Trion Binding Energy Research Articles

Excited-State Trions in Monolayer WS_{2}.

We discover an excited bound three-particle state, the 2s trion, appearing energetically below the 2s exciton in monolayer WS_{2}, using absorption spectroscopy and abinitio GW and Bethe-Salpeter equation calculations. The measured binding energy of the 2s trion (22meV) is smaller compared to the 1s intravalley and intervalley trions (37 and 31meV). With increasing temperature, the 1s and 2s trions transfer their oscillator strengths to the respective neutral excitons, establishing an optical fingerprint of trion-exciton resonance pairs. Our discovery underlines the importance of trions for the entire excitation spectrum of two-dimensional semiconductors.

Experimental Evidence of Anisotropic and Stable Charged Excitons (Trions) in Atomically Thin 2D ReS2

AbstractExperimentally observed, stable trions with large binding energy (≈25 meV) in atomically thin monolayer 2D transition metal dichalcogenides MX2 (M = Mo, W, X = S, Se, and Te) with an isotropic crystal structure have been extensively studied. In contrast, the characteristics of trions in atomically thin 2D materials with an anisotropic crystal structure are not completely understood. Low‐temperature photoluminescence (PL) spectroscopy in few‐layer ReS2 with an anisotropic crystal structure by applying a gate voltage is described. A new PL peak that emerges below the lower‐energy side of neutral excitons obtained by tuning the gate voltages is attributed to emission from negative trions. Furthermore, the trion binding energy that is strongly dependent on the layer thickness reaches a large value of ≈60 meV in 1L–ReS2, which is ≈2 times larger than that in other isotropic 2D materials (MX2). The enhancement of the binding energy reflects the quasi‐1D nature of the trions in anisotropic atomically thin ReS2. These experimental observations will promote a better understanding of the optical response and applications in new categories of the anisotropic atomically thin 2D materials with a quasi‐1D nature.

Charged excitons in two-dimensional transition metal dichalcogenides: Semiclassical calculation of Berry curvature effects

We theoretically study the role of the Berry curvature on neutral and charged excitons in two-dimensional transition-metal dichalcogenides. The Berry curvature arises due to a strong coupling between the conduction and valence bands in these materials that can to great extent be described within the model of massive Dirac fermions. The Berry curvature lifts the degeneracy of exciton states with opposite angular momentum. Using an electronic interaction that accounts for non-local screening effects, we find a Berry-curvature induced splitting of $\sim 17$ meV between the 2$p_{-}$ and 2$p_{+}$ exciton states in WS$_2$, consistent with experimental findings. Furthermore, we calculate the trion binding energies in WS$_2$ and WSe$_2$ for a large variety of screening lenghts and different dielectric constants for the environment. Our approach indicates the prominent role played by the Berry curvature along with non-local electronic interactions in the understanding of the energy spectra of neutral and charged excitons in transition-metal dichalcogenides and in the the interpretation of their optical properties.

Polaronic Trions at the MoS2 /SrTiO3 Interface.

The reduced electrical screening in 2D materials provides an ideal platform for realization of exotic quasiparticles, that are robust and whose functionalities can be exploited for future electronic, optoelectronic, and valleytronic applications. Recent examples include an interlayer exciton, where an electron from one layer binds with a hole from another, and a Holstein polaron, formed by an electron dressed by a sea of phonons. Here, a new quasiparticle is reported, "polaronic trion" in a heterostructure of MoS2 /SrTiO3 (STO). This emerges as the Fröhlich bound state of the trion in the atomically thin monolayer of MoS2 and the very unique low energy soft phonon mode (≤7 meV, which is temperature and field tunable) in the quantum paraelectric substrate STO, arising below its structural antiferrodistortive (AFD) phase transition temperature. This dressing of the trion with soft phonons manifests in an anomalous temperature dependence of photoluminescence emission leading to a huge enhancement of the trion binding energy (≈70 meV). The soft phonons in STO are sensitive to electric field, which enables field control of the interfacial trion-phonon coupling and resultant polaronic trion binding energy. Polaronic trions could provide a platform to realize quasiparticle-based tunable optoelectronic applications driven by many body effects.

Charge‐Accumulation Effect in Transition Metal Dichalcogenide Heterobilayers

Charge transfer in transition-metal-dichalcogenides (TMDs) heterostructures is a prerequisite for the formation of interlayer excitons, which hold great promise for optoelectronics and valleytronics. Charge accumulation accompanied by a charge-transfer process can introduce considerable effect on interlayer exciton-based applications; nevertheless, this aspect has been rarely studied up to date. This work demonstrates how the charge accumulation affects the light emission of interlayer excitons in van der Waals heterobilayers (HBs) consisting of monolayer WSe2 and WS2 . As excitation power increases, the photoluminescence intensity of interlayer excitons increases more rapidly than that of intralayer excitons. The phenomenon can be explained by charge-accumulation effect, which not only increases the recombination probability of interlayer excitons but also saturates the charge-transfer process. This scenario is further confirmed by a careful examination of trion binding energy of WS2 , which nonlinearly increases with the increase of the excitation power before reaching a maximum of about 75 meV. These investigations provide a better understanding of interlayer excitons and trions in HBs, which may provoke further explorations of excitonic physics as well as TMDs-based devices.

Few-Body Systems in Condensed Matter Physics

This review focuses on the studies and computations of few-body systems of electrons and holes in condensed matter physics. We analyze and illustrate the application of a variety of methods for description of two- three- and four-body excitonic complexes such as an exciton, trion and biexciton in three-, two- and one-dimensional configuration spaces in various types of materials. We discuss and analyze the contributions made over the years to understanding how the reduction of dimensionality affects the binding energy of excitons, trions and biexcitons in bulk and low dimensional semiconductors and address the challenges that still remain.

Virtual Trions in the Photoluminescence of Monolayer Transition-Metal Dichalcogenides.

Photoluminescence experiments from monolayer transition-metal dichalcogenides often show that the binding energy of trions is conspicuously similar to the energy of optical phonons. This enigmatic coincidence calls into question whether phonons are involved in the radiative recombination process. We address this problem, unraveling an intriguing optical transition mechanism. Its initial state is a localized charge (electron or hole) and delocalized exciton. The final state is the localized charge, phonon, and photon. In between, the intermediate state of the system is a virtual trion formed when the localized charge captures the exciton through emission of the phonon. We analyze the difference between radiative recombinations that involve real and virtual trions (i.e., with and without a phonon), providing useful ways to distinguish between the two in experiment.

Binding energies of excitonic complexes in type-II quantum rings from diffusion quantum Monte Carlo calculations

Excitonic complexes in type-II quantum-ring heterostructures may be considered as artificial atoms due to the confinement of only one charge-carrier type in an artificial nucleus. Binding energies of excitons, trions, and biexcitons in these nanostructures are then effectively ionization energies of these artificial atoms. The binding energies reported here are calculated within the effective-mass approximation using the diffusion quantum Monte Carlo method and realistic geometries for gallium antimonide rings in gallium arsenide. The electrons form a halo outside the ring, with very little charge density inside the central cavity of the ring. The de-excitonization and binding energies of the complexes are relatively independent of the precise shape of the ring.

Trions and biexcitons in ZnO/ZnMgO, CdSe/ZnS and CdSe/CdS core/shell nanowires

A study of the trion and biexciton in a nanowire (NW) in the framework of the effective-mass model is presented. We consider the formation of trions and biexcitons under the action of both the lateral confinement and the localization potential. The analytical expressions for the binding energy and eigenfunctions of the trion and biexciton are obtained and expressed by means of matrix elements of the effective one-dimensional cusp-type Coulomb potentials whose parameters are determined self-consistently by employing eigenfunctions of the confined electron and hole states. Our calculations for the ZnO/ZnMgO, CdSe/ZnS and CdSe/CdS core/shell cylindrical shaped NWs show that the trion and biexciton binding energy in NWs are size-dependent and for the same input parameters the biexciton binding energy in NWs is always larger than the binding energy of the trion. The trion and biexciton remain stable in CdSe/ZnS NW with the increase of the dielectric shell, while in ZnO/ZnMgO NW they become unstable when the surrounding dielectric shell exceeds 2.5 nm and 2 nm for each, respectively. The associative ionization of biexciton antibonding states into trion bonding states that leads to the formation of trions is studied. Based on the results for size dependence of biexciton binding energy and probability associative ionization an optimal radius for optoelectronic application NW is suggested.

Экситоны и трионы в двухслойных ван-дер-ваальсовых гетероструктурах

The theoretical study of excitons and trions in bilayer structures based on transitional metal diсhalcogenides is carried out. The expressions for effective interaction between charge carriers in such a system with taking into account the dielectric contrast had been obtained. The simple and physically relevant trial functions for electron-hole complexes were suggested. The variational calculation of the dependences of exciton and trion binding energies on the interlayer separation was made with taking into account the details of the screening of the Coulomb interaction. The accuracy of the variational approach is validated by the direct numerical calculation of the exciton binding energy as a function of the interlayer distance.

Stark shift of excitons and trions in two-dimensional materials

The effect of an external in-plane electric field on neutral and charged exciton states in two-dimensional (2D) materials is theoretically investigated. These states are argued to be strongly bound, so that electron-hole dissociation is not observed up to high electric field intensities. Trions in the anisotropic case of monolayer phosphorene are demonstrated to be especially robust under electric fields, so that fields as high as 100 kV/cm yield no significant effect on the trion binding energy or probability density distribution. Polarizabilities of excitons are obtained from the parabolicity of numerically calculated Stark shifts. For trions, a fourth order Stark shift is observed, which enables the experimental verification of hyperpolarizability in 2D materials, as observed in the highly excited states of the Rydberg series of atoms and ions.

Excitonic complexes in anisotropic atomically thin two-dimensional materials: Black phosphorus and TiS3

The effect of anisotropy in the energy spectrum on the binding energy and structural properties of excitons, trions, and biexcitons is investigated. To this end we employ the stochastic variational method with a correlated Gaussian basis. We present results for the binding energy of different excitonic complexes in black phosphorus (bP) and TiS$_3$ and compare them with recent results in the literature when available, for which we find good agreement. The binding energies of excitonic complexes in bP are larger than those in TiS$_3$. We calculate the different average interparticle distances in bP and TiS$_3$ and show that excitonic complexes in bP are strongly anisotropic whereas in TiS$_3$ they are almost isotropic, even though the constituent particles have an anisotropic energy spectrum. This is also confirmed by the correlation functions.

Spatially selective reversible charge carrier density tuning in WS2 monolayers via photochlorination

Chlorine-doped tungsten disulfide monolayer (1L-WS2) with tunable charge carrier concentration has been realized by pulsed laser irradiation of the atomically thin lattice in a precursor gas atmosphere. This process gives rise to a systematic shift of the neutral exciton peak towards lower energies, indicating reduction of the crystal’s electron density. The capability to progressively tune the carrier density upon variation of the exposure time is demonstrated; this indicates that the Fermi level shift is directly correlated to the respective electron density modulation due to the chlorine species. Notably, this electron withdrawing process enabled the determination of the trion binding energy of the intrinsic crystal, found to be as low as 20 meV, in accordance to theoretical predictions. At the same time, it is found that the effect can be reversed upon continuous wave laser scanning of the monolayer in air. Scanning auger microscopy (SAM) and x-ray photoelectron spectroscopy (XPS) are used to link the actual charge carrier doping to the different chlorine configurations in the monolayer lattice. The spectroscopic analyses, complemented by density functional theory calculations, reveal that chlorine physisorption is responsible for the carrier density modulation induced by the pulsed laser photochemical reaction process. Such bidirectional control of the Fermi level, coupled with the capability offered by lasers to process at pre-selected locations, can be advantageously used for spatially resolved doping modulation in 1L-WS2 with micrometric resolution. This method can also be extended for the controllable doping of other TMD monolayers.

Photoluminescence Study of B‐Trions in MoS2 Monolayers with High Density of Defects

Photoluminescence spectroscopy has been used to investigate the details of B band emission from single‐layer MoS2 samples grown by chemical vapor deposition. The evolution of the peak shape upon variable excitation power is well described by a combination of exciton and trion contributions, from which B trion binding energy of 18 meV has been extracted. It has been suggested that the absence of accompanying A trion emission in our samples, as well as the enhanced intensity of the B band, can be ascribed to a fast non‐radiative recombination channel arising from the large defect density in our samples. It has been found that band‐selective recombination channels or formation of dark/bright trions are possible microscopic scenarios for our observations.

Trions in bulk LiF and at the LiF(001) surface

We study the neutral and charged optical excitations (excitons and trion) in the prototypical wide-gap insulator LiF using the first-principles $GW/\mathrm{BSE}$ approach and its extension for trions. In addition to neutral excitons we find bound trion states with a trion binding energy of 20--30 meV. At the same time the lowest bright exciton and trion are well separated by about 400 meV in the absorption spectrum both for the bulk and the (001) surface crystal. Even though the charged trions are slightly more extended compared to their neutral counterparts, they remain localized on a few atoms only and keep the Frenkel-like character of the neutral excitons. With such strongly localized trions, LiF stands out from currently investigated trionic materials and highlights itself for further studies.

Coulomb interaction in monolayer transition-metal dichalcogenides

Recently, the celebrated Keldysh potential has been widely used to describe the Coulomb interaction of few-body complexes in monolayer transition-metal dichalcogenides. Using this potential to model charged excitons (trions), one finds a strong dependence of the binding energy on whether the monolayer is suspended in air, supported on SiO$_2$, or encapsulated in hexagonal boron-nitride. However, empirical values of the trion binding energies show weak dependence on the monolayer configuration. This deficiency indicates that the description of the Coulomb potential is still lacking in this important class of materials. We address this problem and derive a new potential form, which takes into account the three atomic sheets that compose a monolayer of transition-metal dichalcogenides. The new potential self-consistently supports (i) the non-hydrogenic Rydberg series of neutral excitons, and (ii) the weak dependence of the trion binding energy on the environment. Furthermore, we identify an important trion-lattice coupling due to the phonon cloud in the vicinity of charged complexes. Neutral excitons, on the other hand, have weaker coupling to the lattice due to the confluence of their charge neutrality and small Bohr radius.

Molecular screening effects on exciton-carrier interactions in suspended carbon nanotubes

Photoluminescence spectroscopy measurements are performed on suspended carbon nanotubes in a field-effect configuration, and the gate voltage dependence of photoluminescence spectra are compared for the pristine and the molecularly adsorbed states of the nanotubes. We quantify the molecular screening effect on the trion binding energies by determining the energy separation between the bright exciton and the trion emission energies for the two states. The voltage dependence shows narrower voltage regions of constant photoluminescence intensity for the adsorbed states, consistent with a reduction in the electronic bandgap due to screening effects. The charge neutrality points are found to shift after molecular adsorption, which suggests changes in the nanotube chemical potential or the contact metal work function.

Unraveling the not-so-large trion binding energy in monolayer black phosphorus

Black phosphorus (bP) is a promising two-dimensional (2D) material for opto-electronic applications. Strongly bound excitons with binding energies up to 0.3 eV and remarkably large trion binding energies up to 100 meV have been observed for supported monolayer bP. Surprisingly, this trion binding energy is significantly larger than those found in other 2D materials (e.g. about 30 meV in transition metal dichalcogenides). This has previously been ascribed to the quasi-1D nature of bP. In this work we show, using first principles calculations, that the trion binding energy of bP is indeed large (80 meV) when referenced to the lowest bright exciton but only 30 meV when its energy is measured relative to the lowest dark exciton. Our analysis thus shows that the trion binding energy in bP is not larger than in other 2D materials, and the previous conclusions have to be understood incorporating the large splitting between the dark and bright excitons in bP. We also explore the effect of substrate and in-plane strain of the exciton and trion binding energies and show that these effects do not change the main conclusions. Our results correct the misconception that trion binding energies in monolayer bP are particularly large due to its quasi-1D structure and contribute to the establishment of more a detailed understanding of optical properties of atomically thin semiconductors.

Effect of Phonons on Valley Depolarization in Monolayer WSe2

In this paper, temperature dependence of the excitonic bands in a mechanically exfoliated tungsten diselenide (WSe2) monolayer is studied using photoluminescence and circular dichroic photoluminescence (PL) in the temperature range between 8 and 300 K. The peak energies associated with the neutral exciton (A), charged exciton (trion) and localized excitons are extracted from the PL spectra revealing a trion binding energy of around 30 meV. The circular dichroic PL measured at 8 K shows about 45% valley polarisation that sharply reduces with increasing temperature to 5% at 300 K with photoexcitation energy of 1.96 eV. A detailed analysis of the emission line-width suggests that the rapid decrease of valley polarisation with the increase of temperature is caused by the strong exciton–phonon interactions which efficiently scatter the excitons into different excitonic states that are easily accessible due to the supply of excess photoexcitation energy. The emission line-width broadening with the increase of temperature indicate residual exciton dephasing lifetime < 100 fs, that correlates with the observed rapid valley depolarisation. Circular dichroic photoluminescence spectra in monolayer WSe2 and the influence of temperature on valley depolarization is shown.

Evidence of exciton complexes in non polar ZnO/(Zn,Mg)O A-plane quantum well

Excitons complexes in ZnO/(Zn, Mg)O non-polar quantum well have been studied by using continuous-wave photoluminescence according to temperature and to the density of excitation. The spectrum of photoluminescence of the quantum well consists of three different lines. The ratio between the intensities of these lines depends of the temperature but also of the density of excitation. The lines are attributed to the free exciton, the negatively charged trion and the biexciton. The binding energy of trion and biexciton are found to be respectively 19.5 ± 2 meV and 45 ± 5 meV.