Peierls-Hubbard Model Research Articles

Peierls Transitions in Ionic Organic Charge-Transfer Crystals with Spin and Charge Degrees of Freedom

The quasi-one-dimensional electronic structure of organic charge-transfer (CT) salts rationalizes Peierls transitions in mixed or segregated stacks of pi-electron donors (D) and acceptors (A). A microscopic Peierls-Hubbard model, HCT, is presented for CT salts with mixed stacks (Drho+Arho-)n and ionicity rho > 0.7. Dimerization opens a Peierls gap that, due to electron correlation, is the singlet-triplet gap, EST. In contrast to spin-Peierls systems, such as Heisenberg spin chains with rho = 1 and TSP < 20 K, Peierls transitions in CT salts with rho < 1 occur at higher TP and involve both spin and charge degrees of freedom. Linear electron-phonon coupling and an adiabatic approximation for a harmonic lattice are used to model the dimerization amplitude deltaT for T < TP, the magnetic (spin) susceptibility chiT, and the relative infrared intensity of totally symmetric molecular modes. Exact thermodynamics of HCT for stacks up to N = 12 sites are applied to two CT salts with TP approximately 50 and 120 K whose magnetism and infrared have not been modeled previously and to CT salts with inaccessibly high TP > 350 K whose description has been difficult. Ionic CT salts are correlated Peierls systems with a degenerate ground state (GS) at T = 0 whose elementary excitations are spin solitons, while dimerized ion-radical stacks that support triplet-spin excitons have nondegenerate GS. In less ionic CT salts, modulation of HCT parameters on cooling or under pressure leads to Peierls and/or neutral-ionic transitions of the GS, without appreciable thermal population of excited states. Correlations change the gap equation that relates EST at T = 0 to TP compared to free electrons, and size convergence is fast in stacks with large delta0 and high TP.

Nonlinear lattice relaxation of photoexcited diplatinum-halide chain compounds

In order to reveal the relaxation mechanism of photogenerated charge-transfer excitations in quasi-one-dimensional halogen-bridged diplatinum complexes, we calculate the low-lying adiabatic potential energy surfaces of a one-dimensional extended Peierls-Hubbard model. High-energy excitations above the electron-hole continuum may relax into polarons, while excitons pumped within the optical gap are self-localized and then either decay by luminescence or divide into solitons. Neutral solitons, charged solitons, and polarons may be simultaneously photogenerated in a diplatinum-halide chain, which has never been observed in any conventional platinum-halide chain. Optical conductivity is also simulated along the decay paths for experimental verification.

Electronic and structural instabilities of mixed-stack organic charge-transfer salts

Electronic (valence) and structural (Peierls) instabilities occur either separately or together in organic charge-transfer (CT) crystals with mixed stacks of donors (D) and acceptors (A). A Peierls–Hubbard model, H CT, with site D, A energies and linear electron–phonon coupling in a harmonic lattice is shown to provide a unified microscopic description and to distinguish between thermal and quantum Peierls transitions. Vibrational, magnetic and structural data are interpreted as thermal Peierls transitions in two ionic CT salts and as dimerized ground states with spin solitons in other salts. Quantum Peierls transitions are identified in largely neutral salts, and a neutral–ionic crossover is discussed in a salt with dipolar disorder that suppresses the Peierls instability. The coincident Peierls and neutral–ionic transition of tetrathiafulvalene-chloranil (TTF-CA) is another special case of H CT.

Polaron Formation in a Model Hamiltonian with Covalent Electron–Phonon Interactions

We have performed an exact diagonalization of a many body Hamiltonian that includes electron correlations and electron-phonon interactions. Electronic and phononic parameters entering in the Hamiltonian were chosen for the cluster O(4)Cu-O(4) cluster in YBa 2 Cu 3 O 7 . Electronic and phononic degrees of freedom are coupled through the bare electron hopping, as in the Su-Schieffer-Heeger (SSH) Hamiltonian [W. P. Su et al., Phys. Rev. Lett. 42, 1698 (1979); A. J. Heeger, Rev. Mod. Phys. 60, 781 (1988)]. Fixing all parameters entering in the model Hamiltonian, the electron-phonon coupling was varied in order to reproduce structural short-range distortions found in the z-axis direction for YBa 2 Cu 3 O 7 . Although the inferred structural distortions are reproduced, we find that this type of coupling, unlike the electron-phonon coupling introduced in Peierls-Hubbard models, does not lead to excitations with polaronic energies and negative isotopic shifts typical of polaronic excitations.

Spin solitons in organic charge-transfer salts

Organic charge-transfer (CT) salts that crystallize in face-to-face stacks of π-electron donors (D) and acceptors (A) are one-dimensional electronic systems with strong coupling to lattice and molecular vibrations. Peierls–Hubbard models of CT salts resemble π-electron theory of conjugated polymers, although transfer integrals t along mixed DA stacks are considerably smaller. Strong D and A yield Peierls systems with dimerized ground states of ion radicals, D + and A −. Topological spin solitons separate regions of opposite dimerization, similarly to solitons in trans-polyacetylene, but are thermally accessible in ionic CT salts due to small t. Salts with still smaller t have Peierls transitions at T P < 300 K to undimerized stacks. A Peierls–Hubbard model, H CT, describes both types of salts and estimates of t are consistent with T P < 300 K in some salts and spin solitons in others with higher T P. Electron paramagnetic resonance (epr) spectra of single crystals provide direct evidence for spin solitons and one-dimensional electronic states. Spin solitons and H CT resolve longstanding conflicts between vibrational and magnetic data that indicate dimerized stacks in several prototypical CT salts, while structural data point to undimerized stacks with large thermal ellipsoids. The low energy scale, availability of single crystals and diversity of CT salts offer opportunities for detailed modeling.

Effects of the electron-phonon interaction of the charge ordering in quasi-one-dimensional charge-transfer salts

The Bechgaard salts and their sulfur analogs are considered to be in quasi-one-dimensional correlated electron systems with a quarter-filled π band and exhibit various types of charge and/or spin ordering. A variety of mechanisms have been proposed in an attempt to interpret the variety of instabilities, featuring dimensionality, which can be turned by pressure as well as chemically, intrachain dimerization due to the anion columns, and competing on-site and even long-range Coulomb repulsions. Here we investigate quantum and thermal phase transitions in the Bechgaard salts and their sulfur analogs with particular emphasis on lattice degree of freedom. We consider the one-dimensional extended Peierls-Hubbard model with long-range Coulomb and electron-lattice interactions. Due to the intrinsic dimerization accompanied by the anion columns, we introduce alternation to transfer integrals, nearest-neighbor Coulomb interactions and spring constants. We fully demonstrate the interplay between charge ordering and lattice instability within the Hartree approximation. Besides the purely electronic charge and spin density waves which are well established both experimentally and theoretically, we reveal a lattice-tetramerized phase stabilized essentially in Peierls-Hubbard model. Our results inspected and compared with the results of experiments.

Polarization in Organic Molecular Crystals and Charge‐Transfer Salts

AbstractFor Abstract see ChemInform Abstract in Full Text.

Perturbation theory for optical excitations in the one-dimensional extended Peierls–Hubbardmodel

For the one-dimensional, extended Peierls–Hubbard model we calculate analytically theground-state energy and the single-particle gap to second order in the Coulomb interactionfor a given lattice dimerization. The comparison with numerically exact data fromthe density-matrix renormalization group shows that the ground-state energy isquantitatively reliable for Coulomb parameters as large as the bandwidth. Thesingle-particle gap can almost triple from its bare Peierls value before substantialdeviations appear. For the calculation of the dominant optical excitations, wefollow two approaches. In Wannier theory, we perturb the Wannier excitonstates to second order. In two-step perturbation theory, similar in spirit to theGW-BSEapproach (where the Bethe–Salpeter equation is solved for quasi-particles which are calculated in theGW-approximation), we form excitons from dressed electron–hole excitations. We find theWannier approach to be superior to the two-step perturbation theory. For singlet excitons,Wannier theory is applicable up to Coulomb parameters as large as half the bandwidth.For triplet excitons, second-order perturbation theory quickly fails completely.

Phase diagram and isotope effects of the quasi-one-dimensional electron gas coupled to phonons

Using a multistep renormalization group method, we study the low-temperature phases of the interacting one-dimensional (1D) electron gas coupled to phonons. We obtain analytic expressions for the weak-coupling quantum phase boundaries of the 1D extended Holstein-Hubbard model and the 1D extended Peierls-Hubbard model for general band-filling and phonon frequency. Away from half-filling, the phase diagrams are characterized by a delicate competition between spin density wave, charge density wave, and superconducting orders. We study the dependence of the ground state on the electron-phonon (el-ph) and electron-electron (el-el) coupling strengths, the screening length, electron bandwidth, phonon frequency, doping, and type of phonon. Unlike the case in Fermi liquids, in 1D the el-ph coupling is strongly renormalized, often to stronger values. Even when the bare phonon-induced attraction is weak compared to the bare el-el repulsion, a small amount of retardation can cause the renormalized el-ph interaction to dominate the problem. We find cases in which a repulsive el-el interaction enhances the superconducting susceptibility in the presence of a retarded el-ph interaction. The spin gap and superconducting susceptibility are found to be strongly dependent on the deviation from half-filling (doping). In some cases, the superconducting susceptibility varies nonmonotonically with doping and exhibits a maximum at a particular doping. For a quasi-1D array of weakly coupled, fluctuating 1D chains, the superconducting transition temperature T_c also exhibits a maximum as a function of doping. The effect of changing the ion mass (isotope effect) on T_c is found to be largest near half-filling and to decrease rapidly with doping.

The Peierls–Hubbard model at weak coupling

We investigate the Peierls transition in the one-dimensional Peierls–Hubbardmodel at half-filling in the adiabatic approximation for the lattice.Depending on the value of the electron–lattice coupling constantg the equilibrium dimerization can be either enhanced or suppressed by the Hubbard interactionU. Applying second-order perturbation theory we determine the critical valuegc = 0.689 348 below which the Hubbard interaction enhances the dimerization.

Solitons in magnetic nanographite ribbons investigated with a Peierls-Hubbard model

The hydrogenated nanographite ribbons are numerically investigated with a Peierls-Hubbard model. In the ferrimagnetic ground state, an antiferromagnetic spin density wave and perfect dimerization exist. The dependences of the dimerization and the spin density on the width of the ribbon, electron-phonon coupling $\ensuremath{\lambda}$, and the on-site Hubbard repulsion $U$ are studied in detail. Because the ground state is degenerate, a domain wall describing the lattice deformation and the spin soliton describing the localization of spin exist. The creation energy of the soliton is much smaller than that in polyacetylene because the localized state of soliton is not in the gap. Due to the interplay between $\ensuremath{\lambda}$ and $U$, the solitons exist only in a range of $U$, which depends on $\ensuremath{\lambda}$.

Spin-Peierls Transition Temperature in Quarter-Filled Organic Conductors

We examine the transition temperature of spin-Peierls state, T SP , in the one-dimensional quarter-filled Peierls–Hubbard model with lattice dimerization and intersite repulsive interaction, V , by applying the bosonization and the renormalization-group method. It is shown that for large V the transition temperature T SP is suppressed due to the appearance of the charge ordering. In the spin-Peierls state, the location of the spin-singlet state is shifted continuously from the bond of the lattice to the on-site by the increase of the charge ordering. The result is compatible with our previous results of the ground state. We discuss the pressure effect on T SP , which has been observed in the NMR measurement.

Quantum phase transitions in one-dimensional half-filled ionic Peierls–Hubbard model

Density matrix renormalization group methods are used to investigate the quantum phase transitions of a one-dimensional half-filled ionic Peierls–Hubbard model at the antiadiabatic limit. We found that two continuous phase transitions always exist from dimerized spin–gapped (bond-order-wave) state to band–insulator and undimerized spin–gapless (Mott–insulator) phase while undimerized spin–gapless phase vanishes at the adiabatic limit.

Photoinduced dynamics and nonequilibrium characteristics in quasi-one-dimensional effectron systems: Mott insulators vs band insulators

Effectron-effectron interactions play an important role in nonequilibrium properties of molecular materials. First, we show differences between photoinduced ionic-to-neutral and neutral-to-ionic transitions in quasi-one-dimensional extended Peierls Hubbard models with alternating potentials. Cooperative dynamics lead to nonlinear ionicity in the former, while uncooperative dynamics lead to quite linear ionicity in the latter, as a function of the energy supplied from the oscillating effectric field. Interchain effectron-effectron interactions bring about initial competition among metastable and stable domains in neighboring chains, slowing down the phase transition. Interchain elastic couplings are necessary to form a ferroeffectric long-range order. Second, we show differences between field-effect characteristics of Mott insulators and those of band insulators in one-dimensional Hubbard models, to which tight-binding models are attached for metallic effectrodes and scalar potentials are added for interfacial barriers. Ambipolar characteristics are found in the former, while unipolar characteristics generally appear in the latter. In the former, charge transport is cooperative so that the drain current is insensitive to the difference between the work function of the channel and that of the effectrodes, and thus insensitive to the polarity of the gate bias.

Disorder in organic charge-transfer single crystals: Dipolar disorder in ClMePD-DMeDCNQI

The unusual electronic, vibrational, and structural properties of the title compound are associated with the polar donor D=2-chloro-5-methyl-p-phenylenediamine, which is twofold disordered in single crystals. Its 3 D dipole generates random site energies with standard deviation sigma=0.35 eV that significantly alter the standard description of charge-transfer (CT) salts with nonpolar donors and acceptors. The average structure at 298 and 150 K is centrosymmetric, space group P1, and consistent with increasing degree of CT (or ionicity rho) on cooling. Vibrational spectra indicate that rho increases from approximately 0.3 at 400 K to approximately 0.6 at 80 K, with coincident Raman and infrared (IR) molecular modes in contrast with the centrosymmetric structure. Dipolar disorder is modeled by adding random site energies to Peierls-Hubbard models of CT salts, and sigma=0.35 eV is shown to suppress the Peierls instability for typical bandwidth and lattice stiffness, in agreement with the structural data. Disorder also breaks inversion symmetry and rationalizes coincident Raman and IR modes. The combination of site energies xp and the dipole operator P for systems with periodic boundary conditions leads at molecule p to (partial differentialP/ partial differentialxp)2 for the IR intensity polarized along the DA stack. The ensemble average of (partial differentialP/ partial differentialxp)2 for sigma=0.35 eV as a function of the ground-state ionicity rho accounts for the intensity variations of totally symmetric molecular modes of D and A, either on cooling at ambient pressure or on squeezing at ambient temperature.

Phase Transition in a One-dimensional Extended Peierls–Hubbard Model with a Pulse of Oscillating Electric Field: III. Interference Caused by a Double Pulse

In order to study consequences of the differences between the ionic-to-neutral and neutral-to-ionic transitions in the one-dimensional extended Peierls–Hubbard model with alternating potentials for the TTF–CA complex, we introduce a double pulse of oscillating electric field in the time-dependent Schrödinger equation and vary the interval between the two pulses as well as their strengths. When the dimerized ionic phase is photoexcited, the interference effect is clearly observed owing to the coherence of charge density and lattice displacements. Namely, the two pulses constructively interfere with each other if the interval is a multiple of the period of the optical lattice vibration, while they destructively interfere if the interval is a half-odd integer times the period, in the processes toward the neutral phase. The interference is strong especially when the pulse is strong and short because the coherence is also strong. Meanwhile, when the neutral phase is photoexcited, the interference effect is almost invisible or weakly observed when the pulse is weak. The photoinduced lattice oscillations are incoherent due to random phases. The strength of the interference caused by a double pulse is a key quantity to distinguish the two transitions and to evaluate the coherence of charge density and lattice displacements.

BOW–SDW Transition in the Two-dimensional Peierls–Hubbard Model

The periodic lattice distortion BOW owing to the electron–lattice interaction and the spin density wave SDW owing to the electron–electron interaction in the two-dimensional Peierls–Hubbard model having a half-filled electronic band are studied numerically within the Hartree–Fock approximation. It is shown that the phase transition from the BOW to the SDW behaves as the first order phase transition when the on-site electron–electron interaction U is increased continuously. There is no region of U where the BOW and the SDW coexist as a uniform phase.

Theory of photoinduced phase dynamics in organic charge-transfer complexes

In the quasi-one-dimensional mixed-stack organic charge-transfer complex, TTF-CA, photoirradiation is known to trigger transitions between the neutral and ionic phases. Here we use a one-dimensional extended Peierls–Hubbard model with alternating potentials and calculate the mean-field dynamics of charge density coupled with that of lattice displacements. We show qualitative differences between the photoinduced ionic-to-neutral and neutral-to-ionic transitions, which are consistent with recent experimental findings. That is, the ionic-to-neutral transition proceeds cooperatively, characterized by threshold behavior, while the neutral-to-ionic transition proceeds uncooperatively, characterized by linear behavior. The threshold absorption in the former depends on the strength or the duration of the pulse. The coherence during the transition dynamics is also different between the two transitions. In the ionic-to-neutral transition, a clear interference effect is observed as a function of the interval when the pulse is spilt into two.

Soliton-induced optical absorption of halogen-bridged mixed-valence binuclear metal complexes

Employing the one-dimensional single-band extended Peierls-Hubbard model, we investigate optical conductivity for solitonic excitations in halogen-bridged binuclear metal (MMX) complexes. Photoinduced soliton absorption spectra for MMX chains possibly split into two bands, forming a striking contrast to those for conventional mononuclear metal (MX) analogs, due to the broken electron-hole symmetry combined with relevant Coulomb and/or electron-phonon interactions.

Polarization in organic molecular crystals and charge-transfer salts

Polarization in insulators is a general phenomenon that extends over nanometer distances. Two special cases illustrate recent theoretical progress. Polarization energies of localized charges in organic molecular crystals exceed the bandwidth and redistribute the charge density. A systematic treatment of electronic polarization is summarized in the limit of zero intermolecular overlap for pentacene crystals or thin films on metallic substrates, with special attention to the transport gap for producing a separated electron–hole pair and the optical dielectric tensor of the crystal. When overlap cannot be neglected, the general formulation of polarization in extended insulators is in terms of the exact ground state's phase. This formulation is applied to organic charge-transfer (CT) salts whose correlated electronic structure is described by one-dimensional Peierls–Hubbard models. Near the Peierls instability, coupling to lattice modes generates large peaks in the dielectric response that is primarily due to lattice vibrations. Comparisons with experiment are mentioned for both organic molecular crystals and CT salts.