Two-dimensional Excitons Research Articles

Two-dimensional exciton–polariton—light guiding by transition metal dichalcogenide monolayers

Two-dimensional (2D) monolayer-thick materials with a direct bandgap, such as MoS2, WSe2, and other transition metal dichalcogenides (TMDCs), are being actively explored for future nanophotonic applications in the visible and UV ranges. Here I show that a monolayer of TMDCs is capable of supporting a guided optical mode below the exciton resonance—a 2D exciton–polariton. I evaluate the characteristics of these guided modes and conditions required for their existence, including derivations of mode dispersion relations, mode confinements, and propagation lengths. The visible or near-IR mode is confined to within roughly a micrometer of the monolayer and has a propagation length exceeding 100 μm. This light guiding ability in the visible and IR ranges makes TMDC monolayers a versatile and potentially attractive platform for future optoelectronic devices.

Giant Rabi Splitting of Whispering Gallery Polaritons in GaN/InGaN Core-Shell Wire.

The hybrid nature of exciton polaritons opens up possibilities for developing a new concept nonlinear photonic device (e.g., polariton condensation, switching, and transistor) with great potential for controllability. Here, we proposed a novel type of polariton system resulting from strong coupling between a two-dimensional exciton and whispering gallery mode photon using a core-shell GaN/InGaN hexagonal wire. High quality, nonpolar InGaN multiple-quantum wells (MQWs) were conformally formed on a GaN core nanowire, which was spatially well matched with whispering gallery modes inside the wire. Both high longitudinal-transverse splitting of nonpolar MQWs and high spatial overlap with whispering gallery modes lead to unprecedented large Rabi splitting energy of ∼180 meV. This structure provides a robust polariton effect with a small footprint; thus, it could be utilized for a wide range of interesting applications.

Optically active quantum dots in monolayer WSe2.

Semiconductor quantum dots have emerged as promising candidates for the implementation of quantum information processing, because they allow for a quantum interface between stationary spin qubits and propagating single photons. In the meantime, transition-metal dichalcogenide monolayers have moved to the forefront of solid-state research due to their unique band structure featuring a large bandgap with degenerate valleys and non-zero Berry curvature. Here, we report the observation of zero-dimensional anharmonic quantum emitters, which we refer to as quantum dots, in monolayer tungsten diselenide, with an energy that is 20-100 meV lower than that of two-dimensional excitons. Photon antibunching in second-order photon correlations unequivocally demonstrates the zero-dimensional anharmonic nature of these quantum emitters. The strong anisotropic magnetic response of the spatially localized emission peaks strongly indicates that radiative recombination stems from localized excitons that inherit their electronic properties from the host transition-metal dichalcogenide. The large ∼1 meV zero-field splitting shows that the quantum dots have singlet ground states and an anisotropic confinement that is most probably induced by impurities or defects. The possibility of achieving electrical control in van der Waals heterostructures and to exploit the spin-valley degree of freedom renders transition-metal-dichalcogenide quantum dots interesting for quantum information processing.

Organic–inorganic heterostructures for nonlinear optics

We consider a hybrid heterostructure made of an inorganic quantum well in close proximity with an organic material overlayer, whereby the latter is used to funnel excitation energy to the former in order to exploit the optical nonlinearities of the two-dimensional Wannier excitons. The resonant optical pumping of the Frenkel excitons and their diffusion to the organic–inorganic interface can lead to an efficient indirect pumping of the inorganic quantum well turning on the corresponding nonlinearities. As organic material we consider a layer of anthracene or of tetracene. In the latter case, the singlet exciton has an energy which is close to twice the one of a triplet exciton and singlet exciton fission into two triplets can be efficient. In tetracene based hybrid heterostructures, the temperature dependence of fission opens the possibility to turn on and off the indirect pumping due to energy transfer from the organic into the inorganic subsystem. Finally, we show how a generic mechanism of dipole–dipole hybridization may lead to the formation of virtual heterodimers of organic molecules with an enhanced nonlinear optical response.

Optical-phonon resonances with saddle-point excitons in twisted-bilayer graphene.

Twisted-bilayer graphene (tBLG) exhibits van Hove singularities in the density of states that can be tuned by changing the twisting angle θ. A θ-defined tBLG has been produced and characterized with optical reflectivity and resonance Raman scattering. The θ-engineered optical response is shown to be consistent with persistent saddle-point excitons. Separate resonances with Stokes and anti-Stokes Raman scattering components can be achieved due to the sharpness of the two-dimensional saddle-point excitons, similar to what has been previously observed for one-dimensional carbon nanotubes. The excitation power dependence for the Stokes and anti-Stokes emissions indicate that the two processes are correlated and that they share the same phonon.

Excitons in two-dimensional sheets with honeycomb symmetry

In this paper, we present results concerning ab initio calculations of the optical properties of group IV two-dimensional sheets and compare them with the prediction of an analytical model for excitons in two dimensions, which we explicitly derive. This comparison helps to understand the physics at the basis of the strong many-body effects present in the optical spectra of this class of materials. Although it demonstrates the need of full ab initio calculations for an accurate description of the two-dimensional excitons, it validates, at the same time, this simple approach to estimate, through a density functional theory calculation of the two-dimensional electronic and optical properties, the binding energy and the radius of the excitons in this class of materials.

Surface plasmons mediated energy transfer from a semiconductor quantum well to an organic overlayer

We consider the resonant energy transfer from a two-dimensional Wannier exciton (donor) to a Frenkel exciton of a molecular crystal overlayer (acceptor) when the active medias are separated by a metallic layer, possibly an electrode. We characterize the effect of the surface plasmon on this process. Using realistic values of material parameters, we show that it is possible to change the transfer rate within typically a factor of 5 (up to 44 according to geometrical configuration). We then take into account the quenching of the organic luminescence due to the proximity with the metal. This latter is significant and affect negatively the total internal efficiency that we discuss for different geometries.

Two-dimensional excitons in three-dimensional hexagonal boron nitride

The recombination processes of excitons in hexagonal boron nitride (hBN) have been probed using time-resolved photoluminescence. It was found that the theory for two-dimensional (2D) exciton recombination describes well the exciton dynamics in three-dimensional hBN. The exciton Bohr radius and binding energy deduced from the temperature dependent exciton recombination lifetime is around 8 Å and 740 meV, respectively. The effective masses of electrons and holes in 2D hBN deduced from the generalized relativistic dispersion relation of 2D systems are 0.54mo, which are remarkably consistent with the exciton reduced mass deduced from the experimental data. Our results illustrate that hBN represents an ideal platform to study the 2D optical properties as well as the relativistic properties of particles in a condensed matter system.

Two-dimensional spatial coherence of excitons in semicrystalline polymeric semiconductors: Effect of molecular weight

The electronic properties of macromolecular semiconductor thin films depend profoundly on their solid-state microstructure, which in turn is governed, among other things, by the processing conditions selected and the polymer chemical nature and molecular weight. Specifically, low-molecular-weight materials form crystalline domains of cofacially $\pi$-stacked molecules, while the usually entangled nature of higher molecular-weight polymers leads to microstructures comprised of molecularly ordered crystallites interconnected by amorphous regions. Here, we examine the interplay between extended exciton states delocalized along the polymer backbones and across polymer chains within the $\pi$-stack, depending on the structural development with molecular weight. We combine optical spectroscopies, thermal probes, and theoretical modeling, focusing on neat poly(3-hexylthiophene) (P3HT), one of the most extensively studied polymer semiconductors, of weight-average molecular weight of 3-450\,kg/mol. The spatial coherence within the chain is significantly reduced (by nearly 30\%). These observations give valuable structural information; they suggest that the macromolecules in aggregated regions of high-molecular-weight P3HT adopt a more planar conformation compared to low-molecular-weight materials. This results in the observed increase in intrachain exciton coherence. In contrast, shorter chains seem to lead to torsionally more disordered architectures. A rigorous, fundamental description of primary photoexcitations in $\pi$-conjugated polymers is hence developed: two-dimensional excitons are defined by the chain-length dependent molecular arrangement and interconnectivity of the conjugated macromolecules, leading to interplay between intramolecular and intermolecular spatial coherence.

Analytical solutions of the Schrödinger equation for a two-dimensional exciton in magnetic field of arbitrary strength

The Feranchuk-Komarov operator method is developed by combining with the Levi-Civita transformation in order to construct analytical solutions of the Schrödinger equation for a two-dimensional exciton in a uniform magnetic field of arbitrary strength. As a result, analytical expressions for the energy of the ground and excited states are obtained with a very high precision of up to four decimal places. Especially, the precision is uniformly stable for the whole range of the magnetic field. This advantage appears due to the consideration of the asymptotic behaviour of the wave-functions in strong magnetic field. The results could be used for various physical analyses and the method used here could also be applied to other atomic systems.

Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength

Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength are obtained for not only the ground state but also high excited states. Toward this goal, the operator method is developed by combining with the Levi-Civita transformation which transforms the problem under investigation into that of a two-dimensional anharmonic oscillator. This development of the non-perturbation method is significant because it can be applied to other problems of two-dimensional atomic systems. The obtained energies and wave functions set a new record for their precision of up to 20 decimal places. Analyzing the obtained data we also find an interesting result that exact analytical solutions exist at some values of magnetic field intensity.

Absorption of surface acoustic waves by a gas of two-dimensional indirect excitons

Absorption of a Bleustein-Gulyaev surface acoustic wave interacting with a gas of two-dimensional indirect excitons has been calculated. It has been shown that the absorption is changed considerably when the excitons undergo Bose-Einstein condensation. This can serve as experimental evidence of such a transition.

Electronic energy transfer in tetracene-doped p-terphenyl nanoparticles: Extraordinarily high fluorescence enhancement and quenching efficiency

A series of tetracene (Tc)-doped p-terphenyl (pTP) nanoparticles (Tc/pTP-NPs) were produced at various doping ratios by reprecipitation in water. The Tc/pTP-NPs are disk-like with a mean diameter of 75nm and height of 7nm, which were determined by scanning electron microscopy and atomic force microscopy, and exhibited electronic delocalization through H-type aggregation of the pTP molecules. Electronic energy transfer in the Tc/pTP-NPs was examined using steady-state and time-resolved fluorescence spectroscopy and fluorescence anisotropy experiments: pTP-NPs serve as an excellent light-harvesting nano-matrix with a large absorption coefficient that exceeds 109M−1cm−1. Furthermore, Stern–Volmer analysis of the donor emission was performed by changing the dopant concentration; this showed that a single Tc acceptor quenched more than 104pTP donors. Comparison of the experimental and theoretical energy transfer efficiencies indicated that the efficient energy transfer can be attributed to two-dimensional exciton diffusion in the host nanoparticles.

Exciton migration dynamics between phenylene moieties in the framework of periodic mesoporous organosilica powder

To understand the excitation migration process between the phenylene (Ph) moieties in the framework of periodic mesoporous organosilicas (PMOs), the exciton–exciton annihilation behavior between the Ph moieties is studied. The dependence of the excitation light intensity on the fluorescence decay curve of the Ph exciton was successfully analyzed with a two-dimensional exciton diffusion and collision model. The quenching distance and diffusion length of the Ph exciton are estimated to be 0.4–0.8 nm and at least 4 nm, respectively. It is suggested that the Ph exciton is delocalized between up to three Ph moieties and moved between approximately nine Ph moieties in the pore wall of Ph–PMO.

Efficient optical pumping of organic-inorganic heterostructures for nonlinear optics

We theoretically consider a hybrid heterostructure made of an inorganic quantum well in close proximity with an organic material overlayer whereby the latter is used to funnel excitation energy to the former in order to exploit the optical nonlinearities of the two-dimensional Wannier excitons. On the one hand, the diffusion length of Frenkel excitons in the organic medium is assumed to be comparable or larger than the corresponding absorption length. On the other hand, the nonradiative energy transfer from the organic to the inorganic subsytem can be very efficient when the Frenkel exciton energy is significantly higher than the band gap of the inorganic semiconductor. We show in this regime that the resonant optical pumping of the Frenkel excitons can lead to an efficient indirect pumping of the Wannier excitons (or electron-hole plasma) in the inorganic quantum well turning on the corresponding nonlinearities.

On the radiative lifetime of free-moving two-dimensional excitons

A simple microscopic mechanism explaining the linear dependence of the radiative lifetime of free-moving two-dimensional excitons on their effective temperature is suggested. It is shown that there exists a characteristic effective temperature (of about few Kelvin) defined by the exciton–acoustic phonon interaction at which the radiative lifetime is minimal. Below this temperature the lifetime starts to increase with decreasing temperature. The correspondence with previous theoretical and experimental results is discussed.

Role of anisotropy in the Förster energy transfer from a semiconductor quantum well to an organic crystalline overlayer

We consider the non-radiative resonant energy transfer from a two-dimensional Wannier exciton (donor) to a Frenkel exciton of a molecular crystal overlayer (acceptor). We characterize the effect of the optical anisotropy of the organic subsystem on this process. Using realistic values of material parameters, we show that it is possible to change the transfer rate within typically a factor of two depending on the orientation of the crystalline overlayer. The resonant matching of donor and acceptor energies is also partly tunable via the organic crystal orientation.

Different exciton behaviors in blue and green wells of dual-wavelength InGaN/GaN MQWs structures

Staggered structures with blue and green quantum wells (QWs) were grown by metal organic vapor phase epitaxy (MOVPE) and characterized by photoluminescence (PL) and time resolved photoluminescence (TRPL) at various temperatures from 10 K to 300 K. High efficiency green light was observed, accompanying with decreased intensity of blue light. Efficiency of the green band was lower than that of the blue band below 100 K, but became two times greater than the efficiency of blue when temperature increased to room temperature. Three-dimensional and two-dimensional exciton behaviors were observed by TRPL measurements corresponding to blue and green bands, respectively. It is considered that carrier tunneling from blue wells is a key process for high efficiency luminescence in green QWs.

Quantum and classical solutions for statically screened two-dimensional Wannier-Mott excitons

Quantum solutions and classical orbits are discussed for statically screened Wannier-Mott excitons for two closely related potentials: the Stern-Howard potential and a suggested simple focusing one. Bound states and exact ``quantized'' values of screening are obtained as well. For the suggested potential, the scattering matrix, the Regge poles, and the transmission coefficient are calculated exactly. We argue that the simple potential can be utilized in applications instead of the Stern-Howard potential, which is difficult to handle.

Seeing Many-Body Effects in Single- and Few-Layer Graphene: Observation of Two-Dimensional Saddle-Point Excitons

Significant excitonic effects were observed in graphene by measuring its optical conductivity in a broad spectral range including the two-dimensional π-band saddle-point singularities in the electronic structure. The strong electron-hole interactions manifest themselves in an asymmetric resonance peaked at 4.62 eV, which is redshifted by nearly 600 meV from the value predicted by ab initio GW calculations for the band-to-band transitions. The observed excitonic resonance is explained within a phenomenological model as a Fano interference of a strongly coupled excitonic state and a band continuum. Our experiment also showed a weak dependence of the excitonic resonance in few-layer graphene on layer thickness. This result reflects the effective cancellation of the increasingly screened repulsive electron-electron (e-e) and attractive electron-hole (e-h) interactions.