Theory of two-phonon modes in layered charge-density-wave systems

A theoretical model with electron-phonon and anharmonic interactions is proposed to explain the two-phonon mode observed in the Raman spectra of layered transition metal dichalcogenides, which exhibit charge density wave (cdw) phase transition. The phonon self-energy, which involves the electron response function and the two-phonon Green’s function, is calculated using the double-time Green’s function formalism. It is shown that in these low-dimensional systems there exists an anharmonicity-mediated two-phonon mode in the phonon spectral function both in the normal and in thecdw phases. In the normal phase since the phonon Raman scattering proceeds through a single optic phonon the calculations are carried out for zero wave vector and hence the contribution of the electron response function to the self-energy vanishes. On the other hand explicit evaluation of the two-phonon Green’s function shows that the frequency of the two-phonon mode is twice that of the Kohn anomaly phonon and decreases with decreasing temperature. The strength of two-phonon peak is found to be comparable to that of the original optic phonon. In thecdw phase the phonon which enters into the Raman scattering is taken to be the one with thecdw wave vectorQ, which when zone-folded becomes equivalent to zero wave vector. The evaluation of the electron response function in this phase generates a phonon corresponding to thecdw-amplitude mode. The two-phonon Green’s function is assumed to be of similar form as in the normal phase. The spectral function evaluated at zero temperature shows a weak two-phonon peak besides the prominentcdw-amplitude mode. Numerical results are presented for the system 2H-NbSe₂ and are found to be in qualitative agreement with the experimental data.     

Sm atomic dynamics in a charge density wave compound SmNiC2

¹⁴⁹Sm nuclear resonant inelastic scattering was carried out in a charge density wave compound SmNiC₂. We have investigated temperature dependences of the Sm partial phonon density of states and recoil-free fraction at the Sm site and the average sound velocity estimated from the Sm partial density of states. The Sm partial density of states exhibits temperature dependence, suggesting that the phonon modes between 20 and 25 meV may correlate with the charge density wave. Temperature dependence of the recoil-free fraction is difficult to prove the correlation with either the charge density wave or ferromagnetic ordering. The average sound velocity obtained by the Sm partial phonon density of states exhibits temperature dependence, agreeing qualitatively with very recent elastic constant measurements.     

Charge order driven by Fermi-arc instability and its connection with pseudogap in cuprate superconductors

The recently discovered charge order is a generic feature of cuprate superconductors, however, its microscopic origin remains debated. Within the framework of the fermion-spin theory, the nature of charge order in the pseudogap phase and its evolution with doping are studied by taking into account the electron self-energy (then the pseudogap) effect. It is shown that the antinodal region of the electron Fermi surface is suppressed by the electron self-energy, and then the low-energy electron excitations occupy the disconnected Fermi arcs located around the nodal region. In particular, the charge order state is driven by the Fermi-arc instability, with a characteristic wave vector corresponding to the hot spots of the Fermi arcs rather than the antinodal nesting vector. Moreover, although the Fermi arc increases its length as a function of doping, the charge order wave vector reduces almost linearity with the increase of doping. The theory also indicates that the Fermi arc, charge order and pseudogap in cuprate superconductors are intimately related to each other, and all of them emanates from the electron self-energy due to the interaction between electrons by the exchange of spin excitations.     

HfSe2 monolayer stability tuning by strain and charge doping

Strain and charge doping are the effective ways to modulate the electronic and phonon properties of materials. The effects of biaxial tensile strains and charge dopings on the stabilities of HfSe₂ monolayer have been systematically investigated using first-principles methods. Its two-dimensional Young's modulus is only 65.4 N/m, and it is easy to be stretched. When the tensile strain is applied on HfSe₂ monolayer, two of its phonon modes soften with one frequency decreasing to zero at critical strain. Our results show that electron and hole dopings could suppress the softening of phonon modes, and significantly enhance the ideal strength by 28% and 36%, respectively. The calculations for electronic structures and phonon dispersions provide the theoretical references for future nano-device designing.     

Effect of temperature on phonon contribution to Green function of high-temperature superconducting cuprates

The phonon contribution to the nodal electron Green function in cuprates is considered. It is shown that the temperature dependence of the real part of the self-energy component of the Green function for cuprates with a hole doping level close to optimal is described by the electron-phonon interaction in the framework of the extended Eliashberg model.     

Microscopic theory of longitudinal sound velocity in CDW and SDW ordered cuprate systems

We address here the self-consistent calculation of the spin density wave and the charge density wave gap parameters for high-T_c cuprates on the basis of the Hubbard model. In order to describe the experimental observations for the velocity of sound, we consider the phonon coupling to the conduction band in the harmonic approximation and then the expression for the temperature dependent velocity of sound is calculated from the real part of the phonon Green’s function. The effects of the electron–phonon coupling, the frequency of the sound wave, the hole doping concentration, the CDW coupling and the SDW coupling parameters on the sound velocity are investigated in the pure CDW phase as well as in the co-existence phase of the CDW and SDW states. The results are discussed to explain the experimental observations.     

Orbital correlations in doped manganites

We review our recent X-ray scattering studies of charge and orbital order in doped manganites, with specific emphasis on the role of orbital correlations in Pr_1-xCa_xMnO₃. For x=0.25, we find an orbital structure indistinguishable from the undoped structure and long-range orbital order at low temperatures. For dopings 0.3≤x≤0.5, we find scattering consistent with a charge and orbitally ordered CE-type structure. While in each case the charge order peaks are resolution limited, the orbital order exhibits only short-range correlations. We report the doping dependence of the correlation length and discuss the connection between the orbital correlations and the finite magnetic correlation length observed on the Mn³⁺ sublattice with neutron-scattering techniques. The physical origin of these domains, which appear to be isotropic, remains unclear. We find that weak orbital correlations persist well above the phase transition, with a correlation length of 1–2 lattice constants at high temperatures. Significantly, we observe similar correlations at high temperatures in La_0.7Ca_0.3MnO₃, which does not have an orbitally ordered ground state, and we conclude that such correlations are robust to variations in the relative strength of the electron–phonon coupling. Received: 22 May 2001 / Accepted: 4 July 2001 / Published online: 5 October 2001     

Electrical resistivity of alkali metal doped manganites LaxAyMnwO3 (A = Na,K, Rb): Role of electron–phonon,electron–electron and electron–magnon interactions

The electrical resistivity behaviour of alkali metal (Na, K, Rb) substitutions at La site in La_xA_yMn_wO₃ (A = Na, K, Rb) manganites is studied caused by electron–phonon, electron–electron and electron–magnon scattering. Substitutions affect average mass and ionic radii of A-site and hence resulting lattice and optical phonon softening. Estimated resistivity compared with reported metallic resistivity, accordingly ρ_diff. = [ρ_exp ? {ρ₀ + ρ_e–ph (=ρ_ac + ρ_op)}], infers electron–electron and electron–magnon dependence over most of the temperature range. Electron–phonon contribution indicates that alkali metal K doping provoked larger lattice distortion, while electron–electron interaction is more dominating process for Na and Rb doped compound favouring motion of excess charge carrier. Semiconducting nature is discussed with variable range hopping and small polaron conduction model. The change in activation energies and the density of states at the Fermi-level is consistently explained by cationic disorder and Mn valence.     

Impurity band in SnBi<Subscript>4</Subscript>Se<Subscript>7</Subscript>: thermoelectric power and electrical resistivity measurements

Thermoelectric power and electrical resistivity measurements on polycrystalline samples of Bi₂Se₃ and stoichiometric ternary compound in the quasi-binary system SnSe–Bi₂Se₃ in the temperature range of 90–420 K are presented and explained assuming the existence of an impurity band. The variation of the electron concentration with temperature above 300 K is explained in terms of the thermal activation of a shallow donor, by using a single conduction band model. The density of states effective mass m ^*=0.15m ₀ of the electrons, the activation energy of the donors, their concentration, and the compensation ratio are estimated. The temperature dependence of the electron mobility in conduction band is analyzed by taking into account the scattering of the charge carriers by acoustic phonon, optical phonon, and polar optical phonon as well as by alloy and ionized impurity modes. On the other hand, by considering the two-band model with electrons in both the conduction and impurity bands, the change in the electrical resistivity with temperature between 420 and 90 K is explained.     

Dynamic charge susceptibility and softening of longitudinal phonon modes in cuprates

The dynamic charge susceptibility as a function of the wave vector and the frequency has been analyzed in the context of the existing experimental data on the plasmon frequencies, softening of the longitudinal phonon modes, and charge density waves in the electron subsystem of the high-temperature superconducting cuprates. It is emphasized that a set of all experimental data can be explained only under the assumption that the interaction via the phonon field plays an important role and differs in different regions of the Fermi surface; i.e., the parameters of the electron-phonon coupling depend not only on the value of the momentum transfer q but also on the wave vector k.     

Soft plasmon theory of the new high-temperature superconductors

The newly-discovered high-temperature superconductors are close to, but on the metallic side of, a Mott metal — insulator transition. The incipient Mott transition manifests itself as a tendency towards a charge density wave instability, characterized by wave vectors appropriate for Fermi-surface nesting. In La₂CuO₄, this charge-density wave is commensurate with the lattice, and leads to a structural transition to a non-metallic state. We show that in the new superconducting materials, this incipient instability causes a drastic softening of the plasmon modes at these wave vectors. Indeed, there is some experimental evidence for such soft plasmons in these materials. Although these modes have a much lower frequency than ordinary plasmons, it is still much higher than the Debye-cut-off phonon frequency. They are strongly coupled to the conduction electrons, and induce an electron - electron attraction in a way analogous to phonons. Moreover, the soft-plasmon wave vectors are automatically those required for Cooper pairing, since they connect points on the Fermi surface. The Debye-energy prefactor in the BCS expression for the transition temperature is replaced by the considerably larger plasmon energy. Furthermore the strength of the interaction will ensure that the exponential factor is not too small. Note that this mechanism will lead to zero isotope effect. We suggest that the Ba or La f-orbitals play an important role in softening these plasma modes and strengthening the electron - plasmon coupling. This would explain why the presence of Ba or La seems to be favourable for high-temperature superconductivity.     

Apparent electron-phonon interaction in strongly correlated systems

We study the interaction of electrons with phonons in strongly correlated solids, having high-T(c) cuprates in mind. Using sum rules, we show that the apparent strength of this interaction strongly depends on the property studied. If the solid has a small fraction (doping) delta of charge carriers, the influence of the interaction on the phonon self-energy is reduced by a factor delta, while there is no corresponding reduction of the coupling seen in the electron self-energy. This supports the interpretation of recent photoemission experiments, assuming a strong coupling to phonons.     

Thermal conductivity of NbSe3

The thermal conductivity, κ, of NbSe₃ has been measured by novel self-heating techniques that allowed the electric field dependence of κ to also be measured. Measurements were made from 35 K to room temperature. Above the charge density wave transitions, the phonon thermal conductivity is 4–7 times the electron thermal conductivity, and it rises smoothly below the transitions, indicating that phonon-phonon scattering predominates. Phonon mean free parths have been estimated at 187 A° at 60 K and 60 A° at 150 K. No clear anomalies were observed at the phase transitions, giving upper limits to changes in the phonon mean free path. No field dependence of κ was observed.     

Raman scattering by electron and phonon excitations in FeSi

The temperature evolution of Raman scattering by electron and phonon excitations in FeSi is studied within the range of 10–500 K. At low temperatures, the frequency dependence for the spectra of light scattered by electrons exhibits vanishing intensity in the range up to 500–600 cm^–1, which suggests the existence of an energy gap of about 70 meV. The calculations of the electronic excitation spectra based on the band structure determined using the LDA+DMFT technique (local electron density + dynamic mean field approximation) are in good agreement with the low-temperature experimental data and confirm that FeSi is a material with intermediate electron correlations. The changes in the shape of the electronic excitation spectrum and in the self-energy of optical phonons indicate a transition to the metallic state above 100 K. The analysis of experimental data demonstrates an appreciable decrease in the electron lifetime with the growth of temperature determining the (insulator–poor metal) transition.     

Correlation effects obtained from optical spectra of Fe-pnictides using an extended Drude-Lorentz model analysis

We introduce an analysis model, an extended Drude–Lorentz model, and apply it to Fe-pnictide systems to extract their electron–boson spectral density functions (or correlation spectra). The extended Drude–Lorentz model consists of an extended Drude mode for describing correlated charge carriers and Lorentz modes for interband transitions. The extended Drude mode can be obtained by a reverse process starting from the electron–boson spectral density function and extending to the optical self-energy and, eventually, to the optical conductivity. Using the extended Drude–Lorentz model, we obtained the electron–boson spectral density functions of K-doped BaFe₂As₂ (Ba-122) at four different doping levels. We discuss the doping-dependent properties of the electron–boson spectral density function of K-doped Ba-122. We also can include pseudogap effects in the model using this approach. Therefore, this approach is very helpful for understanding and analyzing measured optical spectra of strongly correlated electron systems, including high-temperature superconductors (cuprates and Fe-pnictides).     

Reconstruction of bands in metallic hydrogen

The generalized theory of normal properties of a metal for the case of the properties of the electronic band of electron–phonon systems with a variable electron density of states is used to study the normal phase of metallic hydrogen at a pressure of 500 GPa and a temperature of 200 K. We calculated the frequency dependence of the real ReΣ(ω) and imaginary ImΣ(ω) parts of the self-energy part of the electron Green’s function Σ(ω), as well as the electron density of states N(ε) of the stable phase of metallic hydrogen with the I41/amd symmetry at a pressure of 500 GPa, renormalized by the strong electron–phonon coupling. It is found that the electron conduction band of the I41/amd phase of metallic hydrogen undergoes insignificant reconstruction near the Fermi level because of the renormalization by the electron–phonon coupling.     

The high temperature superconductivity in cuprates: physics of the pseudogap region

We discuss the physics of the high temperature superconductivity in hole doped copperoxide ceramics in the pseudogap region. Starting from an effective reduced Hamiltonianrelevant to the dynamics of holes injected into the copper oxide layers proposed in aprevious paper, we determine the superconductive condensate wavefunction. We show that thelow-lying elementary condensate excitations are analogous to the rotons in superfluid⁴He. We arguethat the rotons-like excitations account for the specific heat anomaly at the criticaltemperature. We discuss and compare with experimental observations the London penetrationlength, the Abrikosov vortices, the upper and lower critical magnetic fields, and thecritical current density. We give arguments to explain the origin of the Fermi arcs andFermi pockets. We investigate the nodal gap in the cuprate superconductors and discussboth the doping and temperature dependence of the nodal gap. We suggest that the nodal gapis responsible for the doping dependence of the so-called nodal Fermi velocity detected inangle resolved photoemission spectroscopy studies. We discuss the thermodynamics of thenodal quasielectron liquid and their role in the low temperature specific heat. We proposethat the ubiquitous presence of charge density wave in hole doped cuprate superconductorsin the pseudogap region originates from instabilities of the nodal quasielectrons drivenby the interaction with the planar CuO₂ lattice. We investigate the doping dependence of thecharge density wave gap and the competition between charge order and superconductivity. Wediscuss the effects of external magnetic fields on the charge density wave gap andelucidate the interplay between charge density wave and Abrikosov vortices. Finally, weexamine the physics underlying quantum oscillations in the pseudogap region.     

Variational treatment for the dynamical pseudo Jahn-Teller system

We present a variational treatment for the E × e pseudo Jahn-Teller system. Through canonical transformation the electron and phonon states are decoupled. An analytical form is obtained for the ground state energy by scaling transformation. Including both the dynamical displacement of phonon modes and the softening of phonon frequency, this approach yields fairly accurate results for the ground state energy. The energy splitting and Ham's reduction factor are calculated, which also generates fairly good results compared with other perturbation results. We argue that our variational wave function is valid for the weak and intermediate coupling range.     

Interaction of the single-particle and collective degrees of freedom in non-magic nuclei: The role of phonon tadpole terms

A method of consistent treatment of phonon contributions to the self-energy and gap terms in non-magic nuclei is developed in so-called g ² approximation, where g is the creation amplitude of a low-lying phonon. The method simultaneously takes into account both usual non-local and local phonon tadpole terms. Relations that allow the tadpoles to be calculated without introduction of new parameters are derived. As an application of the method, the effect of the phonon tadpoles on the single-particle strength distribution, single-particle energies and gap values is considered. Hypothesis of the surface nature of pairing correlations is discussed in the light of the tadpole effect.     

Synthesis of nitrogen-doped single-walled carbon nanotubes and monitoring of doping by Raman spectroscopy

Nitrogen-doped single-walled carbon nanotubes （CNx-SWNTs） with tunable dopant concentrations were synthesized by chemical vapor deposition （CVD）, and their structure and elemental composition were characterized by using transmission electron microscopy （TEM） in combination with electron energy loss spectroscopy （EELS）. By comparing the Raman spectra of pristine and doped nanotubes, we observed the doping-induced Raman G band phonon stiffening and 2D band phonon softening, both of which reflect doping-induced renormalization of the electron and phonon energies in the nan- otubes and behave as expected in accord with the n-type doping effect. On the basis of first principles calculations of the distribution of delocalized carrier density in both the pristine and doped nanotubes, we show how the n-type doping occurs when nitrogen heteroatoms are substitutionally incorporated into the honeycomb tube-shell carbon lattice.