Correlation and dimensional effects of trions in carbon nanotubes

Rønnow, Troels F.; Pedersen, Thomas Garm; Cornean, Horia D.

doi:10.1103/physrevb.81.205446

Cited by 38 publications

(56 citation statements)

References 32 publications

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“…2), suggesting E contains a contribution from the singlet-triplet exciton splitting in addition to the trion binding energy. The fitted trion binding energy constant, A=85 meV.nm, is consistent with a dielectric constant of 2.2 according to reference [13], close to that experienced by nanotubes in our experiment. The fitted exchange interaction constant, B=48 meV.nm², is in agreement with the theoretical value [23].…”

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confidence: 90%

“…In contrast to Matsunaga et al, however, no chemical doping is involved in our study, the carriers being photo-generated. Trion binding energy in SWCNTs is predicted to scale as 1/d, (d being the tube diameter) and to range, for (6,5) nanotubes, between 50 meV and 132 meV depending on dielectric screening, =4 and =2, respectively [13]. However, E~190 meV measured here for (6,5) nanotubes is found to be significantly larger than the predicted range of E assuming reasonable values of  for surfactantwrapped SWCNTs in aqueous environments.…”

mentioning

confidence: 50%

“…Theorists have predicted biexcitons to have a binding energy larger than the thermal energy k B T [10,11]. No experimental evidence for these bound states has been reported so far, however, in agreement with recent theoretical studies [12].Charged excitons, or trions, are another class of many-body bound states predicted to possess a significant binding energy in SWCNTs [13]. Very recently, Matsunaga et al[14] observed new spectral features in p-doped nanotube suspensions, which have been assigned to hole-exciton bound states (positively charged trions).…”

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confidence: 68%

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All-Optical Trion Generation in Single-Walled Carbon Nanotubes

et al. 2011

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We present evidence of all optical trion generation and emission in undoped single walled carbon nanotubes (SWCNTs). Luminescence spectra, recorded on individual SWCNTs over a large CW excitation intensity range, show trion emission peaks red-shifted with respect to the bright exciton peak. Clear chirality dependence is observed for 22 separate SWCNT species, allowing for determination of electron-hole exchange interaction and trion binding energy contributions.Luminescence data together with ultrafast pump probe experiments on chirality sorted bulk samples suggest that exciton-exciton annihilation processes generate dissociated carriers that allow for trion creation upon a subsequent photon absorption event.It is well established that the optical properties of semiconducting single walled carbon nanotubes (SWCNTs) are dominated by tightly bound one-dimensional excitons [1,2]. The recombination of these excitons results in narrow emission peaks. As it dominates the luminescence spectra, the lowest lying optically active exciton in SWCNTs has attracted much experimental and theoretical attention over the past decade [3]. Since SWCNTs consist only of surface atoms, exciton dynamics, and hence nanotube luminescence intensity, are extremely sensitive to the local environment and the presence of quenching sites or structural defects [4,5]. Such extrinsic effects are thought to be responsible for the fairly short luminescence lifetimes (100 ps or less [4,6]) and low luminescence quantum yields (of a few percent) reported for individual SWCNTs in the low excitation intensity regime [6,7].For sufficiently strong CW or pulsed excitation intensities multiple excitons are likely to exist simultaneously. In this regime, nanotube photophysics is governed by the interplay between onedimensional exciton diffusion along the nanotube sidewall [5] and strong coulomb interactions between carriers. When two or more excitons are present, their interaction can lead to two different situations. On one hand, they can undergo Auger processes such as exciton-exciton annihilation (EEA) which open-up additional, efficient nonradiative recombination pathways. Experimental evidence for this has been reported by several groups using ultrafast spectroscopy on ensemble samples [8,9 ]. On the other hand, excitons may form many-body bound states. Theorists have predicted biexcitons to have a binding energy larger than the thermal energy k B T [10,11]. No experimental evidence for these bound states has been reported so far, however, in agreement with recent theoretical studies [12].Charged excitons, or trions, are another class of many-body bound states predicted to possess a significant binding energy in SWCNTs [13]. Very recently, Matsunaga et al.[14] observed new spectral features in p-doped nanotube suspensions, which have been assigned to hole-exciton bound states (positively charged trions).Here we show that trions can be efficiently generated, on demand and in-situ, in highly luminescent undoped carbon nanotubes through control of photo-e...

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All-Optical Trion Generation in Single-Walled Carbon Nanotubes

et al. 2011

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“…Linear optical spectroscopy has revealed the richness of the exciton manifold. 5,6 For sufficiently high excitation rates, many-body bound states such as biexcitons [7][8][9][10] (XX) or charged excitons 11,12 (trions, X * ) should form. Because of the strong Coulomb interaction between photogenerated charge carriers, such SWNT states have been predicted to have significant binding energies in the 60-to 250-meV range for biexcitons.…”

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confidence: 99%

Biexciton, single carrier, and trion generation dynamics in single-walled carbon nanotubes

et al. 2013

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We present a study of free carrier photogeneration and multicarrier bound states, such as biexcitons and trions (charged excitons), in semiconducting single-walled carbon nanotubes. Pump-and-probe measurements performed with fs pulses reveal the effects of strong Coulomb interactions between carriers on their dynamics. Biexciton formation by optical transition from exciton population results in an induced absorption line (binding energy 130 meV). Exciton-exciton annihilation process is shown to evolve at high densities towards an Auger process that can expel carriers from nanotubes. The remaining carriers give rise to an induced absorption due to trion formation (binding energy 190 meV). These features show the dynamics of exciton and free carriers populations.

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“…see Ref. [7]). Studying bigger bound complexes, for example bi-exciton pairs, is the next logical step.…”

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Few-Particle Green’s Functions for Strongly Correlated Systems on Infinite Lattices

Berciu

2011

Phys. Rev. Lett.

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We show how few-particle Green's functions can be calculated efficiently for models with nearestneighbor hopping, for infinite lattices in any dimension. As an example, for one dimensional spinless fermions with both nearest-neighbor and second nearest-neighbor interactions, we investigate the ground states for up to 5 fermions. This allows us not only to find the stability region of various bound complexes, but also to infer the phase diagram at small but finite concentrations.PACS numbers: 71.10. Li, 31.15.ac, 71.35.Pq Recently, there has been considerable interest in fewparticle solutions of interacting Hamiltonians. For example, in Ref. [1] it was shown that knowledge of the twoand three-body solutions allows for quantitatively accurate predictions of finite-temperature thermodynamic quantities for many-body systems. As another example, in the context of atomic and molecular physics, the predicted universal three-body Efimov structures [2] have now been seen experimentally [3], giving new impetus to their study and work on various generalizations [4].While the above work is for free space where particles have parabolic dispersions, there is equally strong interest in the lattice version of such few-body problems. For example, while stable excitons -bound pairs comprised of an electron and a hole -appear in many materials, it is less clear when a so-called charged exciton or trion, consisting of two holes and one electron or viceversa, is stable. That this can happen has been recently demonstrated in GaAs quantum wells [5] and in carbon nanotubes [6]. (Note that trion theory is still mostly based on continuous models and variational solutions, e.g. see Ref. [7]). Studying bigger bound complexes, for example bi-exciton pairs, is the next logical step.Few-particle bound states are relevant not only for the materials where they appear, but also in the interpretation of certain spectroscopic data. For instance, the role played by bound two-particle states, leading to atomic-like multiplet structures in the Auger spectra of narrow-band insulating oxides, is well established [8]. At low dopings, more complicated complexes may form and leave their fingerprints in various spectroscopic features. It is therefore useful to be able to study relatively easily few-particle solutions on an infinite lattice.In this Letter we show that few-particle Green's functions can be calculated efficiently for strongly correlated lattice Hamiltonians in the thermodynamic limit, at least so long as the hopping involves only nearest neighbor sites. For simplicity and to illustrate the technique and its usefulness, we focus here on a one-dimensional (1D) model of spinless fermions with nearest-neighbor (nn) and next-nearest-neighbor (nnn) interactions. However, the method generalizes straightforwardly to higher dimensions, longer (but finite) range interactions, mixtures of fermions (including spinful fermions) and/or bosons, etc. Such problems are of direct interest either in solid state physics, or for cold atoms in optical lattic...

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Correlation and dimensional effects of trions in carbon nanotubes

Cited by 38 publications

References 32 publications

All-Optical Trion Generation in Single-Walled Carbon Nanotubes

All-Optical Trion Generation in Single-Walled Carbon Nanotubes

Biexciton, single carrier, and trion generation dynamics in single-walled carbon nanotubes

Few-Particle Green’s Functions for Strongly Correlated Systems on Infinite Lattices

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