One-dimensional Electron-phonon Systems Research Articles

Nonadiabatic Fluctuations and the Charge-Density-Wave Transition in One-Dimensional Electron–Phonon Systems: A Dynamic Self-Consistent Theory

The Peierls instability in one-dimensional electron-phonon systems is known to be qualitatively well described by the Mean-Field theory, however the related self-consistent problem so far has only been able to predict a partial suppression of the transition even with proper account of classical lattice fluctuations. Here the Hartree-Fock approximation scheme is extended to the full quantum regime, by mapping the momentum-frequency spectrum of order-parameter fluctuations onto a continuous two-parameter space. For the one-dimensional half-filled Su-Schrieffer-Heeger model the ratio $d=\Omega/2\pi T_c^0$, where $\Omega$ is the characteristic phonon frequency and $2\pi T_c^0$ the lowest finite phonon Matsubara frequency at the mean-field critical point $T_c^0$, provides a natural measure of the adiabaticity of lattice fluctuations. By integrating out finite-frequency phonons, it is found that a variation of $d$ from the classical regime $d=0$ continuously connects $T_c^0$ to a zero-temperature charge-density-wave transition setting up at a finite crossover $d=d_c$. This finite crossover decreases within the range $0\leq d \approx 1$ as the electron-phonon coupling strength increases but remaining small enough for weak-coupling considerations to still hold. Implications of $T_c$ supression on the Ginzburg criterion is discussed, and evidence is given of a possible coherent description of the charge-density-wave problem within the framework of a renormalized Mean-Field theory encompassing several aspects of the transition including its thermodynamics close to the quantum critical point.

Anharmonicity in One-Dimensional Electron–Phonon System

We investigate the effect of anharmonicity on the one-dimensional half-filled Holstein model by using the determinant quantum Monte Carlo method. By calculating the order parameters we find that with and without anharmonicity there is always an transition from a disorder phase to a dimerized phase. Moreover, in the dimerized phase a lattice dimerization and a charge density wave coexist. The anharmonicity represented by the quartic term suppresses the dimerization as well as the charge density wave, while a double-well potential favors the dimerization. In addition, by calculating the correlation exponents we show that the disorder phase is metallic with gapless charge excitations and gapful spin excitations while in the dimerized phase both excitations are gapful.

Nonlinear Lattice Effect on Ground State of One-Dimensional Electron-Phonon System**The project supported by the Research Foundation of Hunan Normal University under Grant No.200606

We study the nonlinear lattice effect on the ground state in a one-dimensional spinless Holstein model with nonadiabitical coupling and squeezing by means of the parameter variational approach. Our results show that the introduction of a hard quartic term in the lattice potential increases the ground state energy of the system when electron-phonon coupling is strong, and the increment is sensitive to the magnitude of the lattice quartic force constant. In this case the nonlinear lattice effects should be taken into account to describe satisfactorily some physical properties of the coupling system.

Theory of pseudogaps in charge density waves in application to photo electron spectroscopy

For a one-dimensional electron-phonon system we consider the photon absorption involving electronic excitations within the pseudogap energy range. Within the adiabatic approximation for the electron - phonon interactions these processes are described by ronlinear configurations of an instanton type. We calculate the subgap absorption as it can be observed by means of photo electron or tunneling spectroscopies. In details we consider systems with gapless modes: 1D semiconductors with acoustic phonons and incommensurate charge density waves. We found that below the free particle edge the pseudogap starts with the exponential decrease of transition rates changing to a power law deeply within the pseudogap, near the absolute edge.

Theory of subgap photoemission in one-dimensional electron-phonon systems: An instanton approach to pseudogaps

For a one-dimensional electron-phonon system we consider photon absorption involving electronic excitations within the pseudogap energy range. Within the adiabatic approximation for the electron-phonon interactions these processes are described by nonlinear configurations of an instanton type. The one-parameter ansatz for the extremal instanton trajectory allows one to span a wide spectral rang providing qualitatively correct limits. We calculate intensities of the photoemission spectroscopy (PES) including momentum-resolved or angle-resolved PES (ARPES), and supplement known results for the optical subgap absorption. We start with the generic case of a one-dimensional semiconductor with a pronounced polaronic effect. We consider in details the Peierls model for a half-filled band of electrons coupled to a lattice which describes the polyacethylene and some commensurate charge-density waves. Particular attention was required to study the momentum dependences for the ARPES, where we face an intriguing interference between the time evolution and the translational motion of the instantons.

The Stabilities of the Ground State and the Polaron Arising from the Squeezing ? Antisqueezing Effect in Strongly Coupled Electron ? Phonon Systems

The influences of the squeezing–antisqueezing effect arising from variations of the electron density and motion of polarons and nonadiabatic phonon fluctuations on the properties of the ground state and the binding energy of the polaron in the Holstein model of coupled one-dimensional electron–phonon systems with spin 1/2 in the cases of high and low electron densities have been studied by using the Bogolyubov transformation and a new ansatz for states that includes correlation effects among the one-phonon coherent and two-phonon squeezed and polaronic states. The results obtained show that the squeezing–antisqueezing (correlation) effect results in that the ground state energy of the systems is significantly lowered, and the binding energy of the polaron is considerably increased. Thus, the stability of the systems and of the polaron are obviously enhanced in such a case when compared with the uncorrelated case. This shows that the ground state determined by the new state ansatz is most stable, and the new ansatz introduced here is very relevant for the coupled electron–phonon systems, especially in strongly coupled and largely squeezed cases.

The properties of the ground state of the nonadiabatically coupled electron-phonon systems with correlated displacement and squeezing

Effects of the nonadiabatic phonon fluctuations on the ground state of coupled one-dimensional electron-phonon systems with high and low electron-densities were investigated by a new ansatz including correlated interaction of the displacement and squeezing. The correlated effect resulted in noticeable reduction of ground state energy of the systems, and obvious increases of binding energy of the polarons occurred. Thus, the stabilities of the polaron and of the systems were significantly enhanced, exactly steady ground state of the Holstein model, then, was obtained by the new ansatz for the coupled electron-phonon systems. In general, the new ansatz were found to be very relevant for the strong coupling and large squeezing cases in nonadiabatically coupled electron-photon systems.

Role of Bisolitons and their Correlations in Charge Transfer Processes.

The charge transport processes in biological macromolecules are studied within the nonlinear electrosoliton mechanism. The interaction between few electrosolitons in a one-dimensional electron-phonon system is investigated. It is shown that in a singlet state the minimum of energy corresponds to a bisoliton. In a triplet state the autolocalized state is described by two electrosolitons which are separated from one another by some finite distance determined by the nonadiabatic terms of the Hamiltonian.

One-dimensional electron-phonon system at arbitrary coupling constant

The ground state of a quasi-particle (exciton, electron or hole) interacting with optical and acoustic phonons in a one-dimensional chain, is investigated using a variational method. The phase diagrams are obtained which show the regions of the electron-phonon coupling constant and nonadiabaticity parameter where the ground state of a quasiparticle is described as almost free electron state, small polaron, or spontaneously localized state. It is shown that the formation of a soliton-like state has a threshold with respect to the value of electron-phonon interaction. The corresponding critical value of the coupling constant increases with the nonadiabaticity parameter increasing.

The effective hamiltonian of the one-dimensional electron-phonon system nearly at the half filling

We study the effect of acoustic mode phonons around a soliton using the effective Hamiltonian given by the Su-Schrieffer-Heeger model. In the one-dimensional electron-phonon system near the half-filling, the non-linear excitation like a soliton appears as distortions of both the optical and the acoustic component of the order parameter. It is shown that the interaction between the acoustic mode phonon and the moving soliton becomes strong near the phonon velocity. This analytical method is also applicable to phase mode solitons in the case away from the half-filling.

Affine Toda systems coupled to matter fields

We investigate higher grading integrable generalizations of the affine Toda systems, where the flat connections defining the models take values in eigensubspaces of an integral gradation of an affine Kac-Moody algebra, with grades varying from l to − l ( l > 1). The corresponding target space possesses nontrivial vacua and soliton configurations, which can be interpreted as particles of the theory, on the same footing as those associated to fundamental fields. The models can also be formulated by a hamiltonian reduction procedure from the so-called two-loop WZNW models. We construct the general solution and show the classes corresponding to the solitons. Some of the particles and solitons become massive when the conformal symmetry is spontaneously broken by a mechanism with an intriguing topological character and leading to a very simple mass formula. The massive fields associated to nonzero grade generators obey field equations of the Dirac type and may be regarded as matter fields. A special class of models is remarkable. These theories possess a U(1) Noether current, which, after a special gauge fixing of the conformal symmetry, is proportional to a topological current. This leads to the confinement of the matter field inside the solitons, which can be regarded as a one-dimensional bag model for QCD. These models are also relevant to the study of electron self-localization in (quasi-) one-dimensional electron-phonon systems.

Semi-Phenomenological Analysis of Dynamics of Nonlinear Excitations in One-Dimensional Electron-Phonon System

The structure of moving nonlinear excitations in one-dimensional electron-phonon systems is studied semi-phenomenologically by using an effective action in which the width of the nonlinear excitation is treated as a dynamical variable. The effective action can be derived from Su, Schrieffer and Heeger's model or its continuum version proposed by Takayama, Lin-Liu and Maki with an assumption that the nonlinear excitation moves uniformly without any deformation except the change of its width. The form of the action is essentially the same as that discussed by Bishop and coworkers in studying the dynamics of the soliton in polyacetylene, though some details are different. For the moving excitation with a velocity $v$, the width is determined by minimizing the effective action. A requirement that there must be a minimum in the action as a function of its width provides a maximum velocity. The velocity dependence of the width and energy can be determined. The motions of a soliton in p olyacetylene and an acoustic polaron in polydiacetylene are studied within this formulation. The obtained results are in good agreement with those of numerical simulations.

Quantum effects on the phonon excitations of one-dimensional electron-phonon systems.

Quantum effects on the phonon excitations of one-dimensional electron-phonon systems.

Effects of Lattice Fluctuation on an Electron Band in Quasi-One-Dimensional Electron-Phonon System

We investigate the effects of lattice vibrations on an electron gap in the Peierls-Frolich state using the Hartree-Fock approximation with respect to the electron-phonon coupling, considering both amplitude mode and phase mode with anisotropic dispersion. In the one-dimensional electron-phonon system, the electron gap is induced by the Umklapp scattering intermediated by the amplitude-mode phonon with momentum transfer of 2 k F . However, the phase-mode phonon gives the large fluctuation to the electron band and reduces the band gap. The band gap is determined by the competetion between the amplitude mode and the phase mode. We find that the band gap becomes narrower as the velocity of the phase-mode phonon u is increased. The band gap tail appears from the electron-phonon scattering. The electron scattering rate due to phonon is estimated to be π u Δ 0 /2 v F , where Δ 0 is the electron band gap and v F is the Fermi velocity.

Local chiral symmetry and charge-density waves in one-dimensional conductors.

Symmetry-related features of charge-density-wave transport phenomena are studied using a non-mean-field effective Lagrangian approach. It is pointed out that a local chiral symmetry (based on the Ka\ifmmode \check{c}\else \v{c}\fi{}-Moody algebra) emerges in the low-energy structure of one-dimensional electron-phonon systems. From this symmetry follow directly power-law correlations of both electrons and phonons. The Peierls instability is suppressed owing to one-dimensional fluctuations. Still the charge-density wave arises and the chiral anomaly can account for acceleration of a sliding charge-density wave along with a phonon-drag effect. The problem of pinning of charge-density waves is discussed in relation to explicit breakings of the chiral symmetry.

On the effect of impurities in the one-dimensional electron-phonon system

The effect of ordinary impurities on the Peierls-CDW transition is investigated within a normal state side approach. The 2kF-phonon frequency is calculated within the Born approximation for the electron self-energy and ladder approximation for the three-legged vertex function. The critical concentration and critical temperature of the soft-mode instability are obtained; they agree with the conditions for the suppression of the Peierls-CDW distortion. A thermal hysteresis effect is suggested for the doped quasi-1D materials.

Exact solution of a quantum electron-phonon system for a two-site periodic cluster.

The ground state of a one-dimensional electron-phonon system is studied by means of a small-crystal approach: an exact solution of a two-site cluster with two electrons and periodic boundary conditions. A single electron band is considered in the tight-binding approximation, together with two-electron interactions between electrons in the same site (Hubbard model); the electrons are coupled to longitudinal-acoustic phonons through a bilinear interaction. The problem is isomorphic with that of the homopolar diatomic molecule with a vibronic degree of freedom and coupling between the electronic and vibronic modes. In the adiabatic (large-ionic-mass, small-vibrational-frequency) limit there is an analytical solution which indicates that the transition between the nondistorted (weak-coupling) and the distorted (strong-coupling) phases can be either continuous or discontinuous, depending on whether the value of electron-electron interaction is smaller or larger than a critical value. In the extremely-high-frequency limit (ionic mass M..-->..0) it is also possible to find an analytical solution (for M = 0) that shows that the system remains undistorted for any value of the electron-phonon coupling and the electron-electron interaction. In the intermediate case (finite, nonvanishing M), numerical solutions exhibit a continuous transition from the nondistorted to the distorted phase.

A functional integral approach to the one-dimensional electron-phonon problem

The interplay between lattice and electronic fluctuations in one-dimensional electron-phonon systems is analyzed by a path integral approach in terms of both commuting and anticommuting field variables. Both adiabatic and non-adiabatic regimes of lattice fluctuations can be investigated by applying a renormalization group procedure to both the electronic and phonon degrees of freedom. It is shown how this procedure, which is at a microscopic level, can generate the Ginzburg-Landau functional description of lattice correlations. In the adiabatic regime, this theory gives a self-consistent treatment of lattice fluctuations and of the remaining electronic degrees of freedom. Using a single-loop approximation of the quartic phonon field term, it is shown that quantum fluctuations of the phonon field suppress the Peierls order parameter. A numerical application to the spinless half-filled band in the molecular crystal model is in excellent agreement with Monte Carlo simulations.

Thermodynamic and transport properties of one-dimensional electron-phonon systems

We compute thermodynamic and transport coefficients of one-dimensional metals in the presence of electron-electron and electron-phonon interaction. It is found that quantities like the electronic specific heat, the Pauli susceptibility or the Holstein optical conductivity depend on both types of interaction as well as on the frequency of the phonons involved.

Functional-integral approach to an exactly soluble one-dimensional electron-phonon system.

We consider forward-scattering electron-electron and electron-phonon interactions in an extended Tomonaga-Luttinger model. The method of functional integration over anticommuting fields gives us a bosonized effective action. This enables us to obtain the spectrum and the correlation functions of the system exactly. We consider couplings to both acoustic and optical phonons. In the case of acoustic phonons, we obtain $T\ensuremath{\rightarrow}0$ phase diagram in the plane of coupling constants which indicates the existence of a normal phase between the regions of charge-density-wave and superconducting instabilities. This is qualitatively different from previous results.