Trion Binding Energy Research Articles

Electric-field-tuned Binding Energies of Trions in Silicene, Germanene, and Stanene Monolayers

Electric-field-tuned Binding Energies of Trions in Silicene, Germanene, and Stanene Monolayers

Strong Electrostatic Control of Excitonic Features in MoS2 by a Free‐Standing Ultrahigh‐κ Ferroelectric Perovskite

AbstractIntegrating free‐standing complex oxides with two‐dimensional (2D) materials has recently attracted great interest, due to the rich physics evolving from such structures. Enhancing and tuning the opto–electronic properties of these systems is of high importance for a multitude of applications, such as sensors, memory devices or optical communications. The electrostatic control of photoluminescence of monolayer MoS2 at room temperature via integration of free‐standing BaTiO3 (BTO), a ferroelectric perovskite oxide is presented. It is shown that the use of BTO leads to highly tunable exciton emission of MoS2 in a minimal range of gate voltages. Due to BTO's ferroelectric polarization‐induced doping, large peak emission shifts as well as a large and tunable A trion binding energy in the range of 40–100 meV are observed. These measurements are compared with those carried out when the BTO is replaced by a hexagonal boron nitride (hBN) dielectric layer, confirming BTO's superior gating properties and thus lower power consumption. Additionally, advantage of the ferroelectric switching of BTO is taken by fabricating devices where the BTO layer is decoupled from the gate electrode with a SiO2 layer. Choosing to isolate the BTO allows to induce large remanent behavior of MoS2’s excitonic features.

Realizing Topological Superconductivity in Tunable Bose-Fermi Mixtures with Transition Metal Dichalcogenide Heterostructures.

Heterostructures of two-dimensional transition metal dichalcogenides are emerging as a promising platform for investigating exotic correlated states of matter. Here, we propose to engineer Bose-Fermi mixtures in these systems by coupling interlayer excitons to doped charges in a trilayer structure. Their interactions are determined by the interlayer trion, whose spin-selective nature allows excitons to mediate an attractive interaction between charge carriers of only one spin species. Remarkably, we find that this causes the system to become unstable to topological p+ip superconductivity at low temperatures. We then demonstrate a general mechanism to develop and control this unconventional state by tuning the trion binding energy using a solid-state Feshbach resonance.

Size Dependence of Trion and Biexciton Binding Energies in Lead Halide Perovskite Nanocrystals.

Lead halide perovskite nanocrystals (NCs) have attracted much attention as light-source materials for light-emitting diodes, lasers, and quantum light emitters. The luminescence properties of perovskite NCs and the performance of NC-based light-source devices depend on trion and biexciton dynamics. Here, we examined the size dependence of trion and biexciton binding energies by conducting low-temperature single-dot spectroscopy on three different perovskite NCs: CsPbBr3, CsPbI3, and FAPbBr3. While the photoluminescence spectral widths of the all-inorganic CsPbBr3 and CsPbI3 NCs were narrow, compared with those of the organic-inorganic hybrid FAPbBr3 NCs, the binding energies of trions and biexcitons of all three samples showed similar size dependences, independent of the A-site cation and halogen. The effective-mass approximation calculations implied the importance of dynamical dielectric screening on the formation of trions and biexcitons.

On the unique temperature-dependent interplay of a B-exciton and its trion in monolayer MoSe2.

Plasmonics in metal nanoparticles can enhance their near field optical interaction with matter, promoting emission into selected optical modes. Here, using Ga nanoparticles with carefully tuned plasmonic resonance in proximity to MoSe2 monolayers, we show selective photoluminescence enhancement from the B-exciton and its trion with no observable A-exciton emission. The nanoengineered substrate allows for the first direct experimental observation of the B-trion binding energy in semiconducting monolayers. Using temperature-dependent photoluminescence measurements, we show the following features of the MoSe2 B-exciton family: (i) the trion binding energy has an observable temperature dependence with a decreasing trend towards low temperatures and (ii) the exciton-trion emission ratio varies non-monotonically with temperature with a steep increase in the trion emission at lower temperatures. Using detailed models, we identify the particle size required for selective excitation and describe the underlying physical processes. This opens newer avenues for selectively promoting excitonic species and tuning the effective particle lifetimes in monolayer semiconductors. These results demonstrate the excellent plasmonic properties of Ga nanoparticles, which along with facile processing techniques makes it an attractive alternative to the prevalent noble metal plasmonics having applications in flexible/stretchable materials and textiles.

Cross-domain growth and angle-dependent interlayer coupling of twisted bilayer MoS2

Twisted 2D transition metal dichalcogenides (TMDCs) play a significant role in the development of twistronics. However, it is still challenging to prepare high-quality twisted TMDCs by current stacking or folding techniques. Herein, we propose a cross-domain chemical vapor deposition method to synthesize twisted bilayer MoS2 through precisely controlling the supply of molybdenum precursor. It is found that the top layer of a bilayer MoS2 grain maintains its original orientation even when it crosses over to neighboring monolayer MoS2 grain. This suggests that the van der Waals epitaxy can be prevented with the assistance of covalent bonds. Furthermore, the interlayer coupling strength reaches a maximum value at the twisted angle (θ) of 0° or 60° and a minimum at θ = 30°. Moreover, the evolution of in-plane shear mode and out-of-plane breathing mode obtained from low-frequency Raman spectroscopy reveals atomic reconstructions of the moiré pattern. Meanwhile, the shift of the indirect bandgap exhibits an angle dependence consistent with the interlayer coupling strength, which likely comes from the mixing of pz orbitals. The change in A−/A intensity ratio is not mainly originated from the trion binding energy, but the excess electron concentration. Our results offer a feasible approach to prepare high-quality twisted TMDCs and provide a good platform for studying twistronics and related phenomena.

Robustness of Trion State in Gated Monolayer MoSe2 under Pressure.

Quasiparticles consisting of correlated electron(s) and hole(s), such as excitons and trions, play important roles in the optical phenomena of van der Waals semiconductors and serve as unique platforms for studies of many-body physics. Herein, we report a gate-tunable exciton-to-trion transition in pressurized monolayer MoSe2, in which the electronic band structures are modulated continuously within a diamond anvil cell. The emission energies of both the exciton and trion undergo large blueshifts over 90 meV with increasing pressure. Surprisingly, the trion binding energy remains constant at 30 meV, regardless of the applied pressure. Combining ab initio density functional theory calculations and quantum Monte Carlo simulations, we find that the remarkable robustness of the trion binding energy originates from the spatially diffused nature of the trion wave function and the weak correlation between its constituent electron-hole pairs. Our findings shed light on the optical properties of correlated excitonic quasiparticles in low-dimensional materials.

Trion clustering structure and binding energy in two-dimensional semiconductor materials: Faddeev equations approach

In this work, we develop the basic formalism to study trions in semiconductor layered materials using the Faddeev equations in momentum space for three different particles lying in two dimensions. We solve the trion Faddeev coupled integral equations for both short-range one-term separable Yamaguchi potential and Rytova-Keldysh (RK) interaction applied to the MoS$_2$ layer. We devise two distinct regularization methods to overcome the challenge posed by the repulsive electron-electron RK potential in the numerical solution of the Faddeev equations in momentum space. The first method regulates the repulsive interaction in the infrared region, while the second regulates it in the ultraviolet region. By extrapolating the trion energy to the situation without screening, the two methods gave consistent results for the MoS$_2$ layer with a trion binding energy of $-49.5(1)$~meV for the exciton energy of $-753.3$~meV. We analyzed the trion structure for the RK and Yamaguchi potentials in detail, showing their overall similarities and the dominant cluster structure, where the strongly bound exciton is weakly bound to an electron. We found that this property is manifested in the dominance of two of the Faddeev components over the one where the hole is a spectator of the interacting electron pair.

Spectral Fingerprint of Quantum Confinement in Single CsPbBr3 Nanocrystals.

Lead halide perovskite nanocrystals are promising materials for classical and quantum light emission. To understand these outstanding properties, a thorough analysis of the band-edge exciton emission is needed, which is not reachable in ensemble and room-temperature studies because of broadening effects. Here, we report on a cryogenic-temperature study of the photoluminescence of single CsPbBr3 nanocrystals in the intermediate quantum confinement regime. We reveal the size-dependence of the spectral features observed: the bright triplet exciton energy splittings, the trion and biexciton binding energies, and the optical phonon replica spectrum. In addition, we show that bright triplet energy splittings are consistent with a pure exchange model and that the variety of polarization properties and spectra recorded can be rationalized simply by considering the orientation of the emitting dipoles and the populations of the emitting states.

Many-Body Correlations and Exciton Complexes in CsPbBr3 Quantum Dots.

All-inorganic lead-halide perovskite (LHP) (CsPbX3 , X=Cl, Br, I) quantum dots (QDs) have emerged as a competitive platform for classical light-emitting devices (in the weak light-matter interaction regime, e.g., LEDs and laser), as well as for devices exploiting strong light-matter interaction at room temperature. Many-body interactions and quantum correlations among photogenerated exciton complexes play an essential role, for example, by determining the laser threshold, the overall brightness of LEDs, and the single-photon purity in quantum light sources. Here, by combining cryogenic single-QD photoluminescence spectroscopy with configuration-interaction (CI) calculations, the size-dependent trion and biexciton binding energies are addressed. Trion binding energies increase from 7to 17meV for QD sizes decreasing from 30to 9nm, while the biexciton binding energies increase from 15to 30meV, respectively. CI calculations quantitatively corroborate the experimental results and suggest that the effective dielectric constant for biexcitons slightly deviates from the one of the single excitons, potentially as a result of coupling to the lattice in the multiexciton regime. The findings here provide a deep insight into the multiexciton properties in all-inorganic LHP QDs, essential for classical and quantum optoelectronic devices.

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.

Exploring the effect of dielectric screening on neutral and charged-exciton properties in monolayer and bilayer MoTe2

Dielectric engineering of heterostructures made from two-dimensional van der Waals semiconductors is a unique and powerful tool to tailor the electric and optical band gaps solely via the dielectric environment and the crystal thickness modulation. Here, we utilize high quality MoTe2 monolayer and bilayer crystals as a candidate for near-infrared photonic applications. The crystals are exfoliated on various technologically relevant carrier substrates: silicon/silicon dioxide, poly(methyl methacrylate), hexagonal boron nitride, silicon carbide, and silicon nitride. These substrates provide a large range of high frequency dielectric constants from 2.1 to 7.0 for MoTe2-containing heterostructures. We assess the relationship between the environmental dielectric function and Coulomb screening by combining detailed spectroscopic measurements, utilizing low-temperature and high-spatially resolved photoluminescence and contrast reflectivity, with microscopic many-body modeling, to explore the potential of this less-recognized material platform for applications in optoelectronics at photon wavelengths above 1 μm. We observe a redshift of the optical gap emission energy from the monolayer to bilayer regime on the order of 30 meV. Furthermore, the thickness controlled shift is slightly larger than the one induced by the local dielectric environment, which ranges on the order of 20 meV for the MoTe2 monolayers and on the order of 8 meV for the MoTe2 bilayers. We also show that the local dielectric screening barely affects the trion binding energy, which is captured by our microscopic model, accounting for the screened Coulomb potential for the heterostructures.

Disorder of excitons and trions in monolayer MoSe2.

The optical spectra of transition metal dichalcogenide monolayers are dominated by excitons and trions. Here, we establish the dependence of these optical transitions on the disorder from hyperspectral imaging of h-BN encapsulated monolayer MoSe2. While both exciton and trion energies vary spatially, these two quantities are almost perfectly correlated, with spatial variation in the trion binding energy of only ∼0.18meV. In contrast, variation in the energy splitting between the two lowest energy exciton states is one order of magnitude larger at ∼1.7meV. Statistical analysis and theoretical modeling reveal that disorder results from dielectric and bandgap fluctuations, not electrostatic fluctuations. Our results shed light on disorder in high quality TMDC monolayers, its impact on optical transitions, and the many-body nature of excitons and trions.

Polaronic Trions Induced by Strong Interfacial Coupling in Monolayer WSe2

AbstractThe weak dielectric screening in 2D semiconducting transition metal dichalcogenides give rise to strongly bound quasiparticles, which provides a platform to investigate the diverse excitonic phenomena and correlated physics. However, how to effectively control these quasiparticles is still a challenge for their applications in optoelectronic and valleytronic devices. Herein, by means of fabricating monolayer WSe2 and transition metal oxide (TMO) heterostructures, polaronic trion, that is a trion dressed with soft rotational optical (RO) phonons, is realized due to the strong interfacial coupling. This Fröhlich bound state of trion dramatically increases the trion binding energy (BE) from room temperature to 65 meV at 80 K in WSe2/LaAlO3 (LAO). However, the increase of the trion BE for WSe2/SrTiO3 (STO) occurs below the phase transition temperature. This work expands the possibilities of the TMDs/TMOs heterostructures and promotes the development of 2D van der Waals materials for quasiparticle‐based devices.

Absorption and Emission of Chemically and Electrochemically Doped Graphene Nanoribbons

Graphene nanoribbons (GNRs) are narrow stripes of graphene that exhibit unique optical and electronic properties depending on their width and edge type. Recent advances in the bottom-up synthesis of GNRs have enabled precise control over their structure and thus their bandgap. However, the systematic optical and electrical characterization of GNRs obtained from solution-mediated reactions has so far been prevented by the poor stability and processability of GNR dispersions. Here we employ liquid cascade centrifugation (LCC) to obtain size-selected and stable dispersions of bottom-up synthesized 9-aGNRs in toluene and tetrahydrofuran and investigate their intrinsic optical properties. Dispersions and films of these 9-aGNRs show well-defined absorption and photoluminescence bands between 800 and 1000 nm, with relative intensities depending on the LCC-fraction. The best GNR dispersions show photoluminescence quantum yields of up to 70 %. Trions are charged excitons with red-shifted emission that can be created in doped low-dimensional semiconductors, such as carbon nanotubes. Theoretical studies predict large trion binding energies (> 300 meV) in graphene nanoribbons (depending on their width). Hence their optical properties upon doping and possible new features are of interest. Chemical doping of our 9-aGNR dispersions with the strong molecular p-dopant F4-TCNQ and electrochemical doping of GNR thin films in ambipolar electrolyte-gated field-effect transistors results in the expected bleaching of the main absorption bands but also the emergence of new redshifted, charge-induced absorption peaks that may indicate the existence of trions in GNRs.

Stabilization of Three-Particle Excitations in Monolayer MoS2 by Fluorinated Methacrylate Polymers.

While extrinsic factors, such as substrates and chemical doping, are known to strongly influence visible photoemission from monolayer MoS2, key fundamental knowledge for p-type polymeric dopants is lacking. We investigated perturbations to the electronic environment of 2D MoS2 using fluorinated polymer coatings and specifically studied stabilization of three-particle states by monitoring changes in intensities and emission maxima of three-particle and two-particle emissions. We calculated changes in carrier density and trion binding energy, the latter having an additional contribution from MoS2 polarization by the polymer. Polarization is further suggested by Kelvin probe force microscopy (KPFM) measurements of large Fermi level shifts. Changes similar in magnitude, but opposite in sign, were observed in 2D MoS2 coated with an analogous nonfluorinated polymer. These findings highlight the important interplay between electron exchange and electrostatic interactions at the interface between polymers and transition metal dichalcogenides (TMDCs), which govern fundamental electronic properties relevant to next-generation devices.

Charged excitons or trions in 2D parabolic quantum dots?

So far in the literature the terms “charged exciton” and “trion” are often confused with each other and mostly considered as the same. In this work we show this is not the case in 2D quantum dots with a parabolic confinement. By using the unrestricted Hartree-Fock method the energy and binding energy of both charged excitons and trions in 2D parabolic quantum dots are calculated in dependence on the confinements of charge carriers in quantum dot. It is shown that the binding energies of the charged exciton and the trion behave differently in regard to the ratios of the confinements between the electron and hole. The effect of the external magnetic field on the binding energies of charged excitons has been also considered.

Heavy-hole bilayer trions of transition metal dichalcogenides by analytical treatment to model He-isoelectronic ions upto dipole factor of Green’s function expansion of Coulomb interaction

Electronic structures of heavy-hole trions and He-isoelectronic ions show dependence on transitions among two-electron bound states constituted of hydrogenic orbitals for which Coulomb (exchange) interaction causes nontrivial secular divergence to Schrödinger equation (SE). Coulomb interaction between a pair of electrons triggers nonadiabatic transitions due conical intersections and larger vibrational amplitudes of nuclei. Therefore, existing state-of-art theories ubiquitously urge analytical integrals for multipoles of electrostatic Green’s function expansion. Born–Oppenheimer (BO) approximation separates the hamiltonian into electronic and nuclear coordinates at adiabatic limit. Employing associated Laguerre polynomial and Whittaker-M function basis sets of hydrogenic orbitals for the pair of electrons (electronic coordinate) furnishes analytical, terminable, simple and finitely summed integrals in terms of Lauricella functions. The exact integrals also remedy the difficulty arisen from different scaling factors of bound states for higher order perturbation calculations. Analytical perturbation calculations for monopole and dipole factors using singly and doubly excited states (|n2sn4s〉, |n2pn4p〉) with spherical and dumbbell symmetries show sufficient convergence of ground-state energy correction of He-isoelectronic series within 0.20–6.89% of reported results. Calculation of current-density with ground-state upto first order perturbation correction clearly shows that singly and doubly excited spherically symmetric states do not contribute to local current of He-isoelectronic series for monopole factor. Binding energies of heavy-hole trions of transition metal dichalcogenides (TMDCs) are found to be in good agreement with experimentally observed values.

Control of trion-to-exciton conversion in monolayer WS2 by orbital angular momentum of light.

Controlling the density of exciton and trion quasiparticles in monolayer two-dimensional (2D) materials at room temperature by nondestructive techniques is highly desired for the development of future optoelectronic devices. Here, the effects of different orbital angular momentum (OAM) lights on monolayer tungsten disulfide at both room temperature and low temperatures are investigated, which reveal simultaneously enhanced exciton intensity and suppressed trion intensity in the photoluminescence spectra with increasing topological charge of the OAM light. In addition, the trion-to-exciton conversion efficiency is found to increase rapidly with the OAM light at low laser power and decrease with increasing power. Moreover, the trion binding energy and the concentration of unbound electrons are estimated, which shed light on how these quantities depend on OAM. A phenomenological model is proposed to account for the experimental data. These findings pave a way toward manipulating the exciton emission in 2D materials with OAM light for optoelectronic applications.

Exciton–polarons in two-dimensional semiconductors and the Tavis–Cummings model

The elementary optical excitations of a two-dimensional electron or hole system have been identified as exciton-Fermi-polarons. Nevertheless, the connection between the bound state of an exciton and an electron, termed trion, and exciton–polarons is subject of ongoing debate. Here, we use an analogy to the Tavis–Cummings model of quantum optics to show that an exciton–polaron can be understood as a hybrid quasiparticle—a coherent superposition of a bare exciton in an unperturbed Fermi sea and a bright collective excitation of many trions. The analogy is valid to the extent that the Chevy Ansatz provides a good description of dynamical screening of excitons and provided the Fermi energy is much smaller than the trion binding energy. We anticipate our results to bring new insight that could help to explain the striking differences between absorption and emission spectra of two-dimensional semiconductors.