Even-parity Excitons Research Articles

Terahertz radiation by quantum interference of excitons in a one-dimensional Mott insulator

Nearly monocyclic terahertz waves are used for investigating elementary excitations and for controlling electronic states in solids. They are usually generated via second-order optical nonlinearity by injecting a femtosecond laser pulse into a nonlinear optical crystal. In this framework, however, it is difficult to control phase and frequency of terahertz waves. Here, we show that in a one-dimensional Mott insulator of a nickel-bromine chain compound a terahertz wave is generated with high efficiency via strong electron modulations due to quantum interference between odd-parity and even-parity excitons produced by two-color femtosecond pulses. Using this method, one can control all of the phase, frequency, and amplitude of terahertz waves by adjusting the creation-time difference of two excitons with attosecond accuracy. This approach enables to evaluate the phase-relaxation time of excitons under strong electron correlations in Mott insulators. Moreover, phase- and frequency-controlled terahertz pulses are beneficial for coherent electronic-state controls with nearly monocyclic terahertz waves.

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.

Doublon-holon pairing mechanism via exchange interaction in two-dimensional cuprate Mott insulators.

Coupling of charge and spin degrees of freedom is a critical feature of correlated electron oxides, as represented by the spin-related mechanism of a Cooper pair under high-T c superconductivity. A doublon-holon pair generated on an antiferromagnetic spin background is also predicted to attract each other via the spin-spin interaction J, similar to a Cooper pair, while its evidence is difficult to obtain experimentally. Here, we investigate such an excitonic effect by electroreflectance spectroscopy using terahertz electric field pulses in undoped cuprates: Nd2CuO4, Sr2CuO2Cl2, and La2CuO4. Analyses of the spectral changes of reflectivity under electric fields reveal that the splitting of odd-parity and even-parity excitons, a measure of doublon-holon binding energy, increases with J. This trend is reproduced by t-J-type model calculations, providing strong evidence of the spin-related doublon-holon pairing. Agreement with the calculations supports the s-wave symmetry of the doublon-holon pair in contrast to the d-wave Cooper pair in doped cuprates.

Short-living excited states in pristine and C 60-doped disubstituted polyacetylene

We study the primary photoexcitations in pristine and C 60-doped doubly phenyl-substituted polyacetylene films using femtosecond pump–probe spectroscopy. We show that the ultrafast relaxation occurs via branching between two different relaxation pathways. In pristine films mobile emissive odd-parity (1B u) excitons radiatively recombine in the ionic relaxation channel. In C 60-doped films 1B u excitons dissociate and give rise to polarons on 10-ps time scale. Non-emissive even-parity excitons, which are primary excitations in the covalent relaxation channel, give rise to immobile topological solitons. The dynamics of photoexcitations in covalent channel are almost unaffected by C 60 doping.

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.

Low lying optically excited states of conjugated polymers with DMRG

We present the results of a density matrix renormalization group (DMRG) study which reveals the nonlinear optical properties of long chain systems within the extended Hubbard model. We use a combination of the infinite and finite system DMRG methods to calculate the dipole couplings between eigenstates, and are thus able to target the “essential” states which dominate the nonlinear optical response of these materials. Specifically we investigate the 1 B u optical exciton, the mA g (a higher energy even-parity exciton) and the nB u, which has previously been identified as the threshold of the electron-hole continuum.

Frenkel and charge transfer states of conjugated polymers and molecules

Neutral excitations of conjugated polymers resemble molecular π-π ∗ spectra or Frenkel excitons in organic molecular crystals, while charge transfer (CT) between strands is related to ion pairs. The relative energies of Frenkel and CT states depend on Coulomb, polarization, and dispersion forces, as well as molecular and lattice relaxation. Polar substituents and redistribution of delocalized charge are molecular contributions that stabilize CT states. Their roles are illustrated by low-energy CT in PTCDA films and by stilbene dimers. Covalent bonding along the polymer backbone requires generalization of molecular exciton theory and generates extended states with different excitation thresholds indicative of Coulomb interactions. Expanded atomic sites are introduced through a second π-electron approximation for D 2h networks whose low-lying state are in an odd manifold. Expanded sites allow systematic comparisons of perylene and pyrene spectra with those of polyenes, indicate an even-parity exciton to be the lowest singlet of polyperinaphthalene, and represent a step towards molecular sites used in ion-radical salts with narrow bands. The energetics of Frenkel and CT states in organic molecular solids are closely related to excitons and polaron pairs in conjugated polymers, whose appropriate frontier orbitals and correlated excitations are currently sought.

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.

Subpicosecond dynamics of excitons and photoexcited intrinsic polarons in the quasi-one-dimensional solid PtCl

Subpicosecond transient absorption (TA) spectroscopy was used to identify excited states, and to measure their relaxation kinetics as a function of excitation wavelength in the halogen-bridged transition-metal $(\mathrm{MX})$ compound PtCl. For pump photon energies ${E}_{\mathrm{pump}}$ between 1.3 and 1.8 eV, below the threshold for exciton formation, intrinsic polarons are photoexcited and decay within 1--3 ps. Excitation into the exciton absorption tail (2.0--2.3 eV) yields singlet excitons that rapidly decay into an even-parity state, which has a lifetime (\ensuremath{\sim}100 ps) varying with the intial photon energy. Excitation (3.1 eV) well above the exciton threshold appears to generate more slowly decaying excitons, as well as polarons that are formed upon exciton dissociation. The TA spectra also indicate that relaxation of excitons for ${E}_{\mathrm{pump}}>2\mathrm{}\mathrm{eV}$ is mediated by large-amplitude vibrations perpendicular to the chains. Using third-harmonic generation spectroscopy in addition to TA, we develop an energy-level diagram for the excited states, including polaron levels, and the lowest odd- and even-parity excitons.

What do nonlinear optical spectroscopy and picosecond photinduced absorption have to say about excited states in conjugated polymers?

We present a self-consistent picture of the excited state energy spectrum of poly(para-phenylene vinylene) based on theoretical calculations of exicted states and and experimental electroabsorption (EA) and picosecond photoinduced absorption measurements (PA). Our calculations place the one electron—one hole continuum ( nB u ) at 0.9 ± 0.2 eV above the 1 B u exciton. This is in agreement with EA and ps PA in the i.r., which finds an even-parity exciton (the mA g ) about 0.7 eV away from the 1 B u . The high energy ps PA at 1.5–1.7 eV is to a biexciton whose energy is consistent with our estimates.

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.

Investigation of exciton fine structure inCu2O

The even-parity excitons in ${\mathrm{Cu}}_{2}$O show, in contrast to the well known $P$-exciton series: (1) strong deviations from a hydrogenlike behavior, (2) a fine structure for $n\ensuremath{\ge}3$, and (3) an unusual $n$ dependence of the exchange splitting. All the properties of the even-parity-exciton series are explained by the presence of a strong ${H}_{d}$ term and a strong exchange interaction. We have calculated the even- and odd-exciton members of the yellow and green series within the formalism of Baldereschi and Lipari. An excellent agreement with the experimental results is obtained in the spherical limit. The theory predicts for $n=3$ a splitting of the $S$ and $D$ states into five components. All the five components are observed by two-photon absorption in a magnetic field of 7 T.

Assignment of the Even-Parity Excitons inCu2O

This Letter presents for the first time a detailed two-photon spectrum of the even-parity excitons of the yellow series in ${\mathrm{Cu}}_{2}$O. Contrary to one-photon data, it is possible to measure directly $S$ and $D$ exciton contributions without applying external perturbations. The two-photon spectrum gives evidence for a strong mixing between the yellow and the green series which is explained by exchange interaction and nondiagonal parts in the effective-mass Hamiltonian.