Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Europhysics Letters (EPL)

Extremely large nonlinear absorption cross-sections in organic polymeric chains

Swapan Kumar Pati

Published Oct 19, 2004• 5 citations
Publisher

Abstract

We have considered one-dimensional organic conjugated polymeric systems to study the two-photon absorption (TPA) processes. The symmetrized density matrix renormalization group (SDMRG) method has been used to compute the low-energy photonic states and the TPA coefficients, for an extended Hubbard model. We find that the TPA coefficients diverge when the ground state of the system changes from the spin-density wave (SDW) state to the charge-density wave (CDW) state. Although in both phases the system is an insulator, the one-photon and two-photon gaps almost become equal near the transition point. The reason for the TPA coefficients to diverge is the near-degeneracy of these photonic states with strong electric dipole couplings at the transition point region. The picosecond scale nonlinear absorption processes observed in charge transfer insulating systems can be explained due to the formation of a triplet band below the lowest optically allowed state, based on our model calculations.

DOI
10.1209/epl/i2004-10208-4

Related papers

Nonlinear Optical Response of SDW Insulators

S. A. Jafari, Takami Tohyama, Sadamichi Maekawa

We calculate the third order nonlinear optical response in the Hubbard model within the spin density wave (SDW) mean field ansatz in which the gap is due to onsite Coulomb repulsion. We obtain closed-form analytical results in one dimension (1D) and two dimension (2D), which show that nonlinear optical response in SDW insulators in 2D is stronger than both 3D and 1D. We also calculate the two photon absorption (TPA) arising from the stress tensor term. We show that in the SDW, the contribution from stress tensor term to the low-energy peak corresponding to two photon absorption becomes identically zero if we consider the gauge invariant current properly.

arXiv:cond-mat/0507556•Journal of the Physical Society of Japan•May 12, 2006•10 citations

Density-matrix renormalization-group study of low-lying excitations of polyacene within a Pariser-Parr-Pople model

C. Raghu, Y. Anusooya Pati, S. Ramasesha

We have carried out symmetrized density-matrix renormalization-group calculations to study the nature of excited states of long polyacene oligomers within a Pariser-Parr-Pople Hamiltonian. We have used the ${C}_{2}$ symmetry, the electron-hole symmetry, and the spin parity of the system in our calculations. We find that there is a crossover in the lowest dipole forbidden two-photon state and the lowest dipole allowed excited state with size of the oligomer. In the long system limit, the two-photon state lies below the lowest dipole allowed excited state. The triplet state lies well below the two-photon state and energetically does not correspond to its description as being made up of two triplets. These results are in agreement with the general trends in linear conjugated polymers. However, unlike in linear polyenes wherein the two-photon state is a localized excitation, we find that in polyacenes, the two-photon excitation is spread out over the system. We have doped the systems with a hole and an electron and have calculated the charge excitation gap. Using the charge gap and the optical gap, we estimate the binding energy of the ${1}^{1}{B}^{\ensuremath{-}}$ exciton to be 2.09 eV. We have also studied doubly doped polyacenes and find that the bipolaron in these systems, to be composed of two separated polarons, as indicated by the calculated charge-density profile and charge-charge correlation function. We have studied bond orders in various states in order to get an idea of the excited state geometry of the system. We find that the ground state, the triplet state, the dipole allowed state, and the polaron excitations correspond to lengthening of the rung bonds in the interior of the oligomer while the two-photon excitation corresponds to the rung bond lengths having two maxima in the system.

Physical review. B, Condensed matter•Jul 29, 2002•63 citations

Excitons and optical absorption in one-dimensional extended Hubbard models with short- and long-range interactions

Frank B. Gallagher, S. Mazumdar

We show that charge excitations within one-dimensional extended Hubbard models in the limit of large on-site Coulomb interaction can be mapped onto pairs of spin reversals from the ferromagnetic Ising-Heisenberg spin Hamiltonian. The exciton in the extended Hubbard models is equivalent to the bound two-magnon state of the spin Hamiltonian. From exact results for the spin Hamiltonian, for the intersite Coulomb interactions limited between nearest neighbors, the lowest optical exciton is separated in energy from the electron-hole continuum only for the intersite interaction larger than half the one-electron bandwidth. The commutation relationship between spin operators allows us to numerically investigate exciton binding energies and optical absorptions from the ground state in the limit of large on-site Coulomb interaction even for cases where analytic results are not available. For intersite Coulomb interaction limited between nearest neighbors, the binding energy of the lowest optical exciton changes very weakly for realistic Peierls bond dimerization, although there is a profound change in the optical absorption. While in the undimerized chain a single optical exciton can occur, two additional excitons that occur above the threshold of the electron-hole continuum become optically visible in the dimerized case. For long-range intersite Coulomb interactions, multiple excitons can occur even for the undimerized chain, and additional exciton states become optically visible upon dimerization. With the $1/r$ form for the intersite Coulomb interaction, our numerical calculations suggest that the formation of at least one optical exciton is unconditional, unlike the case of nearest-neighbor interaction. The binding energy of the lowest optical exciton again depends weakly on the dimerization for long-range interaction. Our theoretical results can explain the occurrence of two charge-transfer absorption bands in half-filled band segregated stack charge transfer solids below the spin-Peierls dimerization temperature. Our results also suggest that the lowest optical state of \ensuremath{\pi}-conjugated polymers, in which Coulomb interactions are long ranged, is necessarily an exciton.

Physical review. B, Condensed matter•Dec 15, 1997•68 citations

Identification of excitons in conjugated polymers: A density-matrix renormalization-group study

Magnus Boman, Robert J. Bursill

This work addresses the question of whether low-lying excitations in conjugated polymers are comprised of free charge carriers or excitons. States are characterized as bound or unbound according to the scaling of the average particle-hole separation with system size. We critically examine other criteria commonly used to characterize states. The polymer is described by an extended Hubbard model with alternating transfer integrals. The model is solved by exact diagonalization and the density-matrix renormalization-group (DMRG) method. We demonstrate that the DMRG accurately determines excitation energies, transition dipole moments and particle-hole separations of a number of dipole-forbidden ${(A}_{g})$ and dipole-allowed ${(B}_{u})$ states. Within a parameter regime considered reasonable for polymers such as polyacetylene, it is found that the charge gap, often used to define the exciton binding energy, is not a good criterion by which to decide whether a state is bound or unbound. The essential nonlinear optical state ${\mathrm{mA}}_{g}$ is found to mark the onset of unbound excitations in the ${A}_{g}$ symmetry sector. In the ${B}_{u}$ symmetry sector, on the other hand, it is found that all low-lying states are unbound and that there is no well-defined ${\mathrm{nB}}_{u}$ state. That is, the ${1B}_{u}$ state marks the onset of unbound excitations in this sector.

arXiv:cond-mat/9802216•Physical review. B, Condensed matter•Jun 15, 1998•25 citations

Optical excitations in a one-dimensional Mott insulator

Eric Jeckelmann

The density-matrix renormalization-group (DMRG) method is used to investigate optical excitations in the Mott insulating phase of a one-dimensional extended Hubbard model. The linear optical conductivity is calculated using the dynamical DMRG method and the nature of the lowest optically excited states is investigated using a symmetrized DMRG approach. The numerical calculations agree perfectly with field-theoretical predictions for a small Mott gap and analytical results for a large Mott gap obtained with a strong-coupling analysis. It is shown that four types of optical excitations exist in this Mott insulator: pairs of unbound charge excitations, excitons, excitonic strings, and charge-density-wave (CDW) droplets. Each type of excitation dominates the low-energy optical spectrum in some region of the interaction parameter space and corresponds to distinct spectral features: a continuum starting at the Mott gap (unbound charge excitations), a single peak or several isolated peaks below the Mott gap (excitons and excitonic strings, respectively), and a continuum below the Mott gap (CDW droplets).

arXiv:cond-mat/0208480•Physical review. B, Condensed matter•Feb 14, 2003•82 citations

External electric field mediated quantum phase transitions in one-dimensional charge-ordered insulators: a density matrix renormalization group study

Sudipta Dutta, Swapan K Pati

We perform density matrix renormalization group calculations extensively on one-dimensional chains with on-site ( U ) as well as nearest-neighbour ( V ) Coulomb repulsions. The calculations are carried out in full parameter space with explicit inclusion of the static bias and we compare the nature of spin-density-wave (SDW) and charge-density-wave (CDW) insulators under the influence of external electric fields. We find that, although the SDW ( U >2 V ) and CDW ( U <2 V ) insulators enter into a conducting state after a certain threshold bias, CDW insulators require much higher bias than the SDW insulators for insulator–metal transitions at zero temperature. We also find the CDW–SDW phase transition on application of an external electric field. The bias required for the transitions in both cases decreases with increase in system size.

arXiv:0801.0414•Journal of Physics Condensed Matter•Jan 31, 2008•7 citations
We have considered one-dimensional organic conjugated polymeric systems to study the two-photon absorption (TPA) processes. The symmetrized density matrix renormalization group (SDMRG) method has been used to compute the low-energy photonic states and the TPA coefficients, for an extended Hubbard model. We find that the TPA coefficients diverge when the ground state of the system changes from the spin-density wave (SDW) state to the charge-density wave (CDW) state. Although in both phases the system is an insulator, the one-photon and two-photon gaps almost become equal near the transition point. The reason for the TPA coefficients to diverge is the near-degeneracy of these photonic states with strong electric dipole couplings at the transition point region. The picosecond scale nonlinear absorption processes observed in charge transfer insulating systems can be explained due to the formation of a triplet band below the lowest optically allowed state, based on our model calculations.
We calculate the third order nonlinear optical response in the Hubbard model within the spin density wave (SDW) mean field ansatz in which the gap is due to onsite Coulomb repulsion. We obtain closed-form analytical results in one dimension (1D) and two dimension (2D), which show that nonlinear optical response in SDW insulators in 2D is stronger than both 3D and 1D. We also calculate the two photon absorption (TPA) arising from the stress tensor term. We show that in the SDW, the contribution from stress tensor term to the low-energy peak corresponding to two photon absorption becomes identically zero if we consider the gauge invariant current properly.
We have carried out symmetrized density-matrix renormalization-group calculations to study the nature of excited states of long polyacene oligomers within a Pariser-Parr-Pople Hamiltonian. We have used the C2{C}_{2}C2​ symmetry, the electron-hole symmetry, and the spin parity of the system in our calculations. We find that there is a crossover in the lowest dipole forbidden two-photon state and the lowest dipole allowed excited state with size of the oligomer. In the long system limit, the two-photon state lies below the lowest dipole allowed excited state. The triplet state lies well below the two-photon state and energetically does not correspond to its description as being made up of two triplets. These results are in agreement with the general trends in linear conjugated polymers. However, unlike in linear polyenes wherein the two-photon state is a localized excitation, we find that in polyacenes, the two-photon excitation is spread out over the system. We have doped the systems with a hole and an electron and have calculated the charge excitation gap. Using the charge gap and the optical gap, we estimate the binding energy of the ${1}^{1}{B}^{\ensuremath{-}}$ exciton to be 2.09 eV. We have also studied doubly doped polyacenes and find that the bipolaron in these systems, to be composed of two separated polarons, as indicated by the calculated charge-density profile and charge-charge correlation function. We have studied bond orders in various states in order to get an idea of the excited state geometry of the system. We find that the ground state, the triplet state, the dipole allowed state, and the polaron excitations correspond to lengthening of the rung bonds in the interior of the oligomer while the two-photon excitation corresponds to the rung bond lengths having two maxima in the system.
We show that charge excitations within one-dimensional extended Hubbard models in the limit of large on-site Coulomb interaction can be mapped onto pairs of spin reversals from the ferromagnetic Ising-Heisenberg spin Hamiltonian. The exciton in the extended Hubbard models is equivalent to the bound two-magnon state of the spin Hamiltonian. From exact results for the spin Hamiltonian, for the intersite Coulomb interactions limited between nearest neighbors, the lowest optical exciton is separated in energy from the electron-hole continuum only for the intersite interaction larger than half the one-electron bandwidth. The commutation relationship between spin operators allows us to numerically investigate exciton binding energies and optical absorptions from the ground state in the limit of large on-site Coulomb interaction even for cases where analytic results are not available. For intersite Coulomb interaction limited between nearest neighbors, the binding energy of the lowest optical exciton changes very weakly for realistic Peierls bond dimerization, although there is a profound change in the optical absorption. While in the undimerized chain a single optical exciton can occur, two additional excitons that occur above the threshold of the electron-hole continuum become optically visible in the dimerized case. For long-range intersite Coulomb interactions, multiple excitons can occur even for the undimerized chain, and additional exciton states become optically visible upon dimerization. With the 1/r1/r1/r form for the intersite Coulomb interaction, our numerical calculations suggest that the formation of at least one optical exciton is unconditional, unlike the case of nearest-neighbor interaction. The binding energy of the lowest optical exciton again depends weakly on the dimerization for long-range interaction. Our theoretical results can explain the occurrence of two charge-transfer absorption bands in half-filled band segregated stack charge transfer solids below the spin-Peierls dimerization temperature. Our results also suggest that the lowest optical state of \ensuremath{\pi}-conjugated polymers, in which Coulomb interactions are long ranged, is necessarily an exciton.
This work addresses the question of whether low-lying excitations in conjugated polymers are comprised of free charge carriers or excitons. States are characterized as bound or unbound according to the scaling of the average particle-hole separation with system size. We critically examine other criteria commonly used to characterize states. The polymer is described by an extended Hubbard model with alternating transfer integrals. The model is solved by exact diagonalization and the density-matrix renormalization-group (DMRG) method. We demonstrate that the DMRG accurately determines excitation energies, transition dipole moments and particle-hole separations of a number of dipole-forbidden (Ag){(A}_{g})(Ag​) and dipole-allowed (Bu){(B}_{u})(Bu​) states. Within a parameter regime considered reasonable for polymers such as polyacetylene, it is found that the charge gap, often used to define the exciton binding energy, is not a good criterion by which to decide whether a state is bound or unbound. The essential nonlinear optical state mAg{\mathrm{mA}}_{g}mAg​ is found to mark the onset of unbound excitations in the Ag{A}_{g}Ag​ symmetry sector. In the Bu{B}_{u}Bu​ symmetry sector, on the other hand, it is found that all low-lying states are unbound and that there is no well-defined nBu{\mathrm{nB}}_{u}nBu​ state. That is, the 1Bu{1B}_{u}1Bu​ state marks the onset of unbound excitations in this sector.
The density-matrix renormalization-group (DMRG) method is used to investigate optical excitations in the Mott insulating phase of a one-dimensional extended Hubbard model. The linear optical conductivity is calculated using the dynamical DMRG method and the nature of the lowest optically excited states is investigated using a symmetrized DMRG approach. The numerical calculations agree perfectly with field-theoretical predictions for a small Mott gap and analytical results for a large Mott gap obtained with a strong-coupling analysis. It is shown that four types of optical excitations exist in this Mott insulator: pairs of unbound charge excitations, excitons, excitonic strings, and charge-density-wave (CDW) droplets. Each type of excitation dominates the low-energy optical spectrum in some region of the interaction parameter space and corresponds to distinct spectral features: a continuum starting at the Mott gap (unbound charge excitations), a single peak or several isolated peaks below the Mott gap (excitons and excitonic strings, respectively), and a continuum below the Mott gap (CDW droplets).
We perform density matrix renormalization group calculations extensively on one-dimensional chains with on-site ( U ) as well as nearest-neighbour ( V ) Coulomb repulsions. The calculations are carried out in full parameter space with explicit inclusion of the static bias and we compare the nature of spin-density-wave (SDW) and charge-density-wave (CDW) insulators under the influence of external electric fields. We find that, although the SDW ( U >2 V ) and CDW ( U <2 V ) insulators enter into a conducting state after a certain threshold bias, CDW insulators require much higher bias than the SDW insulators for insulator–metal transitions at zero temperature. We also find the CDW–SDW phase transition on application of an external electric field. The bias required for the transitions in both cases decreases with increase in system size.