Beyond Eliashberg Superconductivity inMgB2: Anharmonicity, Two-Phonon Scattering, and Multiple Gaps

Abstract

Density-functional calculations of the phonon spectrum and electron-phonon coupling in MgB2 are presented. The E2g phonons, which involve in-plane B displacements, couple strongly to the px,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 λ in the clean limit is calculated to be significantly larger. The E2g phonons are strongly anharmonic, and the non-linear contribution to the coupling between the E2g modes and the px,y bands is significant.The recent discovery of superconductivity near 40 K in MgB 2 has generated much interest in the properties of this simple intermetallic compound [1]. A significant B isotope effect strongly suggests phonon-mediated pairing [2]. To explain the large T c , an electron-phonon coupling (EPC) constant of λ ≈ 1 is needed. Yet estimates of the coupling strength based on the latest measurements of the low-temperature specific heat [3], combined with the density of states (DOS) from density-functional calculations [4], yield λ ≈ 0.6-0.7. Further, the measured temperature dependence of the electrical resistivity [5] is consistent with λ tr 0.6. First-principles calculations of the EPC give λ ≈ 0.7 − 0.9 [4,6,7]. Clearly there is a problem in reconciling all these numbers. Another puzzle involves tunneling measurements of the gap. Values of 2∆/k B T c ranging from 1.2 to 4 have been reported. The values below the BCS weak coupling limit of 3.5 have been attributed to surface effects, but the best-quality spectra [8] show a very clean gap with 2∆/k B T c = 1.25. Sharvin contact measurements [9] reveal a gap at 4.3 meV (2∆/k B T c = 2.6), and additional structures at 2∆/k B T c = 1.5 and 3, raising the possibility of multiple gaps. Careful analysis of the temperature and magnetic field dependence of the specific heat suggests anisotropic or multiple gap structure as well [3]. Thus, even if superconductivity in MgB 2 is phonon-mediated, it is likely that an analysis beyond the simple isotropic Eliashberg model is needed.The MgB 2 lattice consists of two parallel systems of flat layers. One layer contains B atoms in a honeycomb lattice, the other Mg atoms in a triangular lattice halfway between the B layers. First-principles calculations [4] find that the electronic states near the Fermi level are primarily B in character and the Fermi surface (FS) comprises four sheets: two nearly cylindrical hole sheets about the Γ-A line arising from quasi-2D p x,y B bands, and two tubular networks arising from 3D p z bonding and antibonding bands [4]. The difference in character between the sheets raises the possibility that each has a distinct gap that could be observed in the clean limit. Such interband anisotropy enhances the effective EPC constant relevant to superconductivity and decreases the coupling constant for transport, compared to the average values [10][11][12]. This could explain the discrepant values of λ deduced from different types of experiments.In this pa...

Electronic Structure of Single-Crystalline MgxAl1−xB2 Probed by X-ray Diffraction Multipole Refinements and Polarization-Dependent X-ray Absorption Spectroscopy

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Chirald-wave superconductivity in doped graphene

“…Due to a large charge transfer, the Fermi surface is located inside the bonding σ-band of the honeycomb lattice [229]. Despite the high transition temperature, superconductivity has been established to be phonon-driven and have an s-wave symmetry, however, with an unusual two-gap structure [230,231]. Closely related to MgB 2 are the ternary silicides M AlSi (M = alkaline-earth atoms), which are also superconducting, albeit at lower temperatures.…”

Pressure dependence of critical temperature in MgB2 and two-bands Eliashberg theory

“…4). The last possibility is suggested by recent bandstructure calculations that show M gB 2 is a traditional sp metal superconductor [3]. The pressure dependence of I has long been an interesting issue in the research of pressure effects in simple sp metals [26].…”

“…The magnesium diboride has stimulated intense investigation, both from the theoretical and the experimental point of view. Now the electronic structure of M gB 2 is well understood and the Fermi surface consists of two three-dimensional sheets, from the π bonding and antibonding bands, and two nearly cylindrical sheets from the two-dimensional σ bands [3]. There is a large difference in the electronphonon coupling on different Fermi surface sheets and this fact leads to a multiband description of superconductivity.…”