arXiv subjects

W. Barford

Publications and source records attributed to W. Barford.

13 recordsLinked to original sources

arXiv2002

Large scale numerical investigation of excited states in poly(phenylene)

A density matrix renormalisation group scheme is developed, allowing for the first time essentially exact numerical solutions for the important excited states of a realistic semi-empirical model for oligo-phenylenes. By monitoring the evolution of the energies with chain length and comparing them to the experimental absorption peaks of oligomers and thin films, we assign the four characteristic absorption peaks of phenyl-based polymers. We also determine the position and nature of the nonlinear optical states in this model.

cond-mat↗

arXiv2001

The low-lying excitations of polydiacetylene

The Pariser-Parr-Pople Hamiltonian is used to calculate and identify the nature of the low-lying vertical transition energies of polydiacetylene. The model is solved using the density matrix renormalisation group method for a fixed acetylenic geometry for chains of up to 102 atoms. The non-linear optical properties of polydiacetylene are considered, which are determined by the third-order susceptibility. The experimental 1Bu data of Giesa and Schultz are used as the geometric model for the calculation. For short chains, the calculated E(1Bu) agrees with the experimental value, within solvation effects (ca. 0.3 eV). The charge gap is used to characterise bound and unbound states. The nBu is above the charge gap and hence a continuum state; the 1Bu, 2Ag and mAg are not and hence are bound excitons. For large chain lengths, the nBu tends towards the charge gap as expected, strongly suggesting that the nBu is the conduction band edge. The conduction band edge for PDA is agreed in the literature to be ca. 3.0 eV. Accounting for the strong polarisation effects of the medium and polaron formation gives our calculated E(nBu) ca. 3.6 eV, with an exciton binding energy of ca. 1.0 eV. The 2Ag state is found to be above the 1Bu, which does not agree with relaxed transition experimental data. However, this could be resolved by including explicit lattice relaxation in the Pariser- Parr-Pople-Peierls model. Particle-hole separation data further suggest that the 1Bu, 2Ag and mAg are bound excitons, and that the nBu is an unbound exciton.

cond-mat↗

arXiv2000

Effect of Quantised Lattice Fluctuations on the Electronic States of Polyenes

We solve a model of interacting electrons coupled to longitudinal phonons using the density matrix renormalisation group method. The model is parametrised for polyenes. We calculate the ground state, and first excited odd-parity singlet and triplet states; and we investigate their energies, and bond length changes and fluctuations for up to 30 sites. The transition energy and the soliton width of the triplet state show deviations from the adiabatic approximation for chain lengths larger than the classical soliton size, because of de-pinning by the quantised lattice fluctuations.

cond-mat.str-el↗

arXiv1999

Molecular Orbital Models of Benzene, Biphenyl and the Oligophenylenes

A two state (2-MO) model for the low-lying long axis-polarised excitations of poly(p-phenylene) oligomers and polymers is developed. First we derive such a model from the underlying Pariser-Parr-Pople (P-P-P) model of pi-conjugated systems. The two states retained per unit cell are the Wannier functions associated with the valence and conduction bands. By a comparison of the predictions of this model to a four state model (which includes the non-bonding states) and a full P-P-P model calculation on benzene and biphenyl, it is shown quantitatively how the 2-MO model fails to predict the correct excitation energies. The 2-MO model is then solved for oligophenylenes of up to 15 repeat units using the density matrix renormalisation group (DMRG) method. It is shown that the predicted lowest lying, dipole allowed excitation is ca. 1 eV higher than the experimental result. The failure of the 2-MO model is a consequence of the fact that the original HOMO and LUMO single particle basis does not provide an adequate representation for the many body processes of the electronic system.

cond-mat↗

arXiv1998

DMRG Calculations of the Low-lying Excitations and Nonlinear Optical Properties of poly(para-phenylene)

The two state molecular orbital (2-MO) model of the phenyl based semiconductors is used to calculate the low-lying spectra of the Ag and Bu states of poly(para-phenylene) (PPP). The model parameters are determined by fitting its predictions to exact Pariser-Parr-Pople model calculations of benzene and biphenyl, and it is solved using the density matrix renormalisation group method. It is shown that there exists a band of Bu (s-wave) excitons below the band states. In the long chain limit the lowest exciton is situated 3.3 eV above the ground state, consistent with experimental data. The calculated particle-hole separation of these excitons indicates that they are tightly bound, extending over only a few repeat units. The lowest band state is found to be a covalent 2Ag state, whose energy almost coincides with the charge gap Eg. Lying just above the 2Ag state is a band Bu state (the nBu state). The particle-hole separation of the band states scales linearly with oligomer size. The binding energy of the 1Bu exciton is determined rigorously as 0.74 eV. The dipole matrix elements and oscillator strengths for the transitions between the lowest Ag and Bu states are calculated and the NLO properties of PPP, such as electroabsorption (EA) and third harmonic generation, are investigated. A comparison of the EA spectrum with the experimental data shows that the main features of the experimental spectrum are well described by the 2-MO Hamiltonian. Only five states account for most of the calculated EA. These are the 1Ag, 1Bu, 2Ag, nBu and another band Ag state, the kAg, thus confirming the essential states model. An analysis of the particle excitation weight of these states indicates that they are predominately single particle in character.

cond-mat↗

arXiv1995

Charge Transfer Excitons and Possible Exitonic Pairing in the Extended Three Band Hubbard Model

Exact diagonalisations of the extended Hubbard model are performed. In the insulating regime it is shown that the nearest neighbour copper-oxygen repulsion, $V$, leads to Frenkel excitons in the charge transfer gap at values of $V$ of the order of copper-oxygen hybridisation, $t$. In the metallic regime it is shown that the static charge-transfer and density-density correlation functions diverge as a function of $V$, indicating a charge-tansfer instability and phase separation. This is accompanied by a softening of the $q \to 0$ mode of the dynamic correlation functions which is associated with the excitonic excitations responsible for the superconducting correlations observed in the proximity of the phase separation boundary of ref. \cite{cv95b}.

cond-mat↗

arXiv1995

A Variational Estimate of the Binding Energy of Charge-Transfer Excitons in the Cuprate Superconductors.

We present a variational estimate for the binding energy of a Frenkel exciton in the insulating cuprate superconductors. Starting from the three band Hubbard model we perform a canonical transformation to O($t^2$), where $t$ is the bare nearest neighbour copper-oxygen hopping integral. An effective Hamiltonian is then derived to describe the hopping of the exciton through the copper oxide plane. The critical parameter in the model is the nearest neighbour copper-oxygen coulomb repulsion, $V$. It is found that a critical value of $V$ is needed to observe bound Frenkel excitons, and that these excitons have the same symmetry as the parent copper orbital, $d_{x^2-y^2}$. We determine the critical value of $V$ using a variational approach, and attempt to fit the parameters of the model to known experimental results.

cond-mat↗

arXiv1994

Large Phase Separation and Superconductivity in the Copper Oxide Chain

The phase diagram of the copper-oxide chain as a function of density and the nearest-neighbour Coulomb interaction, V, is determined. Phase separation takes place above a critical value of $V$ when the Cu2+ to Cu+ valence fluctuations dominate. In the proximity of the phase separation boundary the superconducting correlations are the most divergent. We identify the parameter regions where the Luttinger Liquid theory applies and calculate the contours of the charge-charge correlation exponent K_ρ. We show that anomalous flux quantization occurs as K_ρ diverges. At n = 1, for V > t, a gap opens in the spectrum and the ground state is a charge-density wave.

cond-mat↗

arXiv1994

Strong Coupling Descriptions of High Temperature Superconductors: Electronic Attraction from a Repulsive Potential

We consider the effect of the nearest neighbour copper-oxygen repulsion, V, when coupled to the charge transfer resonances Cu2+ to Cu3+ and Cu2+ to Cu+ in the high temperature cuprate superconductors. This is done by deriving effective low energy Hamiltonians correct to second order in the copper-oxygen hybridisation. Only hole doping is considered. When Cu2+ to Cu3+ fluctuations dominate we derive an effective one-band model of `Zhang-Rice' singlets with a nearest neighbour repulsion between these singlets. When Cu2+ to Cu+ fluctuations dominate we find rich and complex behaviour. For large V we show that clusters of charge are more stable than isolated charges. On the other hand, for small V the Hamiltonian contains both weak attractive and repulsive two body potentials. Calculations on clusters indicate that the attractive potentials have the same correlations as the more dominate `single particle' terms suggesting the possibility of `s' wave pairing.

cond-mat↗

arXiv1994

Phase Separation and Superconductivity in the Copper Oxide Chain

The phase diagram of the copper-oxide chain as a function of density and the nearest-neighbour Coulomb interaction, V, is determined. Phase separation takes place above a critical value of $V$ when the Cu2+ to Cu+ valence fluctuations dominate. In the proximity of the phase separation boundary the superconducting correlations are the most divergent. We identify the parameter regions where the Luttinger Liquid theory applies and calculate the contours of the charge-charge correlation exponent K_ρ. We show that anomalous flux quantization occurs as$K_ρ diverges. At n = 1, for V > t, a gap opens in the spectrum and the ground state is a charge-density wave.

cond-mat↗

arXiv1994

The Dynamics of the Bean Critical State

A simple one dimensional model to simulate the establishment of the Bean critical state is introduced. It is shown that the dynamics of the flux lines as they enter the superconductor are dominated by `avalanches'. The distribution of distances moved by vortices in the avalanches obeys a power law with an exponent of -1. This suggests that the Bean state is a self-organised critical state. The density of flux lines is parabolic.

cond-mat↗

arXiv1994

Incommensurate and Collinear Phases in a Doped Quantum Anti-ferromagnet

The Schwinger Boson mean field theories of the `t-J' model are extended by the consideration of anisotropic order parameters. This has two effects. First, a collinear phase, in which the spins are anti-ferromagnetically aligned in one direction and ferromagnetically aligned in the other, is found to be stable over a significant range of the phase diagram. Second, the (1,1) and (1,0) spiral phases become very close in energy. The inclusion of weak intra-sublattice coupling may therefore stabilise the (1,0) spiral with respect to the (1,1) spiral, thus harmonising theory and experiment.

cond-mat↗

arXiv1994

Charge Transfer Excitons and the Metal-Insulator Transition in the High Temperature Superconductors

The effects of the nearest neighbour Coulomb repulsion, V, are considered in the one dimensional copper-oxide chain using the modified Lanczos method. Above a critical value of V we find that charge transfer excitons are the lowest lying energy exitations in the insulating phase. Close to the metal-insulator transition and $V=0$ there is good `particle-hole' symmetry, showing that the mapping from a two band model to a one band model is appropriate. The effect of the nearest neighbour repulsion is to create states in the gap and to pin the Fermi level upon hole doping.

cond-mat↗