Arnold resonances and quantum states

The dynamics of one electron interacting with a linear chain of heavy atoms bears a strong similarity with the propagation of a classical wave in a periodic non linear medium. Arnold resonances of the dynamical system play a central role. Some of the quantum states associated with these resonances are delocalized and contribute to phenomena such as Peierls dimerization while other ones are localized and are similar to the gap solitons of the classical wave theory, we call them Braggons. Complex Braggons containing several electrons inside the same localized profile are also described.     

Polaronic effects in asymmetric quantum wire: An all-coupling variational approach

An all-coupling variational calculation based on Lee-Low-Pines-Huybrechts (LLPH) theory is performed to study the ground state and the first excited state in an asymmetric polar semiconductor quantum wire that is valid for the entire range of the electron-phonon coupling constant and arbitrary confinement length. It is shown that the polaronic effects are very important and size dependent, if the effective width of the wire is reduced below a certain length scale. It is also shown that asymmetry in a quantum wire can be used as an extra parameter to increase the stability of the polaron. Finally the theory is applied to a realistic CdS quantum wire.     

Polaron formation and hopping conductivity in the Holstein-Hubbard model

On the basis of the Holstein-Hubbard model the formation of polarons at finite densities is investigated by means of a variational approach appropriate for describing squeezing and correlation effects. An effective Hubbard model for the polarons is derived, where the correlations are treated within the slave-boson saddlepoint approximation. For low enough phonon frequencies, with increasing coupling an abrupt self-trapping transition from light to heavy polarons is found. With increasing density the squeezing effect increases, and the transition is shifted to higher couplings. In the case of an effective Coulomb repulsion, the self-trapping transition is shifted to lower couplings with increasing Hubbard interaction, and the effective polaron mass below the transition is enhanced. In the heavy polaron regime, the frequency-dependent polaron hopping conductivity is calculated. There occur qualitative finite-density and correlation effects on the zero-temperature absorption spectrum which are discussed with respect to their possible relevance to the midinfrared absorption in high-T _c superconductors.     

Ground state description of bound polarons in parabolic quantum wires

The Feynman-Haken variational path integral theory is, for the first time, generalized to calculate the ground-state energy of an electron coupled simultaneously to a Coulomb potential and to a longitudinal-optical (LO) phonon field in parabolic quantum wires. It is shown that the polaronic correction to the ground-state energy is more sensitive to the electron-phonon coupling constant than the Coulomb binding parameter and monotonically stronger as the effective wire radius decreases. We apply our calculations to several semiconductor quantum wires and find that the polaronic correction can be considerably large. Received 16 November 1998     

Polaronic effects on the energy levels of a double donor impurity in quantum wells in the presence of a magnetic field

In the presence of a magnetic field the Hamiltonian of the single or double polaron bound to a helium-type donor impurity in semiconductor quantum wells (QWs) are given in the case of positively charged donor center and neutral donor center. The couplings of an electron and the impurity with various phonon modes are considered. The binding energy of the single and double bound polaron in Al_xlGa _1-xlAs/GaAs/Al_xrGa _1-xrAs QWs are calculated. The results show that for a thin well the cumulative effects of the electron-phonon coupling and the impurity-phonon coupling can contribute appreciably to the binding energy in the case of ionized donor. In the case of neutral donor the contribution of polaronic effects are not very important, however the magnetic field significantly modifies the binding energy of the double donor. The comparison between the binding energies in the case of the impurity placed at the quantum well center and at the quantum well edge is also given. Received 16 February 1999     

Dynamics of a quantum oscillator strongly and off-resonantly coupled with a two-level system

Beyond the rotating-wave approximation, the dynamics of a quantum oscillator interacting strongly and off-resonantly with a two-level system exhibit beatings, whose period equals the revival time of the two-level system. On a longer time scale, the quantum oscillator shows collapses, revivals and fractional revivals, which are encountered in oscillator observables like the mean number of oscillator quanta and in the two-level inversion population. Also the scattered oscillator field shows doublets with symmetrically displaced peaks.     

Magnetic transition and polaron crossover in a two-site single polaron model including double exchange interaction

A two-site double exchange model with a single polaron is studied using a perturbation expansion based on the modified Lang-Firsov transformation. The antiferromagnetic to ferromagnetic transition and the crossover from small to large polaron are investigated for different values of the antiferromagnetic interaction (J) between the core spins and the hopping (t) of the itinerant electron. Effect of the external magnetic field on the small to large polaron crossover and on the polaronic kinetic energy are studied. When the magnetic transition and the small to large polaron crossover coincide for some suitable range of J/t, the magnetic field has very pronounced effect on the dynamics of polarons. Received 1 June 2000     

Theory of photoinduced phase transitions in itinerant electron systems

Theoretical progress in the research of photoinduced phase transitions is reviewed with closely related experiments. After a brief introduction of stochastic evolution in statistical systems and domino effects in localized electron systems, we treat photoinduced dynamics in itinerant-electron systems. Relevant interactions are required in the models to describe the fast and ultrafast charge-lattice-coupled dynamics after photoexcitations. First, we discuss neutral-ionic transitions in the mixed-stack charge-transfer complex, TTF-CA. When induced by intrachain charge-transfer photoexcitations, the dynamics of the ionic-to-neutral transition are characterized by a threshold behavior, while those of the neutral-to-ionic transition by an almost linear behavior. The difference originates from the different electron correlations in the neutral and ionic phases. Second, we deal with halogen-bridged metal complexes, which show metal, Mott insulator, charge-density-wave, and charge–polarization phases. The latter two phases have different broken symmetries. The charge-density-wave to charge–polarization transition is much more easily achieved than the reverse transition. This is clarified by considering microscopic charge-transfer processes. The transition from the charge-density-wave to Mott insulator phases and that from the Mott insulator to metal phases proceed much faster than those between the low-symmetry phases. Next, we discuss ultrafast, inverse spin-Peierls transitions in an organic radical crystal and alkali-TCNQ from the viewpoint of intradimer and interdimer charge-transfer excitations. Then, we study photogenerated electrons in the quantum paraelectric perovskite, SrTiO₃, which are assumed to couple differently with soft-anharmonic phonons and breathing-type high-energy phonons. The different electron–phonon couplings result in two types of polarons, a “super-paraelectric large polaron” with a quasi-global parity violation, and an “off-center-type self-trapped polaron” with only a local parity violation. The former is equivalent to a charged and conductive ferroelectric domain, which greatly enhances both the quasi-static electric susceptibility and the electric conductivity. Finally, we outline the development of time-resolved X-ray diffraction experiments, which directly accesses the dynamics of electronic, atomic and molecular motions in photoexcited materials. They are extremely useful when a three-dimensional structural long-range order is established and changes the symmetry.     

A new approach to electron-electron interactions in strongly correlated systems at arbitrary spin-polarization and temperature

The uniform electron fluid is the reference model for density functional calculations. Even for this system, many-body perturbation theory, and related methods become questionable when the density parameter r_s exceeds unity. Hence, quantum Monte Carlo (QMC) simulation has been almost the only applicable method. We review a new approach, which uses a mapping of the quantum fluid to a classical Coulomb fluid, based on density-functional concepts. It is applicable at finite temperatures and arbitrary spin polarizations as well, and correctly recovers even the logarithmic terms in the exchange and correlations energies close to T=0. We show by detailed comparison with available QMC data that the method yields accurate pair-distribution functions, spin-dependent energies, static local-field factors, Landau parameter-based quantities like m∗ and g∗, for strongly coupled electron fluids.     

Effect of electron-phonon interaction on surface states in a ternary mixed crystal

A variational theory is proposed to study the surface states of electrons in a semi-infinite ternary mixed crystal, by taking the effect of electron-surface optical (SO) phonon interaction into account. The energy and the wave function of the electronic surface-states are calculated. The numerical results of the energies of the surface states of the polarons and the self-trapping energies are obtained as functions of the composition x and surface potential V₀ for several ternary mixed crystal materials. The results show that the electron-phonon interaction lowers the surface-state levels with the energies from several to scores of meV. It is also found that the self-trapping energy of the surface polaron has a minimum at some middle value of the composition x. It is indicated that the electron-phonon coupling effect can not be neglected. Received 4 January 1999 and Received in final form 7 January 2000     

Excitonic-vibronic coupled dimers: A dynamic approach

The dynamical properties of exciton transfer coupled to polarization vibrations in a two site system are investigated in detail. A fixed point analysis of the full system of Bloch-oscillator equations representing the coupled excitonic-vibronic flow is performed. For overcritical polarization a bifurcation converting the stable bonding ground state to a hyperbolic unstable state which is basic to the dynamical properties of the model is obtained. The phase space of the system is generally of a mixed type: Above bifurcation chaos develops starting from the region of the hyperbolic state and spreading with increasing energy over the Bloch sphere leaving only islands of regular dynamics. The behaviour of the polarization oscillator accordingly changes from regular to chaotic.     

Isotope effects on the electronic critical points of germanium: Ellipsometric investigation of the and transitions

Within the past years the optical excitations of electrons have been measured for semiconductor samples of different isotope compositions. The isotope shift observed have been compared with calculations of the effects of electron-phonon interaction on the electronic band structure. While qualitative agreement has been obtained, some discrepancies remain especially concerning the E₁ and transitions. We have remeasured the effect of isotope mass on the E₁ and transitions of germanium with several isotopic compositions. The results, obtained by means of spectroscopic ellipsometry, confirm that the real part of the gap self-energies induced by electron-phonon interaction is larger than found from band structure calculations, while the imaginary part agrees with those calculations, which are based on a pseudopotential band structure and a bond charge model for the lattice dynamics. Our results agree with predictions based on the measured temperature dependence of the gaps. We compare our data for E₁ and with results for the lowest direct (E₀) and indirect (E_g) gaps. The measured values of and increase noticeably with increasing isotope mass. Similar effects have been observed in the temperature dependence of in and . A microscopic explanation for this effect is not available. Received: 6 March 1998 / Revised: 27 April 1998 / Accepted: 15 May 1998     

Jahn-Teller transition and electron-phonon interaction in Cr-doped manganites Sr0.9Ce0.1Mn1−yCryO3

Cr-doped manganites Sr_0.9Ce_0.1Mn_1−yCr_yO₃ (y=0, 0.05, and 0.10) have been systematically investigated by X-ray, magnetic, transport, and elastic properties measurements. For parent compound Sr_0.9Ce_0.1MnO₃, it undergoes a metal-insulator (M-I) transition at 318 K, which is suggested to originate from a first-order structural transition accompanied by Jahn-Teller (JT) transition. With increasing Cr doping content, the JT transition temperature decreases. The Cr doping suppresses the antiferromagnetic (AFM) state and makes the system spin-glass (SG) behavior at low temperatures. In the vicinity of JT transition temperatures, the softening of Young's modulus originating from the coupling of the orbital (quadrupolar) moment of the e_g orbital of Mn³⁺ ion to the elastic strain has been observed. The anomalous Young's modulus properties imply the electron-phonon coupling due to the JT effect may play an important role in the system.     

Effective electron Hamiltonian for a quasi one-dimensional system. The (TMTSF)2X and the (TMTTF)2X systems

In this paper we have introduced a variational approach to investigate the ground state of a model which includes both the Holstein electron-phonon interaction and the extended Hubbard electron-electron interaction. We have considered a variational state for the phonon subsystem which generalizes the previous used forms. This state allows to take into account the possibility of extended phonon mediated correlations. The effective electron Hamiltonian, which we have obtained, includes first and second neighbor electron-electron interaction terms. We have treated exactly, through a Lanczos method, this effective model in the one-dimensional case. We have applied our method to two Bechgaard salts and in these cases we have estimated the correlation parameters. We have shown that the introduction of electron-phonon interaction allows an estimate of the on site U and nearest-neighbor V Coulomb repulsion, which are in agreement with the experimental optical spectra of the above mentioned two compounds. Received: 30 October 1997 / Revised: 28 January 1998 / Accepted: 10 April 1998     

The physical origin of the electron-phonon vertex correction

In the theory of nonadiabatic superconductivity several features are governed by the electron-phonon vertex correction which has a complex structure both in momentum and frequency. We derive a physical interpretation of such nonadiabatic effects that permits to link them to specific material properties. We show how the nonadiabatic vertex correction can be decomposed into two terms with different physical origins. In particular, the first term describes the lattice polarization induced by the electrons and it is essentially a single-electron process whereas the second term is governed by the particle-hole excitations due to the exchange part of the phonon-mediated electron-electron interaction. We show that by weakening the influence of the exchange interaction the vertex takes mostly positive values giving rise to an enhanced effective coupling in the scattering with phonons. This weakening of the exchange interaction can be obtained by lowering the density of the electrons, or by considering only long-ranged (small q) electron-phonon couplings. Received 23 November 1998 and Received in final form 22 January 1999     

Electron-phonon effects on Stark shifts of excitons in parabolic quantum wells: Fractional-dimension variational approach

Electron-phonon effects on Stark shifts of excitons in parabolic quantum wells are studied theoretically by using a fractional dimension method in combination with a Lee-Low-Pines-like transformation and a perturbation theory. The numerical results for the exciton binding energies and electron-phonon contributions to the binding energies as functions of the well width and the electric field in the Al_0.3Ga_0.7As parabolic quantum well structure are obtained. It is shown that both exciton binding energy and electron-phonon contributions have a maximum with increasing the well width. The binding energy and electron-phonon contribution decrease significantly with increasing the electric-field strength, in special in the wide-well case.     

De-excitation process and hot luminescence in the FA(type I) center in KCl:Na

The de-excitation process of F_A(type I) centers in KCl:Na has been investigated by measuring the hot luminescence spectrum from optically excited F_A centers with time-resolved spectroscopy. The experimental results are analyzed by using a model that describes a time evolution of the phonon wave packet during the vibronic relaxation process from the Franck-Condon state to a relaxed excited state. From the analysis of the experimental data, information on the vibronic mixing between 2p and 2s states, whose magnitude varies during the relaxation process, and the adiabatic potential energy curves of 2s and 2p states are extracted. The present results are compared with the already known ones of the F_A(type II) centers.     

Polaron effects on excitons in parabolic quantum wells: fractional-dimension variational approach

Polaron effects on excitons in parabolic quantum wells are studied theoretically by using a variational approach with the so-called fractional dimension model. The numerical results for the exciton binding energies and longitudinal-optical phonon contributions in GaAs/Al_0.3Ga_0.7As parabolic quantum well structures are obtained as functions of the well width. It is shown that the exciton binding energies are obviously reduced by the electron (hole)-phonon interaction and the polaron effects are un-negligible. The results demonstrate that the fractional-dimension variational theory is effectual in the investigations of excitonic polaron problems in parabolic quantum wells.     

Collective quantum tunneling of strongly correlated electrons in commensurate mesoscopic rings

We present a new effect that is possible for strongly correlated electrons in commensurate mesoscopic rings: the collective tunneling of electrons between classically equivalent configurations, corresponding to ordered states possessing charge and spin density waves (CDW, SDW) and charge separation (CS). Within an extended Hubbard model at half filling studied by exact numerical diagonalization, we demonstrate that the ground state phase diagram comprises, besides conventional critical lines separating states characterized by different orderings (e.g. CDW, SDW, CS), critical lines separating phases with the same ordering (e.g. CDW-CDW) but with different symmetries. While the former also exist in infinite systems, the latter are specific for mesoscopic systems and directly related to a collective tunnel effect. We emphasize that, in order to construct correctly a phase diagram for mesoscopic rings, the examination of CDW, SDW and CS correlation functions alone is not sufficient, and one should also consider the symmetry of the wave function that cannot be broken. We present examples demonstrating that the jumps in relevant physical properties at the conventional and new critical lines are of comparable magnitude. These transitions could be studied experimentally e.g. by optical absorption in mesoscopic systems. Possible candidates are cyclic molecules and ring-like nanostructures of quantum dots. Received 27 November 2000