Effective Hamiltonian for HTSC cuprates taking into account electron-phonon interaction in the strong-correlation regime

Electron-phonon interaction is sequentially derived from a realistic p-d multiband model for the cuprates under conditions of strong electron correlations. The electronic structure is described using the representation of the Hubbard X operators in a generalized tight-binding method. Dependences of the diagonal and off-diagonal (on lattice sites) matrix elements of electron-phonon interaction on the wavevectors are found for three phonon modes, namely, breathing, apical breathing, and bending modes. The interactions of the breathing and bending modes with electrons are shown to contribute to the formation of kinks in the (0; 0)-(π; π) and (0; 0)-(π; 0) directions, respectively. A low-energy t-J* model with phonons is developed; apart from electron-phonon interaction, it also includes spin-phonon interaction. The elimination of phonons gives an effective electron-electron interaction that depends on the occupation number of a multielectron term and on the carrier concentration due to strong electron correlations.     

Thermodynamics of phonon-stabilized Fermi distributions with application to uranium

Since phonons are built on the free energy of electrons, their frequencies can be altered by thermal electronic excitations, implying that thermal electronic excitations can alter the phonon entropy. The effect of this extra phonon entropy on electronic distribution functions and thermodynamic properties is calculated in the limit of classical vibrations. The phonon entropy stabilizes electrons above the Fermi level by more than the usual k _B T. The thermodynamic coupling of electron and phonon degrees of freedom allows far more heat capacity than in equivalent independent systems. The method developed is used to explain uranium data from the literature.     

Effects of electric field and size on the electron-phonon interaction in a spherical quantum dot with impurity

The effects of electric field and size on the electron-phonon interaction with an on-center impurity in a Zn_1?x Cd _x Se/ZnSe spherical quantum dot are studied, taking into account the interactions with confined, half-space and surface optical phonons. In addition, the interaction between impurity and phonons has also been considered. The results show that the electron-confined, electron-half-space, and electron-surface optical phonon interaction energies are all negative. The electron-confined optical phonon interaction energy is weakened by the electric field, but the electron-half-space and electron-surface optical phonon interaction energies are strengthened by it. In particular, the electron-surface optical phonon interaction depends strongly on the electric field, and it will vanish when the electric field is absent. It is also found that the electron-confined optical phonon interaction and electron-impurity “exchange” interaction energies reach a peak values as the quantum dot radius increases and then gradually decrease, but the electron-half-space optical phonon interaction energy exponentially quickly approaches 0 as the quantum dot radius increases.     

Raman spectra of IVB and VIB transition metal disulfides using laser energies near the absorption edges

In this paper, we present Raman spectra of ZrS₂, HfS₂, MoS₂ and WS₂ using laser energies near the energies of the absorption edges. The Raman spectra probe the properties of the first-excited electronic state and the nature of the electron-phonon coupling. The spectra of the IVB disulfides are independent of the laser excitation energy, suggesting weak electron-phonon interaction. In contrast, additional Raman bands appear in the spectra of the VIB disulfides as the laser energy approaches the band gap energy. The new modes in the spectra of MoS₂ and WS₂ cannot be assigned as first-order processes nor as combination bands of the phonons with zero momentum. The resonance Raman scattering of MoS₂ is analyzed in terms of second-order scattering due to the coupling of phonon modes of nonzero momentum with an electronic transition associated with excitonic states.     

Bosonization of coupled electron-phonon systems

We calculate the single-particle Green’s function of electrons that are coupled to acoustic phonons by means of higher dimensional bosonization. This non-perturbative method is not based on the assumption that the electronic system is a Fermi liquid. For isotropic threedimensional phonons we find that the long-range part of the Coulomb interaction cannot destabilize the Fermi liquid state, although for strong electron-phonon coupling the quasi-particle residue is small. We also show that Luttinger liquid behavior in three dimensions can be due to quasi-one-dimensional anisotropy in the electronic band structure or in the phonon frequencies.     

Electron—Phonon Interaction,Phonon and Electronic Structures of Layered Electride Ca2N

The phonon and electronic properties, the Eliashberg function and the temperature dependence of resistance of electride Ca₂N are investigated by the DFT-LDA (density functional theory in local density approximation) plane-wave method. The phonon dispersion, the partial phonon density of states and the atomic eigenvectors of zero-center phonons are studied. The electronic band dispersion and partial density of states conclude that Ca₂N is a metal and the Ca 3p, 4s and N 2p orbitals are hybridized. For the analysis of an electron-phonon interaction and its contribution of the Eliashberg function to resistance was calculated and a temperature dependence of resistance due to electron-phonon interaction was found.

     

Second order resonant Raman scattering at the E1 and E1 + Δ1 edges of germanium

The resonance of the 2TO phonon second order Raman band of germanium was investigated in the vicinity of the E₁, E₁ + Δ₁ gaps. The peak reported earlier for 2TO phonons at Γ is interpreted as due to a resonant process of the iterative type, involving two first order electron-phonon vertices. The rest of the 2TO band is interpreted as a process involving a second order electron-two phonon interaction vertex. From these measurements three phonon coupling constants for the electron-two phonon interaction are obtained.     

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 importance of electron correlation in graphene and hydrogenated graphene

Local density approximation (LDA) and Green function effective Coulomb (GW) calculations are performed to investigate the effect of electronic correlations on the electronic properties of both graphene and graphane. The size of band gap in graphane increases from 3.7 eV in LDA to 4.9 eV in GW approximation. By calculating maximally localized Wannier wave functions, we evaluate the necessary integrals to get the Hubbard U and the exchange J interaction from first principles for both graphene and graphane. Our ab-initio estimates indicate that in the case of graphene, in addition to the hopping amplitude t ～ 2.8 eV giving rise to the Dirac nature of low lying excitations, the Hubbard U value of ～8.7 eV gives rise to a super-exchange strength of J _AFM ～ 3.5 eV. This value dominates over the direct (ferromagnetic) exchange value of J _FM ～ 1.6 eV. This brings substantial Mott-Heisenberg aspects into the problem of graphene. Moreover, similarly large values of the Hubbard and super-exchange strength in graphane suggests that the nature of gap in graphane has substantial Mott character.     

On the theory of superconductivity in the extended Hubbard model

A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting T _c by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-T _c mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.     

Analysis of dispersion of long-wavelength optical phonons in zinc with the help of light scattering

The temperature dependences (5–300 K) of the Raman spectra of E _2g phonons and optical constants in zinc single crystals are measured in the excitation energy range 1.4–2.54 eV. It is found that phonon damping decreases upon an increase in the wavelength of exciting radiation. The obtained results are compared with the dependence of the phonon width on the excitation energy (the probed wave vector of the excitations under investigation), which are presented for the first time for the transition metal osmium, as well as with the calculated electron-phonon renormalization of damping, taking into account the actual distribution of wave vectors.     

Investigation of the 4f-electron-phonon-coupling in the ferromagnet LiTbF4 by inelastic scattering of light

The polarized Raman spectra of LiTbF₄ in an external magnetic field (B≦8 T) have been recorded in the wavenumber interval 0≦500 cm^?1 and at temperatures of 1.8 K and 4.2 K. We have studied effects of the 4f electron-phonon (magnetoelastic) coupling manifesting itself in the splitting of a twofold degenerate phonon mode and in anticrossing effects between phonons and electronic transitions. In the spectra probing the scattering tensor elements (xz) and (zy) this anticrossing shows an asymmetry with respect to the frequencies and scattering intensities of the quasi-degenerate components. These effects are discussed in detail and can be interpreted by the theory of magnetoelastic interaction and by taking into consideration the finite widths of the electronic and phonon components (“critical coupling”). Brillouin scattering has been used to determine the sound velocities in thea-direction. No effect of the magneto-elastic interaction could be detected in this case.     

Magnetic moment of phonons in graphene induced by a magnetic field

A magnetic field not only changes the electronic structure in graphene but also affects the phonon excitations via the electron-phonon interaction and even enables the phonons to generate magnetism. In this paper, we evaluate the magnetic moment of phonons in graphene using a generating-functional technique. The calculation results indicate that the phonon magnetic moment exists only in a weak magnetic field. The step-like change of the magnetic moment with the magnetic field reflects a macroscopic quantum effect.     

The effect of the electron-phonon coupling on the thermal conductivity of silicon nanowires

The thermal conductivity of free-standing silicon nanowires (SiNWs) with diameters from 1-3?nm has been studied by using the one-dimensional Boltzmann's transport equation. Our model explicitly accounts for the Umklapp scattering process and electron-phonon coupling effects in the calculation of the phonon scattering rates. The role of the electron-phonon coupling in the heat transport is relatively small for large silicon nanowires. It is found that the effect of the electron-phonon coupling on the thermal conduction is enhanced as the diameter of the silicon nanowires decreases. Electrons in the conduction band scatter low-energy phonons effectively where surface modes dominate, resulting in a smaller thermal conductivity. Neglecting the electron-phonon coupling leads to overestimation of the thermal transport for ultra-thin SiNWs. The detailed study of the phonon density of states from the surface atoms and central atoms shows a better understanding of the nontrivial size dependence of the heat transport in silicon nanowire.     

Electronic structure and phonon spectrum of binary iron-based superconductor FeSe in both nonmagnetic and striped antiferromagnetic phases

Using first-principles calculations, we investigate electronic structure and phonon spectrum of binary iron-based superconductor FeSe in both tetragonal nonmagnetic (NM) phase and orthorhombic striped antiferromagnetic (SAF) phase. It is found that the softening of atomic vibration modes and main electron-phonon coupling contribution from low-frequency Eliashberg spectral function α²F(ω) in SAF phase of FeSe lead to the enhancement of electron-phonon coupling strength λ_ep and logarithmically average frequency ω_ln. However, the obtained superconducting T_c in SAF phase just increases up to 0.34 K, even though Coulomb pseudopotential μ^∗ is limited to zero. As a result, our magnetic phonons calculation still rules out phonon mediated superconductivity, although the electron-phonon coupling through the spin channel play an important role in FeSe.     

Wave-vector dependence of electron-optical phonon coupling in GaAs

Induced non equilibrium distribution of optical phonons allows direct measurement of electron-phonon coupling as a function of phonon wave-vector K. Results indicate that near K=0(K<20, 000 cm^?1 coupling between TO phonons and electrons is independent of K whereas LO phonons show a K^-2 dependence. Results also suggest that electron relaxation in the conduction band by multiple phonon production is quite significant.     

Studies of high-temperature electron–phonon interactions with inelastic neutron scattering and first-principles computations

Several recent studies of phonons combining inelastic neutron scattering and first-principles calculations are summarized. Inelastic neutron scattering was used to measure the phonon densities of states of the A15 compounds V₃Si, V₃Ge, and V₃Co at temperatures from 10 K to 1273 K. It was found that phonons in V₃Si and V₃Ge, which are superconducting at low temperatures, exhibit an anomalous stiffening with increasing temperature, whereas phonons in V₃Co have a normal softening behavior. Additional measurements of the phonon DOS of BCC V alloys were performed, and it was found that a stiffening anomaly present in pure V is suppressed upon introduction of extra d-electrons by alloying. First-principles calculations of the electronic and phonon densities of states show that in both these systems, the anomalous phonon stiffening originates with an adiabatic electron–phonon coupling mechanism. The anomaly is caused by the thermally-induced broadening of sharp peaks in the electronic density of states, which tends to decrease the electronic density at the Fermi level. These results illustrate how the combined use of first-principles calculations and inelastic neutron scattering provides powerful insights into couplings of excitations in condensed-matter.     

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.     

Indirect electronic transitions in alkali halate crystals-I (sodium and potassium chlorate crystals)

The long wavelength tail of the fundamental absorption in NaClO₃ and KClO₃ crystals has been analysed based on the theory of band to band transitions of Bardeen et al.[8] developed in the case of semi-conducting crystals. Evidence of phonon involvement in the transitions giving an indirect band gap is observed. The energies of the phonons involved in the process are the same for both the crystals, and agree well with combinations of prinicple frequencies of ClO₃^? ion, their overtones and also lattice phonons. The indirect band gap in these crystals varies with temperature more or less linearly and the rate of variation is ?3·8 × 10^?4 eV/K and ?5·0 × 10^?4 eV/K for sodium chlorate and potassium chlorate respectively.     

The Effect of the Electron-Phonon Interaction on Giant Magnetoresistance in Magnetic Multilayers

We built electron and phonon free energies and attempted to investigate the effect of the electron-phonon interaction on giant magnetoresistance in magnetic multilayers. Starting from a jellium-like model, we found that the electron-phonon interaction can have an important effect on the spin splitting of electronic energy band. The expression of giant magnetoresistance has been obtained by considering the spin splitting of electronic energy band,indicating that the effect of phonon could not be neglected. Numerical calculations using our approach demonstrate the agreement between experimental and theoretical values.