Superconductivity and electrical resistivity in alkali metal doped fullerides: Phonon mechanism

We consider a two- peak model for the phonon density of states to investigate the nature of electron pairing mechanism for superconducting state in fullerides. We first study the intercage interactions between the adjacent C₆₀ cages and expansion of lattice due to the intercalation of alkali atoms based on the spring model to estimate phonon frequencies from the dynamical matrix for the intermolecular alkali- C₆₀ phonons. Electronic parameter as repulsive parameter and the attractive coupling strength are obtained within the random phase approximation. Transition temperature,T _c, is obtained in a situation when the free electrons in lowest molecular orbital are coupled with alkali-C₆₀ phonons as 5 K, which is much lower as compared to reportedT _c (≈ 20 K). The superconducting pairing is mainly driven by the high frequency intramolecular phonons and their effects enhance it to 22 K. To illustrate the usefulness of the above approach, the carbon isotope exponent and the pressure effect are also estimated. Temperature dependence of electrical resistivity is then analysed within the same model phonon spectrum. It is inferred from the two- peak model for phonon density of states that high frequency intramolecular phonon modes play a major role in pairing mechanism with possibly some contribution from alkali-C₆₀ phonon to describe most of the superconducting and normal state properties of doped fullerides.     

Electron-phonon coupling in A3C60: Contributions from intermolecular modes

An accurate tight-binding fit to the full valence-conduction band region in K₃C₆₀ is used to generate deformation potentials for several phonon modes, including the optic intermolecular vibrations and librations that have not been investigated previously. The resulting electron-phonon coupling constants indicate coupling that is likely to be crucial in understanding electronic transport in the fullerides, and will provide contributions to superconducting pairing. Results for the intramolecularA _g (2) “pentagonal pinch” mode suggests nonadiabatic behavior for this (and possibly other) very high frequency modes.     

Superconductivity of Organic Materials: Beyond the Fullerenes

Abstract

We first briefly review the application of the BCS mechanism with electron-phonon interaction to the superconductivity of the A₃C₆₀ compounds. We then explore an extension of this family of compounds by using aromatic cryptands that we consider as “pseudo fullerene molecules”. Preliminary measurements of low field microwave absorption are consistent with superconducting behavior and a Tc ～ 50K.

     

Electron-phonon coupling in A3C60: Contributions from intermolecular modes

An accurate tight-binding fit to the full valence-conduction band region in K₃C₆₀ is used to generate deformation potentials for several phonon modes, including the optic intermolecular vibrations and librations that have not been investigated previously. The resulting electron-phonon coupling constants indicate coupling that is likely to be crucial in understanding electronic transport in the fullerides, and will provide contributions to superconducting pairing. Results for the intramolecularA _g (2) pentagonal pinch mode suggests nonadiabatic behavior for this (and possibly other) very high frequency modes.     

Prospect of Node-Line Semimetal Cu<Subscript>3</Subscript>PdN to Be a Topological Superconductor

We investigate systematically the vibrational and electron–phonon interaction properties of node-line semimetal Cu₃PdN under strain and electron doping by using first-principles calculations. It is found that vibrational modes interact with electrons at the Fermi level isotropically with a three-dimensional character. The phonon frequency and Eliashberg spectral function can be tuned by strain remarkably, and the maximum transition temperature (T _c) predicted is 0.03 K under strain ε = 0.10. The coexistence of superconductivity and topological physics in Cu₃PdN makes it a promising candidate for future quantum computation platform.     

Fe-Site Doping and Spin Effects on Phonon and Superconductivity in SrFe1−x Co x AsF (x=0,0.125)

First-principles calculations are performed for phonon spectra, phonon density of states and electron-phonon coupling constants of SrFe_1?x Co _x AsF (x=0,0.125) with tetragonal nonmagnetic (NM) and orthorhombic striped antiferromagnetic (SAF) structures. It is found that Co-doping in Fe-site harden phonons in NM structure and soften phonons in SAF structure, and spin interaction makes phonons soften in evidence. Electron-phonon coupling is enhanced by both doping and spin interaction in Fe-site, but does not large enough to produce experimental superconductivity, which rules out phonon mechanism superconductivity in SrFe_1?x Co _x AsF.     

Pairing Mechanism and Superconductivity of Rb3C60 Fullerides

The nature of electron pairing mechanism and the superconducting transition temperature (T _c ) of alkali metal (Rb) doped fullerenes is studied within the framework of strong coupling theory. Chemical substitution of alkali metal in the parent compound introduces free electrons in the lowest unoccupied molecular orbital and for Rb₃C₆₀, the band is filled up to the Fermi level. The intercage interactions between the adjacent C₆₀ cages and expansion of lattice due to the intercalation of Rb atoms are investigated using nearest-neighbor interactions. The free electrons in lowest molecular orbital are coupled with intermolecular phonons. The renormalized Coulomb repulsive parameter * and the attractive coupling strength are obtained for the intermolecular phonon frequency _er. T _c is then estimated as 8.6 K, which is lower as compared with the published data of 30 K. The electrons also couple with the intramolecular phonons and introducing them in ad hoc way, T _c enhances to 34 K. Analytical results on T _c allow one to visualise the relative interplay between the strength of inter- and intramolecular phonons. To illustrate the usefulness of the above approach the carbon isotope effect exponent and the energy gap ratio are estimated which are consistent with the experimental data. The present analysis reveals that both low frequency intermolecular and high frequency intramolecular phonons participate in the pairing mechanism, T _c mainly arises from high frequency intramolecular phonons.     

Phonon Origin of High T c in Superconducting Cuprates

Eliashberg theory (ET), generalized for the account of the peculiar properties of the finite zone width electron-phonon (EP) systems with the non-constant electron density of states, the electron-hole nonequivalence, chemical potential renormalization with doping and frequency, and electron correlations in the vertex function, is used for the study of T _c in cuprates. The phonon contribution to the nodal anomalous electron Green function (GF) in cuprates is considered. The pairing on the full width of the electron zone was taken into account, not just on the Fermi surface. It is found that the finite zone width phenomenon in the newly derived Eliashberg equations for the finite zone width EP system together with the abrupt fall of the density of states above the Fermi surface are the crucial factors for the appearance of the high temperature superconductivity phenomenon. It is shown that near the optimal doping in the hole-doped cuprates high T _c value is reproduced with the EP interaction constant obtained from tunnel experiments.     

Localization and Superconductivity in Intercalated Fullerenes

The model of superconductivity in the intercalated fullerenes based on arising of the valence bond between two neighbouring alkali-metal atoms is proposed. This model explains all the currently available experimental data concerning superconductivity in these compounds. Among them are the absence of superconductivity in A _x C₆₀ with even x, the dependence of the critical temperature on the disorder level and the carrier concentration, and the shape of the density of states near the Fermi level as a function of voltage in tunnelling spectroscopy.     

Charge Transfer and the Route to Superconductivity in the Doped Fullerenes

A brief review is presented discussing the role of charge transfer and the appearance of superconductivity in the three-dimensional (3D) alkali-metal-doped fullerene compounds (A₃C₆₀). An argument is made that similar phenomenology may occur in two dimensions (2D) when a C₆₀ monolayer is doped by charge transfer from an adjacent planar metal layer. Illustrative data are presented showing that charge transfer gives rise to a decrease in resistance when C₆₀ is deposited onto a thin smooth nickel film. Accordingly, the physics of charge transfer and electron delocalization, which plays such an important role in the superconductivity of the 3D A₃C₆₀ compounds, could well play a similar role in these 2D analogues where a C₆₀ monolayer is doped to a conducting state by charge transfer from an underlying metal.     

Fullerene superconductivity by short-range order instability

For the fullerene-group (C₆₀ group) of metastable materials a novel model is conceptualized on the basis of a special dynamic clustering. This clustering is realized by a short-range instability through a collective, cooperative, and coherent displacement of the ions to seek for the most dense and most stable cluster formation. In the C₆₀ superconductivity, mediation by harmonic lattice vibrations (phonons) is replaced by a pairing mechanism with anharmonic collective and coherent cluster vibrations. The suggested model fits the experimental data surprisingly well.     

Fullerene Single Crystals: Structure and Electronic Properties

Abstract

This work covers an advanced investigation of the single crystal growth process for fullerenic materials and the contribution of Raman and IR spectroscopy to the understanding of the fcc high temperature rotor phase and the low temperature sc ratchet phase of pristine C₆₀. In addition substantial research contributions to the understanding of alkali metal doped fullerenes are presented.

Alkali metal doped crystals are studied with particular attention to the line broadening in the superconducting A ₃C₆₀ phase and to the phases with stoichiometry A₁C₆₀. For the former electron-phonon coupling constants could be determined for all fivefold degenerated gerade modes and a total coupling strenght of λ = 0.90 was found. For the latter the different experimental conditions for obtaining the phase separated intermediate state or alternatively the orthorhombic polymeric state are analysed. Vibrational spectra for the polymeric state obtained from phototransformation and from mono alkali metal doping are found to be characteristically different, mainly with respect to the intensity of the Raman or IR response. Finally, research results obtained from the single crystals by various other techniques like thermal expansion or low frequency elastic deformation are summarized.     

Effect of Pressure on Superconducting Properties

It is shown that the existence of superconductivity in a material, and its critical temperature, depends strongly on pressure. Several parameters are pressure-dependent: (1) structure, particularly bond distances, (2) Hubbard U, (3) coupling between sites, and (4) orbital occupation number. Eliashberg theory often leads to incorrect predictions, for example in A₃C₆₀ with A = K, Rb, and Cs. While T _C is correctly predicted to be higher for Rb₃C₆₀ than for K₃C₆₀ and decreasing with pressure in both cases, Cs₃C₆₀ is not superconducting at ambient pressure. The same is the case for pure metals such as Cs and Ca (superconducting at high pressure). A theory for electron pairs, similar to the Marcus model for single electrons, appears to agree with the experiment in most cases.     

Inelastic neutron scattering results on pure and doped fullerenes

Via inelastic neutron scattering (INS) generalized phonon densities of states are obtained for C₆₀ and superconducting A₃C₆₀ (A=K, Rb). Changes in the intramolecular modes agree with and augment recent Raman (RA), infrared (IR), and INS measurements, i.e., in the vicinity of the high-frequency modes of C₆₀ [H _g (8),A _g (2),H _g (7)] we find a pronounced shift of about 10 meV toward smaller energy transfers upon intercalating with potassium. Separated from these vibrations by a gap are the intermolecular spectra which for the doped samples display well-defined optic modes at 11 and 14 meV due to the vibrations of Rb and K ions. Indications of a weak anomalous temperature dependence of low-energy phonons ( <3 meV) nearT _c are observed for K₃C₆₀.     

Coupling to Phonons in the Migdal–Eliashberg Approach

The relevance of the strong correlations in the high critical temperature superconductors (HTSC) is well experimentally documented. However, if the properties of the normal and superconducting state in HTSC oxides are interpreted in terms of the standard Eliashberg theory, which holds in low temperature superconductor systems, the Migdal–Eliashberg approach implies serious limitations in the reproduction of experimental spectroscopies whose contributions are inter-band and not intra-band. Recent angle-resolved photoemission spectroscopy (ARPES) measurements on HTSC oxides whose contributions are intra-band show a kink in the quasiparticle spectrum at characteristic phonon frequencies in the normal and superconducting state. In contrast with our theoretical discussion, we include our theoretical results for the renormalized energy E _k as a function of the bare band energy ε _k obtained from ARPES in a Pb sample and in a Bi₂Sr₂CaCu₂O_8+δ optimally doped sample (Bi2212). This is clear evidence that electron-phonon is strong and involved in pairing.      

Anomalously strong small-q electron-phonon coupling in cuprates due to dielectricity

We consider the role of the enormous ionic dielectric constant ε₀≈ 30–50 in the cuprates. The ionically-screened Thomas-Fermi screening parameter ~q_TF = [4θe²N(E_F)/εin0 ^1/2 is extremely small, namely 0.2-0.3 A^-1. The electron-phonon coupling constant I(q,w) is found to be anomalously large forq ≈ ~q_TF and smallco, accounting for the CDW observed in overdoped BSCCO with wavevector 0.24 A^-1. Using the Eliashberg theory we derive from this I(q,w) a maximumT _c of about 200 K. The small electron-phonon scattering angle △θ = ~q _{F ≈} 0.3 rad acounts for the observedd-wave pairing, as originating from a phonon-mediated mechananism.     

Superconductivity in a Correlated <Emphasis Type="Italic">E</Emphasis>⊗<Emphasis Type="Italic">e</Emphasis> Jahn–Teller System

By numerically solving the Eliashberg equation in the RPA as well as employing the Landau’s theory for phase transitions, we have investigated superconductivity, especially its pairing character, in a two-orbital Hubbard model coupled with E?e Jahn–Teller phonons on a two-dimensional square lattice at half filling. If the electron hopping between neighboring sites keeps the orbital character invariant in this E?e Jahn–Teller crystal, we find that a new superconducting phase characterized by the pairing of spin singlet, orbital singlet, and odd in momentum space, named a chiral p-wave pairing, is brought about by the collaboration of orbital fluctuations enhanced mainly by the electron–phonon interaction with spin fluctuations induced by the electron–electron one.     

High-<Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> Hydrides: Interplay of Optical and Acoustic Modes and Comments Regarding the Upper Limit of <Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript>

The phonon spectrum of many superconducting compounds and, especially, high-T_c hydrides, is broad and rather complicated, because of the presence of high-frequency optical modes. In order to analyze an interplay of optical and acoustic phonon branches, it is convenient to introduce two coupling constants, \(\lambda _{\text {opt.}}\) and \(\lambda _{\text {ac.}}\), along with characteristic frequencies. The correlation between the value of T_c and this interplay is demonstrated for the family of tantal hydrides (TaH₂/TaH₄/TaH₆). The problem of the upper limit of T_c is discussed. The phenomenon of room temperature superconductivity can be provided by the electron-phonon interaction and is described by the strong coupling theory.     

Analysis of Possible Field-Induced Superconductivity in Anthracene, Other Polyacenes, and C60

We consider electronic structure and superconductivity aspects in field-doped polyacenes (PA) and C₆₀. Within a modified Thomas–Fermi approach for typical experimental values of the surface charge density the injected charge is confined to a monolayer. The electron-phonon coupling constant for internal modes _int is estimated using the work of Devos et al. (Phys. Rev. B 58, 8236 (1998)) and the density of states estimated from a 2D-one-band model derived from a full potential LDA band structure calculation for bulk anthracene. The large differences in the reported T _c-values for PA and C₆₀ are ascribed to enhanced empirical Coulomb pseudopotentials * for PA.     

Plasmon-phonon and plasmon-two different phonon interaction in Pb1−xMnxTe mixed crystals

Far-infrared reflection spectra in wide temperature range was used to investigate the vibrational properties of Pb_1−xMn_xTe (x = 0.0002, 0.002, 0.02 and 0.1) mixed crystals. To analyse the experimental results we use dielectric function that takes into account the existence of plasmon-phonon as well as the plasmon-two different phonon interaction. The best fit method revealed two frequencies of plasmon-phonon coupled modes and three frequencies of plasmon-two different phonon coupled modes. Further, the values for two different LO modes and plasma frequency (ω_P) are calculated. Results obtained from experimental spectra as the best fit, are in very good agreement with the theoretical prediction. The model of phonon behaviour based on Genzel's model was developed. It was found that the long wavelength optical phonon modes of these mixed crystals, exhibit an intermediate and two mode behaviour, coincidentally.