Renormalization of the electron-phonon interaction: a reformulation of the BCS-gap equation

A recently developed renormalization approach is used to study the electron-phonon coupling in many-electron systems. By starting from an Hamiltonian which includes a small gauge symmetry breaking field, we directly derive a BCS-like equation for the energy gap from the renormalization approach. The effective electron-electron interaction for Cooper pairs does not contain any singularities. Furthermore, it is found that phonon-induced particle-hole excitations only contribute to the attractive electron-electron interaction if their energy difference is smaller than the phonon energy.     

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     

Two-site two-electron generalized Hubbard-Holstein model: a perturbation study

The two-site two-electron generalized Hubbard-Holstein model is studied within a perturbation method based on a variational phonon basis obtained through the modified Lang-Firsov (MLF) transformation. The ground-state wave function and the energy are found including up to the seventh and eighth order of perturbation, respectively. The convergence of the perturbation corrections to the ground state energy, as well as to the correlation functions, are investigated. The kinetic energy and the correlation functions involving charge and lattice deformations are studied as a function of electron-phonon(e-ph) coupling and electron-electron interactions for different values of the adiabaticity parameter. The simultaneous effect of the e-ph coupling and Coulomb repulsion on the kinetic energy shows interesting features.     

Specific heat jump in BCS superconductors

An exact analytical expression for the specific heat jump at the critical temperature T_c has been obtained directly from the BCS gap equation for any shape of the energy dependent electronic density of states (DOS). We consider a model which takes into consideration electron-electron repulsion, formulated in the Hubbard model along with the electron-electron attraction due to electron-phonon interaction in the BCS formalism. We have analyzed this expression for constant as well as for the Lorentzian forms of DOS. It is shown that the constant DOS in the simple BCS theory cannot explain the large values of , found in some superconductors. The specific heat versus temperature curve has been found to have a peak, similar to that of Eliashberg theory of superconductivity. The influence of repulsive interaction is very small and occurs mainly at higher temperatures. Received: 26 January 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     

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     

Electron correlations and quantum lattice vibrations in strongly coupled electron-phonon systems: A variational slave boson approach

We investigate the ground-state properties of the two-dimensional Hubbard model with an additional Holstein-type electron-phonon coupling on a square lattice. The effects of quantum lattice vibrations on the strongly correlated electronic system are treated by means of a variational squeezed-polaron wave function proposed by Zheng, where the possibility of static (frozen) phonon-staggered ordering is taken into account. Adapting the Kotliar-Ruckenstein slave boson approach to the effective electronic Hamiltonian, which is obtained in the vacuum state of the transformed phonon subsystem, our theory is evaluated within a two-sublattice saddle-point approximation at arbitrary band-filling over a wide range of electron-electron and electron-phonon interaction strengths. We determine the order parameters for long-range charge and/or spin ordered states from the self-consistency conditions for the auxilary boson fields, including an optimization procedure with respect to the variational displacement, polaron and squeezing parameters. In order to characterize the crossover from the adiabatic (=0) to the nonadiabatic (=) regime, the frequency dependencies of these quantities are studied in detail. In the predominant charge (spin) ordered phases the static Peierls dimerization (magnetic order) is strongly reduced with increasing . As the central result we present the slave boson ground-state phase diagram of the Holstein-Hubbard model for finite phonon frequencies.     

Electron-phonon scattering in an asymmetric double barrier resonant tunneling structure

We calculate the electron-phonon scattering rate for an asymmetric double barrier resonant tunneling structure based on dielectric continuum theory, including all phonon modes, and show that interface phonons contribute much more to the scattering rate than do bulk-like LO phonons for incident energies which are approximately within an order of magnitude of the Fermi energy. The maximum scattering rate occurs for incident electron energies near the quantum well resonance. Subband nonparabolicity has a significant influence on electron-phonon scattering in these structures. We show that the relaxation time is comparable to the dwell time of electrons in the quantum well for a typical resonant tunneling structure. Received: 23 December 1997 / Revised: 24 March 1998 / Accepted: 9 March 1998     

Intermediate phase of the one dimensional half-filled Hubbard-Holstein model

We present a numerical study of the Hubbard-Holstein model in one dimension at half filling, including finite-frequency quantum phonons. At half filling, the effects of the electron-phonon and electron-electron interactions compete with the Holstein phonon coupling acting as an effective negative Hubbard on-site interaction U that promotes on-site electron pairs and a Peierls charge-density wave state. Most previous work on this model has assumed that only Peierls or Mott phases are possible at half filling. However, there has been speculation that a third metallic phase exists between the Peierls and Mott phases. We confirm the intermediate phase, and show that the Luttinger liquid correlation exponent K(rho) >1 in this region, indicating dominant superconducting pair correlations. We explore the full phase diagram as a function of Hubbard U, phonon coupling constant, and phonon frequency.     

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     

-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     

Raman study of orbital mediated multiphonons in RMnO3 (R = Pr,Sm,Eu,Tb,Y)

We have studied RMnO₃ manganites (R = Pr, Sm, Eu, Tb, Y) Raman excitations in the 200–2800 cm^-1 range as a function of temperature. Combinations of phonon energies are observed up to the fourth order, indicating the presence of electron-phonon coupling. In comparison to Γ-point phonon combinations, double phonon excitations appear to be blue shifted in large size rare earth ion compounds. The phonon combination intensities decrease rapidly with their increasing order, confirming other studies which conclude that the electron-phonon coupling is not as strong as supposed in the localized limit. Moreover, different intensity order dependences are observed between the phonon combination and the so-called Jahn-Teller mode. These effects are better described in the orbiton-phonon coupling scheme.     

Similarity renormalization of the electron-phonon coupling

We study the problem of the phonon-induced electron-electron interaction in a solid. Starting with a Hamiltonian that contains an electron-phonon interaction, we perform a similarity renormalization transformation to calculate an effective Hamiltonian. Using this transformation singularities due to degeneracies are avoided explicitly. The effective interactions are calculated to second order in the electronphonon coupling. It is shown that the effective interaction between two electrons forming a Cooper pair is attractive in the whole parameter space. For a simple Einstein model we calculate the renormalization of the electronic energies and the critical temperature of superconductivity.     

Van der Waals interaction between flux lines in high- superconductors: A variational approach

In pure anisotropic or layered superconductors thermal fluctuations induce a van der Waals attraction between flux lines. This attraction together with the entropic repulsion has interesting consequences for the low field phase diagram; in particular, a first order transition from the Meissner phase to the mixed state is induced. We introduce a new variational approach that allows for the calculation of the effective free energy of the flux line lattice on the scale of the mean flux line distance a, which is based on an expansion of the free energy around the regular triangular Abrikosov lattice. Using this technique, the low field phase diagram of these materials may be explored. The results of this technique are compared with a recent functional RG treatment of the same system. Received: 25 June 1996 / Revised: 18 August 1998 / Accepted: 21 August 1998     

Insulator-metal transition in biased finite polyyne systems

A method for the study of the electronic transport in strongly coupled electron-phonon systems is formalized and applied to a model of polyyne chains biased through metallic Au leads. We derive a stationary non equilibrium polaronic theory in the general framework of a variational formulation. The numerical procedure we propose can be readily applied if the electron-phonon interaction in the device hamiltonian can be approximated as an effective single particle electron hamiltonian. Using this approach, we predict that finite polyyne chains should manifest an insulator-metal transition driven by the non-equilibrium charging which inhibits the Peierls instability characterizing the equilibrium state.     

电—声系统中的费密超导态

基于推广的电－声相互作用模型，考虑到电子的强关联作用，提出了电子算符的玻戈留玻夫近似，导出了声子在电子场中受到的有效作用；证明了波矢相反的纵声子通过交换虚电子能产生一个有效的吸引力，从而构成带有一个电子的声子对。在适当的声子数密度下，形成稳定的费密高温超导态。     

电-声系统中的费密超导态

基于推广的电－声相互作用模型，考虑到电子的强关联作用，提出了电子算符的玻戈留玻夫近似，导出了声子在电子场中受到的有效作用；证明了波矢相反的纵声子通过交换虚电子能产生一个有效的吸引力，从而构成带有一个电子的声子对。在适当的声子数密度下，形成稳定的费密高温超导态。     

Small bipolarons in the 2-dimensional Holstein-Hubbard model. II. Quantum bipolarons

We study the effective mass of the bipolarons and essentially the possibility to get both light and strongly bound bipolarons in the Holstein-Hubbard model and some variations in the vicinity of the adiabatic limit. Several approaches to investigate the quantum mobility of polarons and bipolarons are proposed for this model. First, the quantum fluctuations are treated as perturbations of the mean-field (or adiabatic) approximation of the electron-phonon coupling in order to calculate the bipolaron bands. It is found that the bipolaron mass generally remains very large except in the vicinity of the triple point of the phase diagram (see [1]), where the bipolarons have several degenerate configurations at the adiabatic limit (single site (S0), two sites (S1) and quadrisinglet (QS)), while the polarons are much lighter. This degeneracy reduces the bipolaron mass significantly. Next we improve this result by variational methods (modified Toyozawa Exponential Ansatz or TEA) valid for larger quantum perturbations away from the adiabatic limit. We first test this new method for the single polaron. We find that the triple point of the phase diagram is washed out by the lattice quantum fluctuations which thus suppress the light bipolarons. Further improvements of the method by hybridization of several TEA states do not change this conclusion. Next we show that some model variations, for example a phonon dispersion may increase the stability of the (QS) bipolaron against the quantum lattice fluctuations. We show that the triple point of the phase diagram may be stable to quantum lattice fluctuations and a very sharp mass reduction may occur, leading to bipolaron masses of the order of 100 bare electronic mass for realistic parameters. Thus we argue that such very light bipolarons could condense as a superconducting state at relatively high temperature when their interactions are not too large, that is, their density is small enough. This effect might be relevant for understanding the origin of the high superconductivity of doped cuprates far enough from half filling. Received 15 September 1999     

Local anharmonic vibrations strong correlations and superconductivity: A quantum simulation study

We investigate the importance of local anharmonic vibrations of the bridging oxygen in the copper oxide high-T _c materials in the context of superconductivity. For the numerical simulation we employ the projector quantum Monte Carlo method to study the ground state properties of the coupled electron-phonon system. The quantum Monte Carlo simulation allows an accurate treatment of electronic interactions which investigates the influence of strong correlations on superconductivity mediated by additional quantum degrees of freedom. As a generic model for such a system, we study the two-dimensional single band Hubbard model coupled to local pseudo spins (bridging oxygen), which mediate an effective attractive electron-electron interaction leading to superconductivity. The results are compared to those of an effective negativeU model.     

The phonon effects on the impurity states in cylindrical quantum wire with a finite confining potential

The variational method and the effective mass approximation are applied to calculate the binding energies of the hydrogenic impurity states in a cylindrical quantum wire with finite deep potential well. The phonon effects on the impurity states are considered by taking both the couplings of the electron-phonon and the impurity ion-phonon into account. The numerical results for the GaAs cylindrical quantum wire are given and discussed. It is found that the ion-phonon interaction reduces the impurity binding energy and supplies key contribution to the energy shift, but the electron-phonon coupling enhances the binding energy less. Longitudinal optical (LO) phonons play more important role than interface optical (IO) phonons in the impurity potential screening. The polaron effect caused by LO phonons is more important when the wire is thinner, otherwise the LO phonons are dominant for the thicker wires.