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Register a new userBeyond Eliashberg superconductivity in MgB2: anharmonicity, two-phonon scattering, and multiple gaps
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Density-functional calculations of the phonon spectrum and electron-phonon coupling in MgB$_2$ are presented. The $E_{2g}$ phonons, which involve in-plane B displacements, couple strongly to the $p_{x,y}$ electronic bands. The isotropic electron-phonon coupling constant is calculated to be about 0.8. Allowing for different order parameters in different bands, the superconducting $lambda$ in the clean limit is calculated to be significantly larger. The $E_{2g}$ phonons are strongly anharmonic, and the non-linear contribution to the coupling between the $E_{2g}$ modes and the p$_{x,y}$ bands is significant.
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Two-phonon contributions to meV-resolved inelastic x-ray scattering spectra of MgB2 at 300K are identified, in good agreement, in both intensity and energy, with a harmonic calculation using the force constant matrix from ab-inito LDA calculations. This contribution impacts the determination of the linewidth of the E2g phonon mode that is so important for the high Tc of this material. To the best of our knowledge, this is the first observation of peaks in measurements of phonon dispersion (q>0) due to 2-phonon scattering in a non-rare-gas solid.
Since the discovery of high transition-temperature (Tc) superconductivity in copper oxides two decades ago, continuous efforts have been devoted to searching for similar phenomenon in other compounds. With the exception of MgB2 (Tc =39 K), however, Tc is generally far lower than desired. Recently, breakthrough has been made in a new class of oxypnictide compounds. Following the initial discovery of superconductivity in LaO1-x FxFeAs (Tc =26 K), Tc onset has been raised to 55 K in ReO1-xFxFeAs (Re: Ce, Pr, Nd, Sm). Meanwhile, unravelling the nature of the energy associated with the formation of current-carrying pairs (Cooper pairs), referred to as the superconducting energy gap, is the first and vital step towards understanding why the superconductivity occurs at such high temperature and is also important for finding superconductors with still higher Tc. Here we show that, on the basis of the nuclear magnetic resonance (NMR) measurements in PrO0.89F0.11FeAs (Tc =45 K), the Cooper pair is in the spin-singlet state (two spins are anti-paralleled), with two energy gaps opening below Tc. The results strongly suggest the existence of nodes (zeros) in the gap. None of superconductors known to date has such unique gap features, although copper-oxides and MgB2 share part of them.
We study the normal-state and superconducting properties of NaFe$_{1-x}$Co$_x$As system by specific heat measurements. Both the normal-state Sommerfeld coefficient and superconducting condensation energy are strongly suppressed in the underdoped and heavily overdoped samples. The low-temperature electronic specific heat can be well fitted by either an one-gap or a two-gap BCS-type function for all the superconducting samples. The ratio $gamma_NT_c^2/H_c^2(0)$ can nicely associate the neutron spin resonance as the bosons in the standard Eliashberg model. However, the value of $Delta C/T_cgamma_N$ near optimal doping is larger than the maximum value the model can obtain. Our results suggest that the high-$T_c$ superconductivity in the Fe-based superconductors may be understood within the framework of boson-exchange mechanism but significant modification may be needed to account for the finite-temperature properties.
We report a detailed study of specific heat, electrical resistivity and thermal expansion in combination with inelastic neutron and inelastic X-ray scattering to investigate the origin of superconductivity in the two silicon clathrate superconductors Ba8Si46 and Ba24Si100. Both compounds have a similar structure based on encaged barium atoms in oversized silicon cages. However, the transition temperatures are rather different: 8 K and 1.5 K respectively. By extracting the superconducting properties, phonon density of states, electron-phonon coupling function and phonon anharmonicity from these measurements we discuss the important factors governing Tc and explain the difference between the two compounds.
The standard Eliashberg - McMillan theory of superconductivity is essentially based on the adiabatic approximation. Here we present some simple estimates of electron - phonon interaction within Eliashberg - McMillan approach in non - adiabatic and even antiadiabatic situation, when characteristic phonon frequency $Omega_0$ becomes large enough, i.e. comparable or exceeding the Fermi energy $E_F$. We discuss the general definition of Eliashberg - McMillan (pairing) electron - phonon coupling constant $lambda$, taking into account the finite value of phonon frequencies. We show that the mass renormalization of electrons is in general determined by different coupling constant $tildelambda$, which takes into account the finite width of conduction band, and describes the smooth transition from the adiabatic regime to the region of strong nonadiabaticity. In antiadiabatic limit, when $Omega_0gg E_F$, the new small parameter of perturbation theory is $lambdafrac{E_F}{Omega_0}simlambdafrac{D}{Omega_0}ll 1$ ($D$ is conduction band half -- width), and corrections to electronic spectrum (mass renormalization) become irrelevant. However, the temperature of superconducting transition $T_c$ in antiadiabatic limit is still determined by Eliashberg - McMillan coupling constant $lambda$. We consider in detail the model with discrete set of (optical) phonon frequencies. A general expression for superconducting transition temperature $T_c$ is derived, which is valid in situation, when one (or several) of such phonons becomes antiadiabatic. We also analyze the contribution of such phonons into the Coulomb pseudopotential $mu^{star}$ and show, that antiadiabatic phonons do not contribute to Tolmachevs logarithm and its value is determined by partial contributions from adiabatic phonons only.
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