Electron-phonon System Research Articles

Thermodynamics of a continuum Su–Schrieffer–Heeger model

The full partition function for an electron–phonon system described by the one dimensional Su–Schrieffer–Heeger model is exactly computed by a path integral method. Mapping the real space Hamiltonian onto the time scale we introduce a temperature dependent range hopping for the electrons. The heat capacity over temperature ratio shows an upturn at low temperatures which is a peculiar feature of the glassy state. The perturbation on the phonon subsystem due to the electron path motion are evaluated by a cumulant expansion of the phonon free energy.

Band-filling effects on electron-phonon properties of normal and superconducting states

We address the effect of band filling on the effective electron mass $m^*$ and the superconducting critical temperature $T_c$ in a electron-phonon system. We compare the vertex corrected theory with the non-crossing approximation of the Holstein model within a local approximation. We identify two regions of the electron density where $m^*$ and $T_c$ are enhanced or decreased by the inclusion of the vertex diagrams. We show that the crossover between the enhancement at low density and the decrease towards half filling is almost independent of the microscopic electron-phonon parameters. These different behaviors are explained in terms of the net sign of the vertex diagrams which is positive at low densities and negative close to half filling. Predictions of the present theory for doped MgB$_2$, which is argued to be in the low density regime, are discussed.

Multiphonon effects in the kink structures of electron states at the Be(0001) surface: The Einstein phonon case

We solve the strong-coupling self-consistent equations of a two-dimensional (2D) electron-phonon interaction system numerically in order to understand the experimental data of Be(0001) surface states. We present the quasiparticle dispersion and inverse lifetime of a 2D electrons interacting with Einstein phonons. The results are in better agreement with Be experiments than former approximative calculations with Einstein phonons and close to those with Debye phonons.

Electron gas with polaronic effects: beyond the mean‐field theory

AbstractThe occurrence of polaronic behaviour in real solids is often accompanied by strong exchange and correlation effects in the electron gas besides being strongly entangled to the phononic degrees of freedom. Such effects can be relevant for the instability towards Wigner crystallization or charge density waves, or yet for the polaron role in high‐Tc superconductors and in manganites. The inclusion of exchange and correlation in the coupled electron–phonon system is thus highly desirable. In this work, we exploit the density functional theory and its time‐dependent extension to construct an appropriate effective potential useful for studying the properties of interacting polarons. The validity and the possible developments of this approach are discussed, and future applications are proposed.

Electron-phonon interaction and coupled phonon-plasmon modes

The theory of Raman scattering by the electron--phonon coupled system in metals and heavily doped semiconductors is developed taking into account the Coulomb screening and the electron--phonon deformation interaction. The Boltzmann equation for carriers is applied. Phonon frequencies and optic coupling constants are renormalized due to interactions with carriers. The $k-$dependent semiclassical dielectric function is involved instead of the Lindhard-Mermin expression. The results of calculations are presented for various values of carrier concentration and electron-phonon coupling constant.

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.

LIGAND-SENSITIZED AND UP-CONVERSION PHOTOLUMINESCENCE IN VACUUM-DEPOSITED THIN FILMS OF AN INFRARED ELECTROLUMINESCENT ORGANIC ERBIUM COMPLEX

We observed ligand-sensitized and up-conversion photoluminescence (PL) in vacuum-deposited thin films of an infrared electroluminescent organic erbium complex, erbium (III) tris(8-hydroxyquinoline) (ErQ). The PL intensity at 1.55 µm was increased by three orders of magnitude by changing the photo-excited species from Er3+ to the organic ligand (Q). This strong enhancement was ascribable to ligand-sensitized PL based on the excited state energy transfer from Q to Er3+. We simultaneously detected up-conversion PL from Er3+ in the ultraviolet region. The up-conversion PL is emitted due to excited state absorption, which indicates that vacuum-deposited ErQ thin films are weak electron-phonon coupling systems.

THE FERMION-BOSON MAPPING APPLIED TO LAGRANGIAN MODELS FOR CHARGE-DENSITY-WAVES IN ONE-DIMENSIONAL SYSTEMS

We use the two-dimensional Fermion-Boson mapping to perform a field theory analysis of the effective Lagrangian model for incommensurate charge-density waves (ICDW) in one-dimensional systems. We consider an approach in which both the phase of the complex phonon field and the electron field are dynamical degrees of freedom contributing to the quantum dynamics and symmetry-related features of the ICDW phenomenon. We obtain the bosonized and fermionized versions of the effective electron–phonon Lagrangian. The phase of the phonon field and the phase of the bosonized chiral density of the electron field condense as a soliton order parameter, carrying neither the charge nor the chirality of the electron–phonon system, leading to a periodic sine-Gordon potential. The phonon field is fermionized in terms of a chiral fermionic condensate and the effective model is mapped into the chiral Gross–Neveu (GN) model with two Fermi field species. The linked electron–phonon symmetry of the ICDW system is mapped into the chiral symmetry of the GN model. Within the functional integral formulation, we obtain for the vacuum expectation value of the phonon field < ϕ > = 0 and < ϕ ϕ* > ≠ 0, due to the charge selection rule associated with the chiral electron–phonon symmetry. We show that the two-point correlation function of the phonon field satisfies the cluster decomposition property, as required by the chiral symmetry of the underlying GN model. The quantum description of the ICDW corresponds to charge transport through the lattice, due to the propagation of a "Goldstone mode" carrying the effective charge of the electron–phonon system, is accomplished by an electron–lattice energy redistribution. This accounts for a dynamical Peierls's energy gap generation.

THE PROPERTIES OF NONADIABATIC FLUCTUATIONS IN STRONGLY COUPLED ELECTRON–PHONON SYSTEMS WITH CORRELATED DISPLACEMENT AND SQUEEZING

A new variational ansatz for the coherent phonons with correlated displacement and squeezing, including interaction with electrons are used to study the properties of (i) the nonadiabatic phonon fluctuation on the ground state, (ii) the uncertainty principle, (iii) the phonon-staggered ordering, and (iiv) the charge-density wave order, of the systems due to fluctuations of the electron density in a coupled electron–phonon systems. The results obtained show that the correlation effect can lower the energy of the ground state of the systems, enhance the stabilization of the polaron and suppress the quantum increase of the classical polaron narrowing of electron band. Moreover, it add to the effects of nonadiabaticity on the minimum quantum uncertainty for the phonon coordinate by a strong coupling with the electron density for a large squeezing as compared with the adiabatic case and the uncorrelated case. Therefore, the new ansatz which can represent the correlation effects of displacement and squeezing is especially relevant for system with sufficiently large squeezing and strong coupling.

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.

EIGEN-FUNCTIONAL METHOD AND EIKONAL-TYPE EQUATIONS IN ONE-DIMENSIONAL STRONGLY CORRELATED ELECTRON SYSTEMS

Using eigen-functional method, we study one-dimensional strongly correlated electron systems with large momentum (2k F and/or 4k F ) transfer term(s), and demonstrate that this kind of problems ends in to solve the Eikonal-type equations, and these equations are universal, and independent of whether or not the system is integrable. In contrast to usual perturbation theory, this method is valid not only for weak electron interaction, but also for strong electron interaction. Comparing with exact solution of some integrable models, it can give correct results in linearization approximation. This method can also be used to study electron-phonon interaction systems, and two coupled spin chain (or quantum wire) systems.

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.

Electron–phonon coupling in degenerate silicon-on-insulator film probed using superconducting Schottky junctions

Energy flow rate in degenerate n-type silicon-on-insulator (SOI) film is studied at low temperatures. The electrons are heated above the lattice temperature by electric field and the electron temperature is measured via semiconductor–superconductor quasiparticle tunneling. The energy flow rate in the system is found to be proportional to T 5, indicating that electron–phonon relaxation rate and electron–phonon phase breaking rate are proportional to T 3. The electron–phonon system in the SOI film is in the “dirty limit” where the electron mean free path is smaller than the inverse of the thermal phonon wave vector.

The region of existence of the three-dimensional continuum bipolaron

The ranges of ɛ*/ɛ∞ and of the electron-phonon coupling constant in which the three-dimensional bipolaron exists are determined. The limits of these ranges correspond to the emergence of the first bound state of two polarons. The criteria for the first bound state to arise are found by solving an integral equation, which corresponds to a Schrodinger equation describing internal vibrations of a bipolaron. The Hamiltonian describing these vibrations is separated from the complete Hamiltonian of the electron-phonon system by using the Bogoliubov-Tyablikov method of canonical transformations of coordinates.

Normal quasiparticle scattering and kinetic effects in degenerate semiconductors

The influence of normal processes of electron-electron and phonon-phonon scattering on quasiparticle momentum relaxation in nonequilibrium electron-phonon systems of degenerate semiconductors is investigated. A system of kinetic equations is solved for the electron and phonon distribution functions, and the kinetic coefficients of a semiconductor are calculated in the linear approximation in the degeneracy parameter. The influence of normal scattering of quasiparticles on the electrical conductivity, thermopower, and heat conductivity of a degenerate semiconductor is analyzed. Redistribution of the phonon momentum in N processes within each branch of the vibrational spectrum, as well as among different branches, is taken into account.

Hierarchic Natures and Dynamics of Photoinduced Structural Phase Transition in Non-Degenerate Charge Density Wave States Via Successive Photoexcitations

We investigate the adiabatic and dynamical natures of the lattice relaxation of excitons in strongly coupled electron-phonon (e-ph) systems using the extended Peierls-Hubbard model, so as to clarify the possible mechanisms of the photoinduced structural phase transition (PISPT) via multi-photon. Focusing on the growth process of relaxed domains that is induced by multi-photoexcitation, we calculate the adiabatic potential energy surfaces relevant to the nonlinear lattice relaxations of excitons in this process. Calculated potentials lead to an essential model of a multi-stepwise potential-crossing (MSPC) system that is composed of many displaced harmonic oscillators as an elementary process of the domain growth in the strongly coupled e-ph systems. We also investigate the dynamical natures in such MSPC systems calculating the time-developments the excited wave packet in this system using the density operator. It is concluded from calculated results that the system possibly develops from the lowest-energy potential state to the higher ones by the effect of the photoexcitations followed by the lattice relaxations.

SUCCESSIVE STRUCTURAL CHANGES AND THEIR DYNAMICS IN MULTI-STEPWISED POTENTIAL-CROSSINGS SYSTEMS VIA MULTI-PHOTOEXCITATIONS

We investigate the dynamical nature in multi-stepwised potential-crossing systems which are proposed as an elementary process of the structural phase transition in the strongly coupled electron-phonon systems, in order to clarify the effects of multi-photoexcitations and lattice relaxations on the successive stuctural changes in this system. We calculate the time-developments of the density operator of this system both for the diabatic and adiabatic cases using an unified model Hamiltonian. It is concluded from calculated results that in the both cases the system develops from the lowest-energy potential state to the higher ones by the effects of the multi-photoexcitation together with the lattice relaxation. In the diabatic case, the photoexcitation is essential for the successive structural changes, because the structural change is not expected only by the weak electronic interaction between potentials. In the adiabatic case, on the other hand, the system changes from the lowest to the higher potential states going up through the adiabatic potential surface of the ground state with the help of the multi-photoexcitations.

Dynamical Peierls' energy gap generation in one-dimensional charge-density waves systems

Abstract Using bosonization methods we consider the Lagrangian model describing the electron–phonon system using a slowly-varying phonon amplitude approximation. The phase of the phonon field is fermionized and the effective model is mapped into the chiral Gross–Neveu model with two Fermi field species. The chiral density of the electron field and the phase of the phonon field condensate as a soliton order parameter. The incommensurate charge-density wave can be pictured as a collective excitation of the combined motion of both the electrons and lattice ions, accomplished by a dynamical electron–lattice energy redistribution (Peierls' energy gap generation).

Examination of the Validity of the Continued-Fraction-Based Theory of Cyclotron-Resonance Lineshape for Electron Systems Interacting with Acoustic Phonons

Time correlation functions are expanded in a hierarchical fractional form following Mori’s projection technique in a rigorous manner. Using this formula, detailed calculations are performed to obtain the cyclotron resonance lineshape function for an electron-phonon interaction system in both incoherent and coherent scattering regimes. We apply this formula to electron-acoustic phonon scattering systems. We carry out the calculation of the cyclotron resonance linewidths for purely two- and three-dimensional electrons in Ge and Si with an appropriate value of the fitting parameter and compare them. It is shown that, although the width increases with temperature in both cases, the width is smaller in two dimensions. This implies that the scattering is weaker in two dimensions. This is a physically reasonable result, and thus our result supports the validity of the theory.

The properties of quantum fluctuations in strongly coupled electron–phonon systems with correlated displacement and squeezing

Influences of the non-adiabatic phonon fluctuations on the ground state, and on the minimum uncertainty principle of phonons were investigated by introducing a new state-ansatz including correlation between the displacement and squeezing of the phonons in the strongly coupled electron–phonon systems. For a large squeezing, the correlation lowers, obviously, the energy of the ground state, and increases the binding energy of the polaron when compared with the uncorrelated case. Thus the stabilization of the polarons and the stability of the systems are all enhanced. The correlation was also found to suppress the quantum reduction of the classical narrowing of the polaron band, and to weaken the tunnelling effect of the polarons, and to enhance the quantum uncertainty for the phonon coordinate due to the coupling with the electron density fluctuation. Generally, the correlated effects and new ansatz introduced here were found to be relevant for a sufficiently large squeezing in the strongly and intermediately coupled electron–phonon systems.