Tc map and superconductivity of simple metals at high pressure

We calculate T_c map in region of weak electron–phonon coupling based on simple phonon spectrum. By using linear-response method and density functional theory, we calculate phonon spectra and Eliashberg functions of simple metals under pressure. Based on the evolutions of superconducting parameters of simple metals on the T_c map with increasing pressure, we find that there are two different responses to pressure for simple metals: (1) enhancing electron–phonon interaction λ such as for La and Li, (2) increasing phonon frequency such as for Pb, Pt. The λ threshold effect is found, which origins from the competition between electron–phonon interaction and electron–electron Coulomb interaction and is the reason why T_c of most superconductors of simple metals are higher than 0.1 K.     

Reconstruction of the conduction band in metallic hydrogen sulfide

The theory of the normal properties of a metal generalized to the case of particular properties of an electron band with a finite width for electron–phonon systems with a varying electron density of states has been used to study the normal state of the SH₃ phase of hydrogen sulfide at a pressure of 225 GPa and a temperature of 200 K. The frequency dependences of the real, ReΣ(ω), and imaginary, ImΣ(ω), parts of the selfenergy part of the Green’s function of the electron Σ(ω), as well as the electron density of states N(ε) of the Im–3m stable orthorhombic structure of SH₃ hydrogen sulfide at a pressure of P = 225 GPa, which is renormalized by the strong electron–phonon coupling, have been calculated. It has been established that a part of the electron conduction band of the SH₃ phase of hydrogen sulfide adjacent to the Fermi level undergoes renormalization-induced reconstruction in the form of a number of energy pockets with the widths equal to fractions of the characteristic phonon energies of the system.     

Prediction of superconductivity of Ta2AlC: in situ Raman spectrometry and density functional investigations

In this paper, in situ Raman spectra of Ta₂AlC are measured in the temperature range of 80–500 K at ambient pressure. The frequencies of the Raman modes decrease with increasing temperature, which have been explained by the anharmonic and thermal expansion effects. The line‐width of E_2g (ω₃) mode increases at elevated temperatures, which is found to be due to the anharmonic phonon–phonon scatterings. On the other hand, the line‐widths of E_2g (ω₁) and A_1g (ω₄) modes decrease continuously with increasing temperature, which is explained by the electron–phonon couplings of these two phonon modes with the Ta 5d electrons. The electron–phonon coupling strengths are obtained both in experiments and density functional calculations. Finally, Ta₂AlC is predicted to be a new superconductive MAX phase. Copyright © 2014 John Wiley & Sons, Ltd.     

Study of spin–phonon coupling in LiFe1 − xMnxPO4olivines

LiFe_{1 − x}Mn_xPO₄ olivines are promising material for improved performance of Li‐ion batteries. Spin–phonon coupling of LiFe_{1 − x}Mn_xPO₄ (x = 0, 0.3, 0.5) olivines is studied through temperature‐dependent Raman spectroscopy. Among the observed phonon modes, the external mode at ~263 cm⁻¹ is directly correlated with the motions of magnetic Fe²⁺/Mn²⁺ ions. This mode displays anomalous temperature‐dependent behavior near the Néel temperature, indicating a coupling of this mode with spin ordering. As Mn doping increases, the anomalous behavior becomes clearly weaker, indicating the spin–phonon coupling quickly decreases. Our analyses show that the quick decrease of spin–phonon coupling is due to decrease of the strength of spin–phonon coupling, but not change of spin‐ordering feature with Mn doping. Importantly, we suggest that the low electrochemical activity of LiMnPO₄ is correlated with the weak spin–phonon coupling strength, but not with the weak ferromagnetic ground state. Our work would play an important role as a guide in improving the performances of future Li‐ion batteries. Copyright © 2015 John Wiley & Sons, Ltd.     

Physical insight of superconductivity of Nb2AlC: in situ Raman spectrometry investigation

Superconductivity of Nb₂AlC has been previously reported, but the origin is not clear. In this paper, in situ Raman spectra of Nb₂AlC are measured in the temperature range from 80 to 380 K at ambient pressure. The line‐width of E_2g (ω₁) mode increases with temperature which originates from the anharmonic phonon–phonon scattering. On the contrary the line‐widths of E_2g (ω₂) and A_1g (ω₄) modes decrease continuously at elevated temperature. The phenomenon is explained by the electron–phonon coupling. The origin of superconductivity is therefore interpreted by the coupling of Nb 4d electrons with E_2g (ω₂) and A_1g (ω₄) phonon modes. Copyright © 2013 John Wiley & Sons, Ltd.     

The effect of surface temperature on H2/D2(v = 0, j = 0)–Ni(100) scattering processes

We carry out both four-dimensional (4D×2D) and six-dimensional (6D) quantum dynamics on a parametrically time- and temperature-dependent effective Hamiltonian for H₂/D₂(v = 0,j = 0)–Ni(100) collision process. Such an effective potential was derived within a theoretical framework of mean-field approximation by considering weakly correlated interaction between molecular degrees of freedom, phonon modes and electron– hole pair (elhp) coupling through a Hartree-product-type wave function, where the initial state distribution of the surface modes and elhp coupling were introduced through Bose– Einstein and Fermi– Dirac probability factor, respectively. The temperature-dependent dissociation and state-to-state transition probabilities for H₂/D₂(v = 0,j = 0)–Ni(100) system are depicted as a function of initial kinetic energ of the incoming diatom. Though such effect appears negligibly small for H₂(v = 0,j = 0)–Ni(100) system, it is prominent in the case of D₂(v = 0,j = 0)–Ni(100) collision. It appears that the change of dissociation and transition probabilities of D₂ with the increase of surface temperature is exclusively dictated by the phonon modes directed along Z-axis, but the effect of elhp coupling particularly for transition probabilities is insignificant.     

Theoretical investigation of superconductivity in ternary silicide NaAlSi with layered diamond-like structure

We have investigated the electronic structure, phonon modes and electron–phonon coupling to understand superconductivity in the ternary silicide NaAlSi with a layered diamond-like structure. Our electronic results, using the density functional theory within a generalized gradient approximation, indicate that the density of states at the Fermi level is mainly governed by Si p states. The largest contributions to the electron–phonon coupling parameter involve Si-related vibrations both in the x–y plane as well as along the z-axis in the x–z plane. Our results indicate that this material is an s-p electron superconductor with a medium level electron–phonon coupling parameter of 0.68. Using the Allen–Dynes modification of the McMillan formula we obtain the superconducting critical temperature of 6.98 K, in excellent agreement with experimentally determined value of 7 K.     

Kinks and d-waves from phonons: The intermediate coupling story

I present results from an approach that extends the Eliashberg theory by systematic expansion in the vertex function; an essential extension at large phonon frequencies, even for weak coupling. In order to deal with computationally expensive double sums over momenta, a dynamical cluster approximation (DCA) approach is used to incorporate momentum dependence into the Eliashberg equations. First, I consider the effects of introducing partial momentum dependence on the standard Eliashberg theory using a quasi-local approximation; which I use to demonstrate that it is essential to include corrections beyond the standard theory when investigating d-wave states. Using the extended theory with vertex corrections, I compute electron and phonon spectral functions. A kink in the electronic dispersion is found in the normal state along the major symmetry directions, similar to that found in photo-emission from cuprates. The phonon spectral function shows that for weak coupling Wλ<ω₀, the dispersion for phonons has weak momentum dependence, with consequences for the theory of optical phonon mediated d-wave superconductivity, which is shown to be 2nd order in λ. In particular, examination of the order parameter vs. filling shows that vertex corrections lead to d-wave superconductivity mediated via simple optical phonons. I map out the order parameters in detail, showing that there is significant induced anisotropy in the superconducting pairing in quasi-2D systems.     

Solvatochromism as an efficient tool to study N,N‐dimethylamino‐ and cyano‐substituted π‐conjugated molecules with an intramolecular charge‐transfer absorption

A representative data set has been gained by the measurement of the electronic absorption spectra of 12 systematically selected push–pull systems with an intramolecular charge‐transfer (CT) absorption and the general structure D–π–A (D = donor, A = acceptor) featuring electron‐withdrawing CN groups, electron‐donating N(CH₃)₂ groups, and various π‐conjugated backbones in 32 solvents with different polarities. The longest‐wavelength absorption maxima λ_max and the corresponding wavenumbers $\tilde {v}_{{\rm max}} $ were evaluated from the UV/Vis spectra measured in 32 well‐selected solvents. The D–π–A push–pull systems were further characterized by quantum‐chemical quantities and simple structural parameters. Structure–solvatochromism relationships were evaluated by multidimensional statistic methods. Whereas solvent polarizability and solvent cavity size proved to be the most important factors affecting the position of λ_max, the solvent polarity was less important. The most important characteristics of organic CT compounds are the energy of the LUMO, the permanent dipole moment, the COSMO (COnductor‐like Screening MOdel) area, the COSMO volume, the number, and ratio of N,N‐dimethylamino and cyano groups, and eventually the number of triple bonds (π‐linkers). A relation between the first‐order polarizability α, the longest‐wavelength absorption maxima λ_max, and the structural features has also been found. The higher‐order polarizabilities β and γ are not related to the observed solvatochromism. Copyright © 2010 John Wiley & Sons, Ltd.     

Electronic Raman scattering and the electron–phonon interaction in YB6

Electronic Raman scattering in YB₆ and in its structural and electronic analog LaB₆ has been studied in the temperature range of 10–730 K. The experimental spectra have been compared to those calculated on the basis of ab initio band structures with renormalization owing to the electron–phonon interaction. Good agreement between the calculation and experiment for LaB₆ has been obtained throughout the entire temperature range. This allows the determination of the coupling constant λ _ep = 0.25. To satisfactorily describe the spectra of electronic light scattering in YB₆, it is necessary to introduce an additional electron relaxation channel. In this case, the estimate of the electron–phonon coupling constant λ _ep is no more than 0.4; for this reason, a high superconducting transition temperature cannot be explained only by the phonon mechanism.     

Theoretical examination of electron–phonon interaction and superconductivity in the hexagonal pnictide SrPtAs

We have calculated the structural and electronic properties of SrPtAs in a hexagonal KZnAs-type of crystal structure using a generalized gradient approximation of the density functional theory and the ab initio planewave pseudopotential method. These results are used to further calculate the phonon dispersions curves and the phonon density of states using a linear response approach based on the density functional theory. Using the electronic and phonon results, the electron–phonon coupling is computed to be of the intermediate strength of 0.78. In large part, this is contributed by the phonon modes dominated by the vibrations of Pt and As atoms. The superconducting critical temperature is estimated to be 1.9 K, in good accord with its experimental value of 2.4 K.     

Polaronic origin of the isotope effect on the London penetration depth in high-temperature superconducting oxides

Direct measurements of the in-plane London penetration depth λ _L have recently been performed on high-temperature superconducting copper oxides by a new low-energy muon spin rotation technique. The results show that λ _L is isotope dependent, evidencing unconventional electron–phonon interactions as its source. The data are interpreted here in terms of polaronic effects on the single-particle energies, which leads to level shifts and exponential band narrowing. Good agreement with the experimental data is obtained.     

Resonance Raman spectroscopic study for radial vibrational modes in ultra‐thin walled TiO2 nanotubes

The study reports the observation of radial vibrational modes in ultra‐thin walled anatase TiO₂ nanotube powders grown by rapid breakdown anodization technique using resonant Raman spectroscopic study. The as‐grown tubes in the anatase phase are around 2–5 nm in wall thickness, 15–18 nm in diameter and few microns in length. The E_{g(ν1,ν5,ν6)} phonon modes with molecular vibrations in the radial direction are predominant in the resonance Raman spectroscopy using 325 nm He–Cd excitation. Multi‐phonons including overtones and combinational modes of E_{g(ν1,ν5,ν6)} are abundantly observed. Fröhlich interaction owing to electron–phonon coupling in the resonance Raman spectroscopy of ultra‐thin wall nanotubes is responsible for the observation of radial vibrational modes. Finite size with large surface energy in these nanotubes energetically favor only one mode, B_1g(ν4) with unidirectional molecular vibrations in the parallel configuration out of the three Raman modes with molecular vibration normal to the radial modes. Enhanced specific heat with increasing temperatures in these nanotubes as compared to that reported for nanoparticles of similar diameter may possibly be related to the presence of the prominent radial mode along with other energetic phonon mode. The findings elucidate the understanding of total energy landscape for TiO₂ nanotubes. Copyright © 2015 John Wiley & Sons, Ltd.     

Superconductivity in ordered LiBe alloy under high pressure: A first-principles study

The electronic, vibrational, and superconducting properties of LiBe alloy in the P2₁/m structure under pressure have been investigated using first-principles calculations. The calculated electron–phonon coupling (EPC) of LiBe with both linear response theory and the rigid muffin-tin approximation suggested that pairing electrons are mainly mediated by the Li low-lying phonon vibrations, and the increase of the Li EPC matrix element $〈I_i^2〉$ with pressure is responsible for the increased EPC parameter $\lambda$. The application of the Allen–Dynes modified McMillan equation reveals high superconducting critical temperatures of 15.2 K at 80 GPa and 18.4 K at 100 GPa for P2₁/m LiBe.     

Electronic Raman scattering and the renormalization of the electron spectrum in LuB<Subscript>12</Subscript>

The electronic Raman scattering in LuB₁₂ single crystals of various isotope compositions is studied in the temperature range 10–650 K. The shape and the energy position of spectral maxima depend on the direction and magnitude of a probe wavevector, the temperature, and the excitation symmetry and remain unchanged when the isotope composition changes. Experimental spectra are compared with the spectra simulated on the basis of a calculated electronic structure. The experimental results are successfully described when the electron spectrum renormalization effects caused by electron–phonon coupling are taken into account. This confirms that the origin of the observed spectra in LuB₁₂ is due to Raman scattering by electrons. A comparison of the calculated and experimental data makes it possible to determine the coupling constant (λ_ep = 0.32) that gives the correct superconducting transition temperature.     

Superconductivity and normal state resistivity of Ba0.6K0.4BiO3: an optical phonon approach

We discuss the nature of the pairing mechanism and the physical properties associated with the normal as well as the superconducting state of cubic perovskites Ba_0.6K_0.4BiO₃using the strong coupling theory. An interaction potential which includes the Coulomb, electron–optical phonon and electron–plasmon interactions is developed to elucidate the superconducting state. A model dielectric function is constructed with these interactions fulfilling thef-sum rule. The screening parameter (μ^* = 0.26) infers the poor screening of charge carriers. The electron–optical phonon strength (λ) estimated as 0.98 is consistent with an attractive electron–electron interaction and supports the moderate to strong coupling theory. The superconducting transition temperature of Ba_0.6K_0.4BiO₃is then estimated as 32 K. Ziman's formula of resistivity is employed to analyse and compare this with the temperature-dependent resistivity of a single crystal. The estimated contribution from the electron–optical phonon together with the residual resistivity clearly infers a difference when a comparison is made with experimental data. The subtracted data infer a quadratic temperature dependence in the temperature domain (30 ≤ T ≤ 200 K). The quadratic temperature dependence of ρ [ = ρ_exp − (ρ₀ + ρ_e–ph)] is understood in terms of 3D electron–electron inelastic scattering. The presence of these el–el and el–ph interactions allows a coherent interpretation of the physical properties. Analysis reveals that a moderate to strong coupling exists in the Ba_0.6K_0.4BiO₃system and the coupling of electrons with the high-energy optical phonons of the oxygen breathing mode will be a reason for superconductivity. The implications of the above analysis are discussed.     

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.     

Raman imaging and stress quantification in self‐assembled graphene oxide fiber ‘Latin Letters’

To probe the intrinsic stress distribution in terms of spatial Raman shift (ω) and change in the phonon linewidth (Γ), here we analyze self‐assembled graphene oxide fibers (GOF) ‘Latin letters’ by confocal Raman spectroscopy. The self‐assembly of GOF ‘Latin letters’ has been explained through surface tension, π–π stacking, van der Waals interaction at the air–water interface and by systematic time‐dependent investigation using field emission scanning electron microscopy analysis. Intrinsic residual stress due to structural joints and bending is playing a distinct role affecting the E_2g mode (G band) at and away from the physical interface of GOF segments with broadening of phonon linewidth, indicating prominent phonon softening. Linescan across an interface of the GOF ‘letters’ reveals Raman shift to lower wavenumber in all cases but more so in ‘Z’ fiber exhibiting a broader region. Furthermore, intrinsic stress homogeneity is observed for ‘G’ fiber distributed throughout its curvature with negligible shift corresponding to E_2g mode vibration. This article demonstrates the significance of morphology in stress distribution across the self‐assembled and ‘smart‐integrable’ GOF ‘Latin letters’. Copyright © 2016 John Wiley & Sons, Ltd.     

Ab initio study on the high superconducting transition temperature in calcium under high pressure

For calcium in the phases IV and V, we estimated the superconducting transition temperature T _c by the use of the Allen–Dynes formula. Setting the effective screened Coulomb repulsion constant μ* at 0.1 in the formula, we obtained T _c =23.42 K at 100 GPa for Ca-IV and T _c =15.87 K at 120 GPa for Ca-V. In order to clarify the origin of such high values of T _c , first, we investigated the band character of electrons and found that the high T _c is not necessarily related to the so called s–d transfer. Then we analyzed the electron–phonon coupling at each phonon mode in Ca-V where the highest T _c in elements has been experimentally observed. As a result, we discovered that an optical mode at the Γ point has the strongest electron–phonon coupling. Such phonon mode can exist only in the complex crystal structure of Ca-V, and the result shows that the high T _c seems to be closely linked with the complex crystal structures like Ca-IV and Ca-V.     

First-principles study on superconductivity of solid oxygen

The superconductivity of solid oxygen in ζ phase was investigated by first-principles calculations based on the density functional theory. Using a monoclinic C2/m structure, we calculated the superconducting transition temperature by the Allen–Dynes formula and obtained 2.4 K at 100 GPa for the effective screened Coulomb repulsion constant μ* of 0.13. The transition temperature slowly decreases with increasing pressure and becomes 1.3 K at 200 GPa. The phonon analysis shows that the electron–phonon coupling is dominantly enhanced by the intermolecular vibrations of O₂ rather than the intramolecular ones. The phonon modes showing the strong electron–phonon coupling were found to be concentrated in the phonon frequency range of 100–150 cm^?1 at around the M-point in the Brillouin zone.