Odd-parity Excitons Research Articles

Biexciton in one-dimensional Mott insulators

Mott insulators sometimes show dramatic changes in their electronic states after photoirradiation, as indicated by photoinduced Mott-insulator-to-metal transition. In the photoexcited states of Mott insulators, electron wave functions are more delocalized than in the ground state, and long-range Coulomb interactions play important roles in charge dynamics. However, their effects are difficult to discriminate experimentally. Here, we show that in a one-dimensional Mott insulator, bis(ethylenedithio)tetrathiafulvalene-difluorotetracyanoquinodimethane (ET-F2TCNQ), long-range Coulomb interactions stabilize not only excitons, doublon-holon bound states, but also biexcitons. By measuring terahertz-electric-field-induced reflectivity changes, we demonstrate that odd- and even-parity excitons are split off from a doublon-holon continuum. Further, spectral changes of reflectivity induced by a resonant excitation of the odd-parity exciton reveals that an exciton-biexciton transition appears just below the exciton-transition peak. Theoretical simulations show that long-range Coulomb interactions over four sites are necessary to stabilize the biexciton. Such information is indispensable for understanding the non-equilibrium dynamics of photoexcited Mott insulators.

Even exciton series in Cu2O

In $\mathrm{Cu_{2}O}$ parity is a good quantum number and thus the exciton spectrum falls into two parts: The dipole-active exciton states of negative parity and odd angular momentum, which can be observed in one-photon absorption ($\Gamma_4^-$ symmetry) and the exciton states of positive parity and even angular momentum, which can be observed in two-photon absorption ($\Gamma_5^+$ symmetry). The unexpected observation of $D$ excitons in two-photon absorption and of $F$ excitons in one-photon absorption has given evidence that the dispersion properties of the $\Gamma_5^+$ orbital valence band is giving rise to a coupling of the yellow and green exciton series. In this paper we show that the even and odd parity exciton system can be consistently described within the same theoretical approach. However, the Hamiltonian of the even parity system needs, in comparison to the odd exciton case, modifications to account for the very small radius of the $1S$ exciton. In the presented treatment we take special care of the central-cell corrections, which comprise a reduced screening of the Coulomb potential at distances comparable to the polaron radius, the exchange interaction being responsible for the exciton splitting into ortho and para states, and the inclusion of terms in the fourth power of $p$ in the kinetic energy. Since the yellow $1S$ exciton state is coupled to all other states of positive parity, we show how the central-cell corrections affect the whole even exciton series. The close resonance of the $1S$ green exciton with states of the yellow exciton series has a strong impact on the energies and oscillator strengths of all implied states. The consistency between theory and experiment with respect to energies and oscillator strengths for the even and odd exciton system in $\mathrm{Cu_{2}O}$ is a convincing proof for the validity of the applied theory.

Multiphoton excited photoconductivity in polyfluorene

We investigate exciton dissociation from even- and odd-parity excited states in poly(9,9 dioctylfluorene) using multiphoton excitation of a photodiode device by femtosecond pulses with tunable photon energies. A transition from cubic to quadratic dependence of the photocurrent on the excitation intensity is observed with increasing photon energy. The cubic dependence is due to a three-photon process consisting of a two-photon absorption followed by further excitation to higher-lying states of weakly bound excitons through absorbing an extra photon. The quadratic dependence corresponds to a direct excitation to higher two-photon states of excitons that are more likely to dissociate into charge carriers. The transition from cubic to quadratic dependence between 2.05 and $2.2\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ establishes the threshold for exciton dissociation from the even-parity states between 4.1 and $4.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The efficient direct dissociation of odd-parity excitons due to single-photon excitation is observed from $4.1\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}5.5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$.

Excitons, polarons, and laser action in poly(p-phenylene vinylene) films

We have used a multitude of linear and nonlinear cw optical spectroscopies to study the optical properties of water precursor poly(p-phenylene vinylene) (PPV) thin films. These spectroscopies include absorption, photoluminescence, photoinduced absorption and their respective optically detected magnetic resonance, and electroabsorption spectroscopy. We have studied singlet and triplet excitons, polarons, and laser action in PPV films. We found that the lowest-lying absorption band is excitonic in origin. It consists of two absorption components due to a bimodal distribution of the polymer chain conjugation lengths. Electroabsorption spectroscopy unambiguously shows the positions of the lowest-lying odd parity exciton 1Bu at 2.59 eV and two of the higher-lying even-parity excitons, namely, mAg at 3.4 eV and kAg at 3.7 eV. From these exciton energies we obtained a lower bound for the exciton binding energy in PPV, Eb(min)=E(mAg)−E(1Bu)=0.8 eV. The quantum efficiency spectrum for triplet exciton photogeneration consists of two contributions; the intersystem crossing and, at higher energies, singlet fission. From the onset of the singlet fission process at ESF=2ET, we could estimate the energy of the lowest-lying triplet exciton, 1 3Bu, at 1.55 eV, with a singlet–triplet splitting as large as 0.9 eV. From photoinduced absorption spectroscopy we measured the triplet–triplet transition, T→T*, to be 1.45 eV. The quantum efficiency spectrum for polaron photogeneration also consists of two contributions: one extrinsic and the other intrinsic. The latter shows a monotonically increasing function of energy with an energy onset at 3.3 eV. The intrinsic photogeneration process is analyzed with a model of free-electron–hole pair photogeneration, which separate more effectively at higher energy. The carrier generation quantum yield at 3.65 eV is estimated to be 0.5%. The quantum efficiency for photoluminescence, on the other hand, shows one single step-function process, with an onset at 2.4 eV. The photoluminescence spectrum is well structured, showing five phonon side bands with 190 meV separation. We have also studied laser action in PPV thin films and microcavities such as microrings and microdisks. The effective gain spectrum is calculated and the estimated threshold excitation intensity for laser action for the 0-1 transition is found to be in good agreement with the data, with an estimated exciton density of 2×1018 cm−3. Lasing from microring devices shows several narrow waveguide modes, with intermode spacing of 0.45 nm that corresponds to an effective mode refractive index, neff=1.45. The spectral width of the laser modes is resolution limited and gives a lower estimate of the cavity quality factor, Q. For microrings we found Q>5000, which is limited by self-absorption in the polymer film.

Theoretical and computational studies of excitons in conjugated polymers

We present a theoretical and computational analysis of excitons in conjugated polymers. We use a tight-binding model of $\ensuremath{\pi}$-conjugated electrons, with $1/r$ interactions for large r. In both the weak-coupling limit (defined by $W\ensuremath{\gg}U)$ and the strong-coupling limit (defined by $W\ensuremath{\ll}U),$ where W is the bandwidth and U is the on-site Coulomb interaction, we derive and analyze effective-particle models. We compare these to density matrix renormalization group (DMRG) calculations, and find good agreement in the extreme limits. We use these analytical results to interpret the DMRG calculations in the intermediate-coupling regime (defined by $W\ensuremath{\sim}U),$ most applicable to conjugated polymers. We make the following conclusions. (1) In the weak-coupling limit the bound states are Mott-Wannier excitons, i.e., conduction-band electrons bound to valence-band holes. Singlet and triplet excitons whose relative wave functions are odd under a reflection of the relative coordinate are degenerate. Thus, the $2{}^{1}{A}_{g}^{+}$ and $1{}^{3}{A}_{g}^{\ensuremath{-}}$ states are degenerate in this limit. (2) In the strong-coupling limit the bound states are Mott-Hubbard excitons, i.e., particles in the upper Hubbard band bound to holes in the lower Hubbard band. These bound states occur in doublets of even and odd parity excitons. Triplet excitons are magnons bound to the singlet excitons, and hence are degenerate with their singlet counterparts. (3) In the intermediate-coupling regime Mott-Wannier excitons are the more appropriate description for large dimerization, while for the undimerized chain Mott-Hubbard excitons are the correct description. For dimerizations relevant to polyacetylene and polydiacetylene both Mott-Hubbard and Mott-Wannier excitons are present. (4) For all coupling strengths an infinite number of bound states exist for $1/r$ interactions for an infinite polymer. As a result of the discreteness of the lattice and the restrictions on the exciton wave functions in one dimension, the progression of states does not follow the Rydberg series. In practice, excitons whose particle-hole separation exceeds the length of the polymer can be considered unbound. (5) The DMRG calculated exciton excitation energies scale as the inverse of the chain length for short chains and the inverse of the square of the chain length for long chains. This fits the effective-particle-in-a-box model.

Multiple pulse transient spectroscopy in luminescent π-conjugated polymers

We closely examined relaxation processes between even and odd parity excitons in poly( p-phenylene vinylene) derivative polymers using a multiple femtosecond pulse transient spectroscopy. By tuning the energy of re-excitation and probe pulses across a wide spectral range, we were able to measure a complete spectrum of the 1B u exciton and also probe its counterparts: higher lying mA g and kA g excitons. Dramatically different relaxation paths were found for two later states: whereas the majority of mA g excitons experience an ultrafast internal conversion back to their 1B u state, most of kA g excitons transform into a non-emissive state, which we attribute to weakly bound polaron pairs.

Reply to “Comment on ‘Odd-parity excitons in semiconductor superlattices’ ”

In his Comment on our work Glutsch raises, on the basis of a calculation for a dimerized three-dimensional superlattice, four points: (1) odd-parity excitons do not contribute to optical absorption, (2) there are no forbidden single-particle transitions, (3) there is a coupling of the $e1$-hh2 exciton (called $\overline{X}$ in Ref. 1) to the underlying $e1$-hh1 continuum that leads to a Fano resonance, and (4) the extension of the exciton wave function is infinite in an all space directions rather than having a small extension. In this Reply these four points are addressed and it is shown that our previous conclusions remain valid.

Comment on “Odd-parity excitons in semiconductor superlattices”

In a recent paper Bott et al. [Phys. Rev. B 56, 12 784 (1997)] predict odd-parity excitons in superlattices, related to forbidden single-particle transitions. These excitons are characterized as Frenkel-type, with small spatial extension, and the interaction with the underlying continuum is described as negligible. In contrast, we show that the described exciton is of even parity, is related to an allowed single-particle transition, and has an infinite spatial extension due to Fano interference.

Effects of film order on the optical properties of α-sexithiophene

The optical properties of ordered and disordered α-sexithiophene (α-6T) thin films are investigated by a variety of spectroscopies. The dominant low-lying even and odd parity excitons are identified by absorption and electroabsorption spectroscopies. Intermolecular interactions in ordered α-6T films results in Davydov splitting of the absorption band of the lowest odd parity exciton. Charged excitations in α-6T films were studied by photoinduced absorption and optically detected magnetic resonance. Both polarons and bipolarons are observed in disordered samples. As a consequence of higher carrier mobilities, only bipolarons were observed in ordered samples. Spin pairing of excitations broadens the observed ODMR spectra.

Electroabsorption spectroscopy of luminescent and nonluminescent π-conjugated polymers

We have measured the quadratic electroabsorption (EA) spectrum of a variety of soluble luminescent and nonluminescent \ensuremath{\pi}-conjugated polymer films in the spectral range of 1.5--4.5 eV. The luminescent polymers include MEH and DOO derivatives of poly(phenylene-vinylene), poly(phenylene ethylene), and polythiophene; the nonluminescent polymers include poly(diethynyl silane) and monosubstituted polyacetylene. All EA spectra show a Stark shift of the low-lying odd-parity exciton ${(1B}_{u})$ and imply the presence of phonon sidebands. There are also higher-energy bands due to transfer of oscillator strength to even-parity exciton states ${(A}_{g}),$ the strongest of which ${(mA}_{g})$ is located at an energy about 1.3 times that of the ${1B}_{u}$ exciton in both luminescent and nonluminescent polymers; in the luminescent polymers the EA spectra also show a second prominent ${A}_{g}$ state ${(kA}_{g})$ at an energy of about 1.6 times that of the ${1B}_{u}.$ We have successfully fitted the EA spectra by calculating the imaginary part of the third order optical susceptibility, $\mathrm{Im}[{\ensuremath{\chi}}^{3}(\ensuremath{-}\ensuremath{\omega};\ensuremath{\omega},0,0)],$ using a summation over states model dominated by the ground state, the ${1B}_{u}$ exciton, two strongly coupled ${A}_{g}$ states (${\mathrm{mA}}_{g}$ and ${\mathrm{kA}}_{g}$), and their most strongly coupled vibrations, using Frank-Condon overlap integrals. A distribution of conjugation lengths, which results in a distribution of excited state energies, was also incorporated into the model. The decomposition of the EA spectra due to the conjugation length distribution was then used to calculate the ${1B}_{u}$ exciton polarizability $(\ensuremath{\Delta}p)$ using first derivative analysis. For the longest conjugation lengths in our films, we found $\ensuremath{\Delta}p$ to be of order ${10}^{4}(\mathrm{\AA{}}{)}^{3}$ in luminescent polymers and ${10}^{3}{\mathrm{\AA{}}}^{3}$ in nonluminescent polymers, respectively, in good agreement with recent subnanosecond transient photoconductivity measurements. We also found that the Huang-Rhys parameter of the ${1B}_{u}$ exciton varies between 0.25 and 0.9, being in general smaller for the luminescent polymers. The consequent exciton relaxation energies were calculated to be of order 100 meV.

Odd-parity excitons in semiconductor superlattices

Optical spectra of semiconductor superlattices with alternating well widths are computed microscopically. Odd-parity Frenkel-type excitons are predicted that are related to dipole forbidden single-particle transitions between parallel bands.

The nonlinear optical susceptibilities of polydiacetylenes

We present a general formalism of the NLO susceptibilities by using the Genkin-Mednis approach for a one-dimensional electron-lattice system. Based on the SSH model, we obtained an analytic expression for the third-order nonlinear optical susceptibilities χ (3)( ω) for polydiacetylenes (PDAs) after considering the case of conjugated chains, in which there is no adjustable parameter. The results are in good agreement with experiments on PDAs. Furthermore, the origin of the second peak in the χ (3)( ω) spectrum of PDAs is discussed, and a transition mechanism is proposed. It is believed that when the external light field is applied along the centrosymmetric polymer backbone, the parity symmetry of the system is broken, there occurs a mixing between the even- and odd-parity exciton states, leading to the transition from the ground state to the A g excited state, and accordingly a second sharp peak appears in the χ (3)( ω) spectrum which could be attributed to the three-photon resonance with the A g exciton generation process at around 2.2 eV.

Optical studies of electronic states and coupled vibrations in substituted polyacetylene

The electronic states and coupled vibrations in films of substituted polyacetylene (poly( o-trimethylsilylphenylacetylene); PTMSiPA) have been studied using the techniques of resonant Raman scattering (RRS) and electroabsorption (EA) spectroscopies. Strong RRS frequency dispersion has been observed for the C--C and C=C stretching vibrations with excitation photon energy from 1.55 to 3.42 eV, which is similar to that of other nonluminescent conducting polymers such as trans-polyacetylene, polydiacetylene and polydiethynylsilane. The RRS dispersion has been analyzed by means of the amplitude mode formalism placing the energy of the first allowed odd-parity exciton E(1Bu) of the longest chains at 1.85 eV. The rather weak EA spectrum is mainly composed of Stark shift of an energy distribution of 1Bu exciton and a positive contribution centered at 2.6 eV due to an even-parity exciton (mAg).

Stark profiles of singlet excitons in conjugated polymers

Abstract Electroabsorption (EA) spectra associated with overlapping vibronics of even- and odd-parity excitons are related in the Condon approximation to the linear absorption of discrete localized states. The EA intensity and profile depend strongly on the linewidth, Λ, with Λ −2 scaling of features due to Stark shifts and Λ −1 scaling of induced absorption and bleaching. Static disorder in polymer films broadens the linear absorption and reduces EA intensity compared to polydiacetylene (PDA) crystals, whose resolved spectra indicate overlapping vibrational sidebands. Similar excitations and transition moments in films conspicuously alter EA profiles and allow estimates of symmetry-breaking perturbations. EA spectra of PDA crystals and films are consistent with Pariser-Parr-Pople theory of linear and nonlinear optical spectra. The high sensitivity of EA also provides direct tests of excited-state displacements at induced transitions of even-parity excitons.

Even-parity excitons in condensed xenon.

Excitation spectra of two-photon excited solid xenon have been obtained in the energy range of 8.4 to 11.1 eV. The measurements were performed at temperatures from 160 to 100 K. The even-parity {Gamma}(3/2) {ital n}=2, 3, and 4 Wannier excitons are observed in solid xenon. The {ital n}=2 and 3 excitons are shifted to higher energies relative to the energy of the corresponding odd-parity excitons by approximately 80 and 50 meV, respectively. In addition, the excitation spectrum revealed a previously unobserved series of excitons between 10.7 and 11 eV. These excitons form a Rydberg series and are possibly assignable as excitons at the {ital X} point of the Brillouin zone. The absorption linewidths (full width at half maximum) of the 2{ital p}, 3{ital p}, and 4{ital p} excitons are measured to be approximately 80, 52, and 22 meV, respectively. Several models are investigated in an attempt to explain the shift in energy between the {ital s} and {ital p} excitons in liquid and solid xenon. {copyright} {ital 1996 The American Physical Society.}

Two-photon absorption in liquid xenon.

Excitation spectra of two-photon excited xenon near the triple point have been obtained in order to study exciton structure near the band edge. While the band gap is suppressed in the low-temperature liquid, absorption due to even-parity exciton states is presented and discussed. The even-parity ${\mathrm{\ensuremath{\Gamma}}}_{3/2}$,n=2 Wannier excitons observed in the liquid are shifted approximately 0.12 eV to higher energies relative to the energy of odd-parity excitons observed in the liquid by Beaglehole. The absorption linewidths (full width at half maximum) are measured to be 0.15 eV. Comparisons are made to one-photon absorption spectra in xenon.

Perturbation of the nonlinear optical response of a conjugated polymer by an adsorbate-induced electronic state

The coupling between ground state vibrations and excited electronic states in the polydiacetylene PTS has been investigated using stimulated inverse Raman scattering. Both Raman resonances and optical Stark effects have been measured and the interference between them has been used to determine several exciton—phonon coupling constants. An unexpected narrow (7.5 meV half-width) electronic features at ≈ 2.23 eV in PTS is observed. An even parity exciton in this spectral region has been postulated before by others. Our work demonstrates that this new electronic feature is resident on the polymer backbone, the same as the odd-parity exciton. This new feature must also possess some odd-parity character. The cause of this odd-parity contribution is likely a complex between molecular oxygen and the diacetylenic backbone.

Microscopic Theory of Far-Infrared Two-Magnon Absorption in Antiferromagnets. I. Perturbation-Theory Search and Application of Fourth-Order Process to FeF2

A microscopic description of the mechanism responsible for an absorption line observed in antiferromagnetic Fe${\mathrm{F}}_{2}$ at 154 ${\mathrm{cm}}^{\ensuremath{-}1}$ is proposed. The mechanism appears to account for the properties of the observed line which are described in the preceding paper. In isolating the proposed mechanism, we set up a model which includes magnon, phonon, exciton, and photon fields and their interactions. The mechanism involves an indirect coupling between odd-parity excitons and magnons which we have previously called the odd-exciton-magnon interaction. This coupling is a consequence of the combined action of the spin-orbit interaction and the quadrupole-dipole part of the spin-orbit interaction. A search through fourth order in perturbation theory in this model yields several other possible processes. Our estimates indicate that the process we propose is the largest contributor in Fe${\mathrm{F}}_{2}$ and that a third process, involving a phonon, may be contributing to the absorption intensity. The proposed process is used to derive the spin Hamiltonian used in the preceding paper and to estimate the intensity and polarization ratio.