Trion Binding Energy Research Articles

Single- and few-particle states in core-shell nanowire quantum dots

The electronic properties of single and few-particles in core-shell nanowire quantum dots (NWQD) are investigated. By performing configuration interaction (CI) calculations we particularly elucidate how elevated symmetry character (C3v or D2d) exhibited by single particle orbitals enhances the phase coherence of exciton-photon wavefunction though suppressing spin flip processes. Detailed calculations presented here demonstrate how strain-induced potentials manipulate the symmetry characters, intrinsic oscillator strength and electron-hole dipole in NWQDs. An orbital-dependent kinetic energy is defined based on single particle dispersion and orbital spreadout in k-space. It is shown the exchange occurring between this kinetic energy and strain-induced potentials is responsible for orbital distortions, and thus the energy reordering of different direct and correlation terms. Various structures have been examined to elaborate on the influence of size and orientation together with axial and lateral symmetry of NWQDs. Our many-body calculations suggest that binding energies of s-shell few particle resonances XX0 and trions are suppressed when axial and lateral localizations become comparable. Then exerting an external perturbation may renormalize the binding energies, realizing a transition from anti-binding to binding regime or reverse. In this regard, we specifically show that kinetic energy of single particles, and thus correlation energies of associated complexes, exposed to an electric field remain relatively unaffected and the interplay between direct Coulomb terms reorders the multiexcitonic resonances. Sub-micro-eV fine structure splitting along with the tunable XX0 binding energy offers NWQDs promising for generating entangled photons in both regular and time reordering schemes.

Observation of Negative and Positive Trions in the Electrochemically Carrier-Doped Single-Walled Carbon Nanotubes

Understanding of electronic and optical features of single-walled carbon nanotubes (SWNTs) has been a central issue in science and nanotechnology of carbon nanotubes. We describe the detection of both the positive trion (positively charged exciton) and negative trion (negatively charged exciton) as a three-particle bound state in the SWNTs at room temperature by an in situ photoluminescence spectroelectrochemistry method for an isolated SWNT film cast on an ITO electrode. The electrochemical hole and electron dopings enable us to detect such trions on the SWNTs. The large energy difference between the singlet bright exciton and the negative and positive trions showing a tube diameter dependence is determined by both the exchange splitting energy and the trion binding energy. In contrast to conventional compound semiconductors, on the SWNTs, the negative trion has almost the same binding energy to the positive trion, which is attributed to nearly identical effective masses of the holes and electrons.

Binding energy of localized trions in quantum wires

We present a finite difference calculation of the binding energies of localized trions in quasi-one-dimensional quantum wires (QWRs). It is found that both the lateral confinement and the localization potential have a strong effect on the relative stability of the trions. It is confirmed that a weak localization potential not only enhances the binding energy but also changes the relative stability of the positive and negative trions. Our theoretical model is in good accord with a recent experiment regarding photoluminescence in disordered QWRs.

Trions in semiconducting single-walled carbon nanotubes

We study trions (charged excitons), a complex of an electron-hole pair and an additional electron or hole, in semiconducting single-walled carbon nanotubes (s-SWCNT), by means of the exact diagonalization of the realistic Hamiltonian based on the $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ scheme and on the screened Hartree-Fock approximation. By comparing different classes of models that partially or fully include the band nonparabolicity, the form factors in the density operators, the screening effects on interaction, and the self-energy correction in the energy bands, we succeed in capturing the essential features of s-SWCNT. It turns out that the trion binding energy is significantly suppressed by the form factor as well as by the screening effect. Further, an unconventional feature of s-SWCNT is found: the trion has a larger binding energy than the biexciton, since the biexcitons are more strongly affected by screening than trions. We also consider the effects of the short-range part of the Coulomb interaction, and clarify the fine structures in the trion energy levels. It is shown that the bright (optically allowed) trion with the lowest energy can be interpreted as a bound state of a dark (optically forbidden) exciton and an extra electron or hole.

All-Optical Trion Generation in Single-Walled Carbon Nanotubes

We present evidence of all-optical trion generation and emission in pristine single-walled carbon nanotubes (SWCNTs). Luminescence spectra, recorded on individual SWCNTs over a large cw excitation intensity range, show trion emission peaks redshifted 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.

Variational quantum Monte Carlo study of charged excitons in fractional dimensional space

In this article we study excitons and trions in fractional dimensional spaces using the model suggested by C. Palmer [J. Phys. A: Math. Gen. 37, 6987 (2004)] through variational quantum Monte Carlo. We present a direct approach for estimating the exciton binding energy and discuss the von Neumann rejection- and Metropolis sampling methods. A simple variational estimate of trions is presented which shows good agreement with previous calculations done within the fractional dimensional model presented by D. R. Herrick and F. H. Stillinger [Phys. Rev. A 11, 42 (1975) and J. Math. Phys. 18, 1224 (1977)]. We explain the spatial physics of the positive and negative trions by investigating angular and inter-atomic distances. We then examine the wave function and explain the differences between the positive and negative trions with heavy holes. As applications of the fractional dimensional model we study three systems: First we apply the model to estimate the energy of the hydrogen molecular ion H${}_{2}^{+}$. Then we estimate trion binding energies in GaAs-based quantum wells and we demonstrate a good agreement with other theoretical work as well as experimentally observed binding energies. Finally, we apply the results to carbon nanotubes. We find good agreement with recently observed binding energies of the positively charged trion.

Influence of electron density and trion formation on the phase-coherent photorefractive effect in ZnSe quantum wells

We investigate the influence of electron density and trion formation on the phase-coherent photorefractive effect in ZnSe single quantum wells by laser energy and temperature dependent degenerate four-wave-mixing experiments using 90-fs pulses. Two different structures with the same quantum well width and confinement energy but different barriers adjacent to the GaAs substrate are studied in order to compare the formation of a photorefractive electron density grating at specific excitation conditions. At temperatures below 35 K and laser excitation energy close to the exciton energy the formation of trions significantly suppresses the generation of an electron density grating. At lower excitation energies increasing space-charge fields reduce the trion binding energy which leads to an enhanced thermal ionization of trions resulting in a strong phase-coherent photorefractive effect. Due to the thermal dissociation of trions at temperatures exceeding 45 K a significant photorefractive effect exists even at exciton resonant excitation. The experimentally observed signal traces obtained at different excitation conditions are in good agreement with model calculations that are based on the optical Bloch equations, including inhomogeneous broadening at strong space-charge fields.

Dimensional and correlation effects of charged excitons in low-dimensional semiconductors

In this paper, we investigate the existence of bound trion states in fractional dimensional nanostructures, in terms of variational calculus. We start with trial states, then we refine the result with the help of the Hartree–Fock approximation and finally we use a partial basis expansion. We show that Hartree–Fock significantly underestimates the trion binding energy and that the correlation energy is comparable with the trion binding energy. Furthermore we calculate the binding energies of positive and negative trions restricted to a large subspace of functions, which we expect to span the low-lying eigenstates of the full Hamiltonian. We find that the difference between the positive and negative trion binding energies varies very little for the electron–hole mass fractions me/mh = σ ∊ [0.8; 1.0] and that the difference between the positive and negative trion energies grows as the dimension decreases. Finally, we compare a cylindrical effective-mass model of a typical carbon nanotube, with a fractional dimensional model with D = 1.71. We find very good agreement between the trion binding energies predicted by the two models.

Energy renormalization of exciton complexes in GaAs quantum dots

Using GaAs/AlGaAs self-assembled quantum dots we study the few-particle dynamics of fully confined systems, which is associated with purely Coulomb interaction and is not affected by the internal strain field. Systematic evolution in the binding energies of positive and negative trions, as well as biexcitons, with dot size is interpreted in terms of a balance between the Hartree mean-field corrections on single-particle states and the interparticle correlations which lead to a nonseparable dynamics. The experimental behaviors are well reproduced by exact many-body calculations within the framework of the quantum Monte Carlo approach.

Correlation and dimensional effects of trions in carbon nanotubes

We study the binding energies of singlet trions, i.e. charged excitons, in carbon nanotubes. The problem is modeled, through the effective-mass model, as a three-particle complex on the surface of a cylinder, which we investigate using both one- and two-dimensional expansions of the wave function. The effects of dimensionality and correlation are studied in detail. We find that the Hartree-Fock approximation significantly underestimates the trion binding energy. Combined with band structures calculated using a non-orthogonal nearest neighbour tight binding model, the results from the cylinder model are used to compute physical binding energies for a wide selection of carbon nanotubes. In addition, the dependence on dielectric screening is examined. Our findings indicate that trions are detectable at room temperature in carbon nanotubes with radius below 8{\AA}.

EFFECTS OF IONIZED IMPURITIES ON BINDING AND RECOMBINATION OF POSITIVE AND NEGATIVE QUASI-TWO-DIMENSIONAL MAGNETO-TRIONS

Binding energies of negative and positive trions in high magnetic fields are compared. Simultaneous inclusion of several Landau levels and quantum well subbands in exact numerical diagonalization allowed quantitative description of the coupling between in-plane dynamics (governed by interplay of cyclotron quantization and Coulomb interactions) and single-particle excitations in the normal direction. Symmetric and asymmetric GaAs quantum wells of different widths were considered, as well as the effect of a possible binding of trions by sparse ionized impurities nearby the quantum well.

The binding energy of excitons and X + and X − trions in one-dimensional systems

The exciton and trion states in semiconductor quantum wires are treated by the variational method. Simple trial functions provide an adequate precision of the calculation over a wide region of wire radii, with an arbitrary relation between the effective masses of charge carriers. The precision of the results obtained by the variational method is checked by numerical diagonalization of the Hamiltonian of excitons and positively and negatively charged trions. The asymptotic behavior of the binding energies of excitons and trions in narrow quantum wires is established in the analytical form. The structure of the excited X+ trion states is analyzed in the context of the adiabatic approximation.

Influence of the shape and size of a quantum wire on the trion binding energy

The binding energy for charged excitons (${X}^{\ensuremath{-}}$ and ${X}^{+}$) is calculated within the single-band effective mass approximation including effects due to strain for rectangular, triangular, and V-shaped quantum wires. Both ${X}^{\ensuremath{-}}$ and ${X}^{+}$ are found to be bound in rectangular $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ quantum wires and V-shaped $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_{0.32}{\mathrm{Ga}}_{0.68}\mathrm{As}$ quantum wires. We found an appreciable dependence of the trion binding energy on the size and shape of the quantum wire. We compare with available experimental data.

Binding energies of 2D laterally confined trions

The localization of two-dimensional (2D) trions on the attractive potential of the arbitrary shape and strength is studied theoretically. We suggest a general method for the construction of a simple and descriptive trial function suitable for the calculation of the ground state binding energy for electron–hole complexes. The limiting cases corresponding to different relations between characteristic parameters are analyzed. Binding energy of the 2D trions, localized on parabolic potential, is calculated in a wide range of values of its parameters.

Magneto‐optics of modulation doped quantum wells based on II–VI semiconductor compounds

AbstractWe review on optical studies of exciton‐electron interaction in modulation doped quantum wells (QWs) based on ZnSe and CdTe semiconductor compounds. The optical properties of QWs containing diluted two‐dimensional electron gases (2DEGs) are well described in terms of charged excitons (trions). Their parameters such as oscillator strength, binding energy, and fine structure are considered in details. In case of moderate densities of 2DEGs, when the Fermi energy falls between the trion and exciton binding energies, the optical properties can be understood in terms of combined exciton‐electron excitations. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Trions in cylindrical nanowires with a dielectric mismatch

We investigated the lowest energy levels of trions (charged excitons) in freestanding nanowires with strong lateral carrier confinement. Within the adiabatic approximation, the three-particle problem reduces to an effective two-dimensional Schr\"odinger equation for the relative motion which is solved numerically. Dielectric mismatch effects are taken into account, which results in a distorted Coulomb interaction between the charged particles. We obtain the ``bright'' singlet and triplet trion binding energies and we found that the negatively charged exciton is always less stable than the positively charged exciton in a wire with a hole to electron mass ratio $\ensuremath{\sigma}>1$. The pair correlation functions and the conditional probabilities are calculated, which visualizes the correlation between the particles in the wire.

Experimental and Theoretical Studies of Free and Acceptor-Bound Positive Magneto-Trions

By combination of polarization-resolved photoluminescence, transport, and realistic numerics we study energy and recombination spectra of free and acceptor-bound positive trions in a quasi-two-dimensional hole gas. The singlet–triplet crossing in the trion ground state is found at B ≈ 12 T, and a slight reduction of all trion binding energies coincident with the formation of a Laughlin hole fluid is observed at B ≈ 14.2 T.

Exact-diagonalization studies of trion energy spectra in high magnetic fields

Binding energies of negative and positive trions in doped GaAs quantum wells in high magnetic fields are studied by exact numerical diagonalization in spherical geometry. Compared to earlier calculations, finite width of the quantum well and its asymmetry caused by one-sided doping are both fully taken into account by using self-consistent subband wave functions in the integration of Coulomb matrix elements, and by inclusion of higher subbands along with several Landau levels in the Hilbert space. Detailed analysis of the accuracy and convergence of the exact diagonalization scheme is presented, including dependence on Landau level and subband mixing, sensitivity to the (not well known) single-particle spectrum in the valence band, and the estimate of finite-size errors. The main results are the exciton dispersion and trion binding energy spectrum calculated as a function of the magnetic field, quantum well width, electron concentration, and the presence of an ionized impurity. As a complementary approach, a combination of the exact diagonalization in the quantum well plane and the variational calculation in the normal direction is used as well.

Optical properties ofCd1−xMnxTequantum wells across the Mott transition: An interband spectroscopy study

The evolution with carrier density of photoluminescence and photoluminescence excitation spectra is studied at zero magnetic field and at low temperatures in $n$-type modulation doped CdMnTe quantum well structures containing free electrons with densities, ${n}_{e}$, ranging between $1\ifmmode\times\else\texttimes\fi{}{10}^{10}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ and $5.9\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. The excitonic phenomena observed at lower concentrations are screened by the carrier presence at higher electron concentrations leading to optical properties determined by phase-space filling. The experimental data show that band-to-band transitions become active when the band-gap renormalization is larger than the exciton plus trion binding energy. For our particular system, the transition between the insulating and metallic regime is overcome when ${n}_{e}>2\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. However, specific features related to excitonic transitions still persist beyond the Mott transition in the emission and absorption spectra for electron concentrations as high as $5.9\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$.

Binding energy of negative trions in a CdTe quantum well at high magnetic fields

We present the results of numerical calculations of electronic states of an exciton (X) and of a trion (X−) in a CdTe quantum well for magnetic fields B up to 150T. Using variational method we estimate the binding energy of the free X− in the singlet state (z component of angular momentum Lz=0), as well the binding energy of the free X− in the triplet state (Lz=−ℏ). Recent experiments have shown that even up to B=44T the binding energy of the negative trion in a singlet state is greater than in the triplet state. We show, however, that the binding energies of these two states should cross one another at very high magnetic fields. Specifically, using material parameters typical for these experiments, we show that the crossing of these levels will take place at field Bc≈65T. The binding energy of free X− in the triplet state exceeding that of the singlet state for fields B>Bc.