Probing electron-phonon coupling in high-Tc superconductors by site-selective isotope substitution

We consider changes in the electron-phonon coupling in high-T _c cuprates caused by site-selective oxygen isotope substitution. Contrary to the total substitution, the site-selective replacement influences the coupling constant for each phonon mode due to the induced changes in the phonon eigenvectors. The relative changes for some modes can be larger than 100%. The measured properties sensitive to these changes are discussed. Received 9 August 2001 and Received in final form 11 January 2002     

Quantum adiabatic polarons by translationally invariant perturbation theory

The translationally invariant diagrammatic quantum perturbation theory (TPT) is applied to the polaron problem on the 1D lattice, modeled through the Holstein Hamiltonian with the phonon frequency ω₀, the electron hopping t and the electron-phonon coupling constant g. The self-energy diagrams of the fourth-order in g are calculated exactly for an intermittently added electron, in addition to the previously known second-order term. The corresponding quadratic and quartic corrections to the polaron ground state energy become comparable at t/ω₀>1 for g/ω₀∼(t/ω₀) ^1/4 when the electron self-trapping and translation become adiabatic. The corresponding non adiabatic/adiabatic crossover occurs while the polaron width is large, i.e. the lattice coarsening negligible. This result is extended to the range (t/ω₀)^1/2>g/ω₀>(t/ω₀)^1/4>1 by considering the scaling properties of the high-order self-energy diagrams. It is shown that the polaron ground state energy, its width and the effective mass agree with the results found traditionally from the broken symmetry side, kinematic corrections included. The Landau self-trapping of the electron in the classic self-consistent, localized displacement potential, the restoration of the translational symmetry by the classic translational Goldstone mode and the quantization of the polaronic translational coordinate are thus all encompassed by a quantum theory which is translationally invariant from the outset. This represents the first example, open to various generalizations, of the capability of TPT to hold through the adiabatic symmetry breaking crossover. Plausible arguments are also given that TPT can describe the g/ω₀>(t/ω₀)^1/2 regime of the small polaron with adiabatic or non-adiabatic translation, i.e., that TPT can cover the whole g/ω₀, t/ω₀ parameter space of the Holstein Hamiltonian.     

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     

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     

One-dimensional moving polarons with extended coherent states

The general properties of one-dimensional large Fr?hlich polarons in motion are investigated with the previous extended coherent states where two-phonon correlations are considered. As a result, the polaron energy, velocity, effective mass, and average number of virtual phonons as a function the polaron total momentum are evaluated in a wide range of the coupling constant. In addition, rich information about virtual phonons emitted by the electron in motion is obtained. More importantly, some intrinsic features of 1D moving polarons are presented for the first time, which may also be suited to moving polarons in more than one dimensions. Received: 23 October 1997 / Revised and Accepted: 27 January 1998     

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     

Synchronization of underdamped Josephson-junction arrays

Our recent experiments show that arrays of underdamped Josephson junctions radiate coherently only above a threshold number of junctions switched onto the radiating state. For each junction, the radiating state is a resonant step in the current-voltage characteristics due to the interaction between the junctions in the array and an electromagnetic cavity. Here we show that a model of a one-dimensional array of Josephson junctions coupled to a resonator can produce many features of the coherent be havior above threshold, including coherent radiation of power and the shape of the array current-voltage characteristic. The model also makes quantitative predictions about the degree of coherence of the junctions in the array. However, in this model there is no threshold; the experimental below-threshold region behavior could not be reproduced.Received: 11 April 2003, Published online: 23 July 2003PACS: 74.50.+r Tunneling phenomena; point contacts, weak links, Josephson effects - 85.25.-j Superconducting devices     

Resonant Raman scattering in the superconducting cuprates: Frozen-phonon versus perturbational approach

We consider in detail Raman scattering by vibration of the apical oxygen ions in the RBa₂Cu₃O₇ superconducting cuprates. The scattering intensity is very sensitive to the ratio of diagonal and off-diagonal matrix elements of electron-phonon coupling, bandstructure, and carrier concentration. Our results show a large quantitative difference between the results of frozen-phonon and perturbational approach to the Raman process. The discrepancy becomes especially large when interband transitions to the states near the Fermi level are close to resonance with the incident light. The calculation of phonon-induced ion charge fluctuations shows an analogous discrepancy. The reason for these effects is the possibility of carrier redistribution between different parts of the Fermi surface arising in the frozen-phonon approximation. Our results show that Raman scattering in superconducting superlattices is very sensitive to the properties of the states near the Fermi level. For this reason experiments performed on the superlattices can help to resolve the discrepancy. Received 8 December 1999     

-wave nonadiabatic superconductivity

The inclusion of nonadiabatic corrections to the electron-phonon interaction leads to a strong momentum dependence in the generalized Eliashberg equations beyond Migdal's limit. For a s-wave symmetry of the order parameter, this induced momentum dependence leads to an enhancement of when small momentum transfer is dominant. Here we study how the d-wave symmetry affects the above behavior. We find that the nonadiabatic corrections depend only weakly on the symmetry of the order parameter provided that only small momentum scatterings are allowed for the electron-phonon interaction. In this situation, We show that also for a d-wave symmetry of the order parameter, the nonadiabatic corrections enhance . We also discuss the possible interplay and crossover between s- and d-wave depending on the material's parameters. Received 12 May 2000     

The stability of magnetobipolarons in low-dimensional systems

We investigate the stability condition of large bipolarons confined in a parabolic potential containing certain parameters and a uniform magnetic field. The variational wave function is constructed as a product form of electronic parts, consisting of center of mass and internal motion, and a part of coherent phonons generated by Lee-Low-Pines transformation from the vacuum. An analytical expression for the bipolaron energy is found, from which the ground and excited-state energies are obtained numerically by minimization procedure. The bipolaron stability region is determined by comparing the bipolaron energy with those of two separate polarons, which is already calculated within the same approximation. It is shown that the results obtained for the ground state energy of bipolarons reduce to the existing works in zero magnetic field. In the presence of a magnetic field, the stability of bipolarons is examined, for three types of low-dimensional system, as function of certain parameters, such as the magnetic-field, the electron-phonon coupling constant, Coulomb repulsion and the confinement strength. Numerical solutions for the energy levels of the ground and first excited states are examined as functions of the same parameters. Received 7 March 2002 and Received in final form 22 April 2002 Published online 25 June 2002     

Next-nearest neighbor interaction and localized solutions of polymer chains

We study localization in polymer chains modeled by the nonlinear discrete Schr?dinger equation (DNLS) with next-nearest-neighbor (n-n-n) interaction extending beyond the usual nearest-neighbor exchange approximation. Modulational instability of plane carrier waves is discussed and it is shown that localization gets amplified under the influence of an enhanced interaction radius. Furthermore, we construct exact localized solitonlike solutions of the n-n-n interaction DNLS. To this end the stationary lattice system is cast into a nonlinear map. The homoclinic orbits of unstable equilibria of this map are attributed to standing solitonlike solutions of the lattice system. We note that in comparison with the standard next-neighbor interaction DNLS which bears only one type of static soliton-like states (either staggering or unstaggering) the one with n-n-n interaction radius can support unstaggering as well as staggering stationary localized states with frequencies lying above respectively below the linear band. Generally, the stronger the n-n-n interaction on the DNLS lattice the smaller are the maximal amplitudes of the standing solitonlike solutions and the less rapid are their exponential decays. Received 4 October 2000     

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     

Imperfect nesting and Peierls instability for a two-dimensional tight-binding model

Based on a half-filled two-dimensional tight-binding model with nearest-neighbour and next nearest-neighbour hopping the effect of imperfect Fermi surface nesting on the Peierls instability is studied at zero temperature. Two dimerization patterns corresponding to a phonon vector (π,π) are considered. It is found that the Peierls instability will be suppressed with an increase of next nearest-neighbour hopping which characterizes the nesting deviation. First and second order transitions to a homogeneous state are possible. The competition between the two dimerized states is discussed. Received 22 December 2000     

A study of Peierls instabilities for a two-dimensional t-t' model

In this paper we study Peierls instabilities for a half-filled two-dimensional tight-binding model with nearest-neighbour hopping t and next nearest-neighbour hopping t' at zero and finite temperatures. Two dimerization patterns corresponding to the same phonon vector (π,π) are considered to be realizations of Peierls states. The effect of imperfect nesting introduced by t' on the Peierls instability, the properties of the dimerized ground state, as well as the competition between two dimerized states for each t' and temperature T, are investigated. It is found: (i). The Peierls instability will be frustrated by t' for each of the dimerized states. The Peierls transition itself, as well as its suppression by t', may be of second- or first-order. (ii). When the two dimerized states are considered jointly, one of them will dominate the other depending on parameters t' and T. Two successive Peierls transitions, that is, the system passing from the uniform state to one dimerized state and then to the other may take place with decrease of temperature. Implications of our results to real materials are discussed. Received 31 July 2001     

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     

Coherent and incoherent phonon processes in artificial atoms

Carrier-phonon interaction in semiconductor quantum dots leads to three classes of phenomena: coherent effects (spectrum reconstruction) due to the nearly-dispersionless LO phonons, incoherent effects (transitions) induced by acoustical phonons and dressing phenomena, related to non-adiabatic, sub-picosecond excitation. Polaron spectra, relaxation times and dressing-related decoherence rates are calculated, in accordance with experiment. Received 30 August 2002 / Received in final form 25 November 2002 Published online 28 January 2003     

Polarized infrared reflectivity study of an oriented ceramic of Bi 2 Sr 2 Ca 2 Cu 3 O 10 + δ (Bi-2223)

The reflectivity spectra of an oriented ceramic of Bi-2223 has been investigated by polarized infrared reflectivity spectroscopy in the energy range 0.005-2.2 eV. It is shown that the data for the polarization parallel to the c axis cannot be fitted with a one-component Drude or extended-Drude model. The conductivity spectrum is then obtained from the best fit of a “double-damping Drude” model to reflectivity spectra, itself derived from the factorized form of the dielectric function, and by a Kramers-Kronig inversion as well. The data and their analysis give a new insight of the 2D character of the system. Received 26 April 2001 and Received in final form 28 August 2001     

Interface phonon assisted transition in double quantum well

A detailed calculation of interface phonon assisted electron intersubband transition in double GaAs/AlGaAs quantum well structure is presented. Our calculation concentrates on the lowest two subbands which can be designed to be in resonance with a given interface phonon mode. Various phonon mode profiles display quasi-symmetric or quasi-antisymmetric shapes. The quasi-antisymmetric phonon modes give rise to much larger transition rates than those assisted by quasi-symmetric ones. The transition rate reaches a maximum when the subband separation coincides with a given phonon mode energy. The calculation procedure presented here can be easily applied to the design and simulation of other low dimensional semiconductor structures, such as quantum cascade lasers. Received 22 December 2002 Published online 23 May 2003 RID="a" ID="a"e-mail: bhwu@263.net     

Interface polarons in a realistic heterojunction potential

The ground states of interface polarons in a realistic heterojunction potential are investigated by considering the bulk and the interface optical phonon influence. A self-consistent heterojunction potential is used and an LLP-like method is adopted to obtain the polaron effect. The numerical computation has been done for the Zn_1-xCd_xSe/ZnSe system to obtain the polaron ground state energy, self energy and effective mass parallel to the interface. A simplified coherent potential approximation is developed to obtain the parameters of the ternary mixed crystal and the energy band offset of the heterojunction. It is found that at small Cd concentration the bulk longitudinal optical phonons give the main contribution for lower areal electron densities, whereas the interface phonon contribution is dominant for higher areal electron densities. The interface polaron effect is weaker than the effect obtained by the three dimensional bulk phonon and by the two dimensional interface phonon models. Received 17 September 1998