Superconducting transition parameters in aluminum-lithium alloys (0-10 at.% Li)

The superconducting transition temperatures T_c of face-centered cubic Al_1−x-Li_x alloys (x=0-0.10) exhibit a minimum near x=0.03 (3 at.% Li). The McMillan strong-coupling T_c equation yields a similar trend of the electron-phonon coupling constant λ. Meanwhile, the density of states at the Fermi level N(0) decreases monotonically with increasing x. It appears that T_c drops initially due to a reduced N(0), which is then overtaken by alloying-enhanced factors of phonon or electron-phonon interaction.     

Atom scattering as a probe of the surface electron-phonon interaction at conducting surfaces

An atomic projectile colliding with a surface at kinetic energies in the thermal or hyperthermal range interacts with and is reflected by the electronic density well in front of the first layer of target atoms, and it is generally accepted that the repulsive interaction potential is proportional to the density of electrons extending outside the surface. This review develops a complete treatment of the elastic and inelastic scattering of atoms from a conducting surface in which the interaction with the electron density and its vibrations is treated using electron-phonon coupling theory. Starting from the basic principles of formal scattering theory, the elastic and inelastic scattering intensities are developed in a manner that identifies the small overlap region in the surface electron density where the projectile atom is repelled. The effective vibrational displacements of the electron gas, which lead to energy transfer through excitation of phonons, are directly related to the vibrational displacements of the atomic cores in the target crystal via electron-phonon coupling. The effective Debye-Waller factor for atom-surface scattering is developed and related to the mean square displacements of the atomic cores. The complex dependence of the Debye-Waller factor on momentum and energy of the projectile, including the effects of the attractive adsorption well in the interaction potential, are clearly defined. Applying the standard approximations of electron-phonon coupling theory for metals to the distorted wave Born approximation leads to expressions which relate the elastic and inelastic scattering intensities, as well as the Debye-Waller factor, to the well known electron-phonon coupling constant λ. This treatment reproduces the previously obtained result that the intensities for single phonon inelastic peaks in the scattered spectra are proportional to the mode specific mass correction components λ_Q,ν defined by the relationship λ = 〈λ_Q,ν〉. The intensities of elastic diffraction peaks are shown to be a weighted sum over the λ_Q,ν, and the Debye-Waller factor can also be expressed in terms of a similar weighted summation. In the simplest case the Debye-Waller exponent is shown to be proportional to λ and for simple metals, metal overlayers, and other kinds of conducting surfaces values of λ are extracted from available experimental data. This dependence of the elastic and inelastic scattering, and that of the Debye-Waller factor, on the electron-phonon coupling constant λ shows that measurements of elastic and inelastic spectra of atomic scattering are capable of revealing detailed information about the electron-phonon coupling mechanism in the surface electron density.     

Electron-phonon interaction in NbB2: a comparison with MgB2

We present a comparison of electron-phonon interaction in NbB₂ and MgB₂, calculated using full-potential, density-functional-based methods in P6/mmm crystal structure. Our results, described in terms of (i) electronic structure, (ii) phonon density of states F(ω), (iii) Eliashberg function α²F(ω), and (iv) the solutions of the isotropic Eliashberg gap equation, clearly show significant differences in the electron-phonon interaction in NbB₂ and MgB₂. We find that the average electron-phonon coupling constant λ is equal to 0.59 for MgB₂ and 0.43 for NbB₂, leading to superconducting transition temperatures T_c at around 22 K for MgB₂ and 3 K for NbB₂.     

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.     

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.

     

Critical temperature of metallic hydrogen sulfide at 225-GPa pressure

The Eliashberg theory generalized for electron—phonon systems with a nonconstant density of electron states and with allowance made for the frequency behavior of the electron mass and chemical potential renormalizations is used to study T _c in the SH₃ phase of hydrogen sulfide under pressure. The phonon contribution to the anomalous electron Green’s function is considered. The pairing within the total width of the electron band and not only in a narrow layer near the Fermi surface is taken into account. The frequency and temperature dependences of the complex mass renormalization ReZ(ω), the density of states N(ε) renormalized by the electron—phonon interactions, and the electron—phonon spectral function obtained computationally are used to calculate the anomalous electron Green’s function. A generalized Eliashberg equation with a variable density of electron states has been solved. The frequency dependence of the real and imaginary parts of the order parameter in the SH₃ phase has been obtained. The value of T _c ≈ 177 K in the SH₃ phase of hydrogen sulfide at pressure P = 225 GPa has been determined by solving the system of Eliashberg equations.     

Theory for superconductivity in Pd-H and Pd-D systems

A theory is presented explaining the recently observed superconductivity at 9 °K in Pd-H and at 11 °K in Pd-D as due to the quenching of the spin-fluctuations and as due to the decrease of the Coulomb pseudo-potential μ present in Pd. That one observes for PdD a larger superconducting transition temperatureT _c than for PdH is explained by the larger lattice expansion resulting for adding H to Pd. The observed non-monotonic dependence ofT _c on the Hydrogen concentration is explained by the fact that approximately λ ∝N(0) for smallN(0), whereN(0) is the electronic density of states at the Fermi-energy and where λ denotes the electron-phonon coupling constant. Superconducting transition temperatures are estimated for PtH and RhH.     

Vibrational and electronic characteristics of Zr<Subscript>70</Subscript>Pd<Subscript>30</Subscript>, Zr<Subscript>80</Subscript>Pt<Subscript>20</Subscript> icosahedral quasicrystals and their amorphous Counterparts

The heat capacity of Zr₇₀Pd₃₀ and Zr₈₀Pt₂₀ icosahedral quasicrystals and their amorphous counterparts is studied in the temperature range 1.5–500 K in order to establish a correlation between the short-range atomic order and the physical properties of these compounds. A comparison of the data made it possible to reveal changes in the vibrational spectra within the low-and high-energy ranges, as well as in the density of states, superconducting characteristics, electron-phonon interaction, and anharmonicity of the lattice thermal vibrations and to calculate the main average frequencies (moments) characterizing the vibrational spectra. The lower superconducting transition temperature T _c of the quasicrystals as compared to that of the amorphous counterparts can be associated with the decrease in the density of states on the Fermi surface, the hardening of the phonon spectrum, and the weakening of the electron-phonon coupling.     

d-Wave superconductivity via buckling-like phonon mode

We follow the classic strong-coupling theory of superconductivity through electron-phonon interaction with a buckling-like phonon mode. We find a nonzero d-wave order parameter in the sense of the Eliashberg theory. We derive a zero temperature gap Δ(0,π) at the gap edge versus the electron-phonon coupling strength g² relation. We find that large enough value for Δ(0,π) as compared to those of high-T_c superconductors cannot be realized in the electron-buckling-like-phonon coupling on the CuO₂ planes.     

Inelastic X-ray scattering investigations of lattice dynamics in SmFeAsO1−xFysuperconductors

We report measurements of the phonon density of states as probed with inelastic X-ray scattering in SmFeAsO_1−xF_y powders. An unexpected strong renormalization of phonon branches around 23 meV is observed as fluorine is substituted for oxygen. Phonon dispersion measurements on SmFeAsO_1−xF_y single crystals allow us to identify the 21 meV A_1g in-phase (Sm,As) and the 26 meV B_1g (Fe,O) modes to be responsible for this renormalization, and may reveal unusual electron-phonon coupling through the spin channel in iron-based superconductors.     

Brillouin zone effects on the critical temperature of superconductors and some related normal metal properties

A Fermi surface passing through a set of Bragg planes gives rise to variations of several normal metal properties, e.g. the electronic density of states N(0), the magnetic susceptibility, the Seebeck coefficient, the Debye temperature and the electron-phonon interaction strength V_ph, and consequently also to variation of the critical temperature for superconductivity, T_c.This behaviour is analysed on the basis of a nearly free electron model and a comparison is made with experimental results in various alloy systems. These systems include alloys of non-transition metals and pseudo-binary alloyed compounds with Cu₃Au- and CuAl₂-type structure.The observed variations of normal metal properties are in reasonable agreement with the theoretical estimates. The variations in T_c indicate that enhancements not only of N(0) but probably also of V_ph occur near Bragg planes.     

Physical properties of the cubic spinel LiMn2O4

We have performed an ab initio study of structural, electronic, magnetic, vibrational and thermal properties of the cubic spinel LiMn₂O₄ by employing the density functional theory, the linear-response formalism, and the plane-wave pseudopotential method. An analysis of the electronic structure with the help of electronic density of states shows that the density of states at the Fermi level (N (E_F)) is found to be governed by the Mn 3d electrons with some contributions from the 2p states of O atoms. It is important to note that the contribution of Mn 3d states to N(_EF)$N\left(E_F\right)$ is as much as 85%. From our phonon calculations, we have obtained that the main contribution to phonon density of states (below 250 cm⁻¹) comes from the coupled motion of Mn and O atoms while phonon modes between 250 cm⁻¹ and 375 cm⁻¹ are characterized by the vibrations of all the three types of atoms. The contribution from Li increases rapidly at higher frequency (above 375 cm⁻¹) due to the light mass of this atom. Finally, the specific heat and the Debye temperature at 300 K are calculated to be 249.29 J/mol K and 820.80 K respectively.     

Strength of the phonon-coupling mode in La2−xSrxCuO4, Bi2Sr2CaCu2O8+x and Y Ba2Cu3O6+x composites along the nodal direction

Despite the intensive efforts for determining the mechanism that causes high-temperature superconductivity in copper oxide materials, no consensus on the pairing mechanism has been reached. Recent advances in high resolution angle-resolved photoemission spectroscopies have suggested that a sizeable electron-phonon coupling exists as the principal cause for kinks in the dispersion relations (energy versus wave vector) of the electronic states. Here, we report on a systematic study about the influence of the electron-phonon coupling parameter “λ” in the electronic quasiparticle dispersions of a wide family of CuO composites. In particular, the influence of the doping level in the cuprate families, La_2−xSr_xCuO₄, Bi₂Sr₂CaCu₂O_8+x and Y Ba₂Cu₃O_6+x over the dressing of the charge carriers, i.e., on the enhancement of the effective mass and the strength of the coupling mode for the nodal direction of the Fermi surface has been analyzed. Universal effects as the nodal kinks at low energies are theoretically reproduced, emphasizing the necessary distinction between the general electron mass-enhancement parameter λ^∗ and the conventional electron-phonon coupling parameter λ. Our analysis shows a remarkable agreement between theory and experiment for different samples and at different doping levels. In fact, in LSCO family, the coupling constant λ calculated consistently with the nodal kink dispersions, reproduces the observed critical temperatures T_c, the gap ratio 2Δ₀/k_BT_c, and other parameters which have been studied from a wide set of natural and empirical equations which have been used along the last decades. It will be concluded that the strong renormalisation of the band structure can be explained in terms of the phonon coupling mode, and must therefore be included in any microscopic theory of superconductivity, even for those materials in which the contribution to the pair formation can be less dominant. Nevertheless, in more anisotropic structures, simulations reducing the Coulomb effects to encourage the phonon mechanism reveal as seems unavoidable to consider additional coupling modes that justify the higher critical temperatures observed in BSCCO and YBCO samples.     

On the inversion of tunneling characteristics in superconductors with spin fluctuations

We have calculated the current-voltage characteristics of a superconductor with spin fluctuations explicitly included in the kernels of the Eliashberg equation along with the electron-phonon spectral density α²(ω)F(ω). These characteristics are then inverted using the method outlined by Galkin et al. to get an effective electron-phonon spectral density assuming no paramagnons are present in the Eliashberg equations during the inversion procedure. The effective electron-phonon spectral density found in this way is, to an excellent approximation, a scaling factor of $\text{1}\text{(1+λ}{}_{\mathrm{sf}}\text{)}$ times the original α²(ω)F(ω), with λ_sf the paramagnon mass renormalization.     

Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians

We consider the integrated density of states (IDS) ρ_∞(λ) of random Hamiltonian H_ω=?Δ+V_ω, V_ω being a random field on ? ^d which satisfies a mixing condition. We prove that the probability of large fluctuations of the finite volume IDS |Λ|^?1ρ(λ, H_Λ(ω)), Λ ? ? ^d , around the thermodynamic limit ρ_∞(λ) is bounded from above by exp {?k|Λ|},k>0. In this case ρ_∞(λ) can be recovered from a variational principle. Furthermore we show the existence of a Lifshitztype of singularity of ρ_∞(λ) as λ → 0⁺ in the case where V_ω is non-negative. More precisely we prove the following bound: ρ_∞(λ)≦exp(?kλ^?d/2) as λ → 0⁺ k>0. This last result is then discussed in some examples.     

Direct measurement of the electron-phonon interaction in Pd,Mo and W by point-contact spectroscopy

The point-contact electron-phonon interaction function α²F has been obtained for the three transition metals Pd, Mo and W. The measured^Pα²F_p-spectra show clear structures which are in agreement with characteristic features in the phonon densities of states and calculated α²(ω)F(ω)-spectra.     

Hyperfeinstrukturuntersuchungen mit einem sphärischen Fabry-Perot-Interferometer mit internem Absorptionsatomstrahl im Tm I- und Eu I-Spektrum

A spherical Fabry-Perot spectrometer with an absorbing atomic beam passing the interior of the interferometer is described. By use of the internal beam it is possible to reduce the amount of material needed for the atomic beam source to a few milligrams per hour. The set-up is especially suitable for hyperfine structure and isotope shift investigations. For the photoelectric recording of the signal the geometrical distance between the spherical mirrors was changed using the piezoelectric effect. In order to reduce the influence of the intensity distribution of the light sourceI ₀(λ) the ratio [I ₀(λ)-I(λ)]/I ₀(λ) was measured, whereI ₀(λ)=I ₀(λ) exp (—V·k(λ)·d) is the observed intensity with absorbing atoms between the mirrors, andV the increase of the absorption signal due to the multiple reflections of the light through the atomic beam (V≈75). For an accurate and easy evaluation of the data this ratio was measured by a digital voltmeter and punched into paper tape. The small line width of the absorption profile obtained in the experiments with Tm and Eu enabled us to measure hyperfine distances of the order of 5 · 10^?3 cm^?1 to 20 · 10^?3 cm^?1 with an error not exceeding 0.1 · 10^?3 cm^?1 in some cases. From the measurements theA-factors for five levels of the configurations 4f ¹³6s 6p and 4f ¹²5d 6s ² in Tm I and theA- andB-factors of the stable Eu isotopes of the 4f ⁷ 6s 6p y ⁸ P _5/2level in Eu I were determined.     

The integrated density of states for the difference Laplacian on the modified Koch graph

We consider the integrated density of statesN(λ) of the difference Laplacian ?Δ on the modified Koch graph. We show thatN(λ) increases only with jumps and a set of jump points ofN(λ) is the set of eigenvalues of ?Δ with the infinite multiplicity. We establish also that $$0< C_1 \leqslant \mathop {\lim }\limits_{\lambda \to 0} \frac{{N(\lambda )}}{{\lambda ^{d_s /2} }}< \overline {\mathop {\lim }\limits_{\lambda \to 0} } \frac{{N(\lambda )}}{{\lambda ^{d_s /2} }} \leqslant C_2< \infty$$ whered _s =2log5/log(40/3) is the spectral dimension of MKG.     

Ab initio prediction of superconductivity in molecular metallic hydrogen under high pressure

We present a first ab initio investigation of the electron-phonon coupling (EPC) of molecular metallic hydrogen with a Cmca structure based on the linear-response approach. This molecular metallic hydrogen with overlapping bands has an elastic instability at lower pressures (<300 GPa), but stabilizes dynamically under further compression as indicated by the absence of phonon softening, thus supporting the choice of Cmca structure as a good candidate for metallic hydrogen. Within the conventional BCS theory, the predicted critical temperature T_c is 107 K at 347 GPa, so indicating good candidacy for a high temperature superconductor. With increasing pressure, interestingly, the EPC parameter λ, hence, T_c increases, resulting from the increased electronic density of states at the Fermi level and EPC matrix element 〈I²〉, in spite of an enhanced average phonon frequency 〈ω²〉.