plexcitons-emerge. The temporal evolution of the system where surface plasmon polaritons are continuously injected into the system is simulated to gain initial insight on potential experimental realizations of these states. The results show a steady state that is dominated by the lower-energy polariton. The study theoretically further establishes the possible existence of propagating plexcitons in atomically thin semiconductors and provides important guidance for the experimental detection and characterization of such states for a wide range of optoelectronic technologies.

First-Principles Study of the Optical Dipole Trap for Two-Dimensional Excitons in Graphane.

Recent studies on excitons in two-dimensional materials have been widely conducted for their potential usages for novel electronic and optical devices. Especially, sophisticated manipulation techniques of quantum degrees of freedom of excitons are in demand. In this Letter we propose a technique of forming an optical dipole trap for excitons in graphane, a two-dimensional wide gap semiconductor, based on first-principles calculations. We develop a first-principles method to evaluate the transition dipole matrix between excitonic states and combine it with the density functional theory and GW+BSE calculations. We reveal that in graphane the huge exciton binding energy and the large dipole moments of Wannier-like excitons enable us to induce the dipole trap of the order of meV depth and μm width. This Letter opens a new way to control light-exciton interacting systems based on newly developed numerically robust abinitio calculations.

Impact of Faddeeva–Voigt broadening on line-shape analysis at critical points of dielectric functions

Faddeeva–Voigt broadening (FVB) couples the physical characteristics of both Lorentzian and Gaussian profiles as a combined analytic function shaping the dielectric response. Accurate extraction of the Gaussian and Lorentzian broadening contents in line-shape analysis is essential for reliable optical characterization of semiconductors and dielectrics. By adding the Gaussian-broadening width to each Lorentzian width, we investigate how FVB affects critical-point (CP) analysis. We revisit a selection of earlier work based on classical Lorentz broadening in modulation spectroscopy and spectral ellipsometry. To generalize CP analysis, we derive the FVB’s analytical representation in terms of fractional derivatives of the Faddeeva function and apply the twenty-pole Martin–Donoso–Zamudio approximation for its precise and efficient computation of the FVB of model dielectric functions and derivatives. We investigate the FVB of the electroreflectance line shape of HgCdTe for three-dimensional M0 transitions and of the photoreflectance line shape of InP excitonic E0 transitions. Furthermore, we explore how FVB affects the dielectric functions of three-dimensional excitonic and two-dimensional M0 transitions vs Tanguy’s analytical two-dimensional exciton E1 and E1+Δ1 fits of GaAs to the second-order derivatives. We use the Akaike information criterion to quantitatively estimate the goodness of fit that statistically penalizes overfitting due to extraneous parameters. By consolidating both Gaussian and Lorentzian broadenings, the FVB significantly affects the CP analysis of modulation-spectroscopy line shapes and second-order derivatives of the dielectric function.

Exciton binding energy and screening length in two-dimensional semiconductors

We approximately solve the Schr\"odinger equation for two-dimensional Wannier-Mott excitons in the effective-mass approximation and derive an expression for the exciton energy levels, hence the exciton binding energy. The electron-hole interaction is described by the Rytova-Keldysh potential in a logarithmic approximation. From the derived expression, we introduce approximate expressions to experimentally determine the exciton binding energy (along with the quasiparticle band gap), the screening length, and the exciton reduced mass from measured exciton transition energies of the ground state ($1s$), and the first ($2s$) and the second ($3s$) excited states. Our results agree well with experimental data and theoretical calculations.

Two-dimensional excitons from twisted light and the fate of the photon's orbital angular momentum

As the bound state of two oppositely charged particles, excitons emerge from optically excited semiconductors as the electronic analogue of a hydrogen atom. In the two-dimensional (2D) case, realized either in quantum well systems or truly 2D materials such as transition metal dichalcogenides, the relative motion of an exciton is described by two quantum numbers: the principal quantum number $n$, and a quantum number $j$ for the angular momentum along the perpendicular axis. Conservation of angular momentum demands that only the $j=0$ states of the excitons are optically active in a system illuminated by plane waves. Here we consider the case for spatially structured light sources, specifically for twisted light beams with non-zero orbital angular momentum per photon. Under the so-called dipole approximation where the spatial variations of the light source occur on length scales much larger than the size of the semiconductor's unit cell, we show that the photon (linear and/or angular) momentum is coupled to the center-of-mass (linear and/or angular) momentum of the exciton. Our study establishes that the selection rule for the internal states of the exciton, and thus the exciton spectrum, is independent from the spatial structure of the light source.

Franz-Keldysh and Stark Effects in Two-Dimensional Metal Halide Perovskites

The established theory of a two-dimensional (2D) Wannier exciton in a uniform electric field is used to analyze the electroabsorption response of an archetypal 2D metal halide perovskite (MHP), phenethylammonium lead iodide. The high level of agreement between the electroabsorption simulation and measurement allows for a deepened understanding of the redshift of exciton energy, according to the quadratic Stark effect, and the continuum wave function leaking, according to the Franz-Keldysh effect. We find the field dependency of each of these effects to be rich with information, yielding measurements of the exciton Bohr radius, transition dipole moment, polarizability, and reduced effective mass of the exciton. Most importantly, the band-gap energy and exciton binding energy are unambiguously determined with 1σ variance of 4 meV. The high precision of these new measurement methods opens the opportunity for determining the influence of chemical and environmental factors on the optoelectronic properties of MHPs, which would enable the fabrication of highly efficient and reproducible light-harvesting and light-emitting optoelectronic devices.8 MoreReceived 21 September 2021Revised 22 December 2021Accepted 2 February 2022DOI:https://doi.org/10.1103/PRXEnergy.1.013001Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasStark effectPhysical SystemsPerovskitesQuantum wellsTechniquesOptical absorption spectroscopyCondensed Matter, Materials & Applied Physics

Strong Light-Matter Interactions between Gap Plasmons and Two-Dimensional Excitons under Ambient Conditions in a Deterministic Way.

Strong exciton-plasmon interactions between layered two-dimensional (2D) semiconductors and gap plasmons show a great potential to implement cavity quantum electrodynamics under ambient conditions. However, achieving a robust plasmon-exciton coupling with nanocavities is still very challenging, because the layer area is usually small in the conventional approaches. Here, we report on a robust strong exciton-plasmon coupling between the gap mode of a bowtie and the excitons in MoS2 layers with gold-assisted mechanical exfoliation and nondestructive wet transfer techniques for a large-area layer. Due to the ultrasmall mode volume and strong in-plane field, the estimated effective exciton number contributing to the coupling is largely reduced. With a corrected exciton transition dipole moment, the exciton numbers are extracted as being 40 for the case of a single layer and 48 for eight layers. Our work paves the way to realize strong coupling with 2D materials with a small number of excitons at room temperature.

Superior optical Kerr effects induced by two-dimensional excitons

Materials with strong optical Kerr effects (OKEs) are crucial for a broad range of applications, such as all-optical data processing and quantum information. However, the underlying OKE mechanism is not clear in 2D materials. Here, we reveal key insights of the OKE associated with 2D excitons. An admirably succinct formalism is derived for predicting the spectra and the magnitude of the nonlinear refractive index ( n 2 ) of 2D materials. The predicted n 2 spectra are consistent with reported experimental data and exhibit pronounced excitonic resonances, which is distinctively different from bulk semiconductors. The n 2 value is predicted to be 3 × 10 − 10 cm 2 / W for a 2D layered perovskite at low temperature as 7 K, which is four orders of magnitude larger than those of bulk semiconductors. The superior OKE induced by 2D excitons would give rise to a narrow refractive index-near-zero region for intense laser light. Furthermore, we demonstrate that the 2D layered perovskite should exhibit the best OKE efficiency ( W FOM = 1.02 , T FOM = 0.14 ) at 1550 nm, meeting the material requirements for all-optical switching. Our findings deepen the understanding of the OKE of 2D semiconducting materials and pave the way for highly efficient all-optical excitonic devices.