Role of electron-phonon interactions versus electron-electron interactions in the broadening mechanism of the electron and hole linewidths in bulk Be

Abstract

We report on ab initio study of electron-phonon ͑e-ph͒ and electron-electron ͑e-e͒ interactions in bulk Be. The calculations show that the e-ph coupling parameter varies from 0.01 to 1.02 as a function of electron energy and momentum, = 0.21 at the Fermi level as averaged over momenta. The e-ph contribution ⌫ e-ph to the electrons and holes lifetime broadening also manifests clear dependence on the momentum and energy of an electron state. We demonstrate that the e-ph coupling matrix elements strongly affect the Eliashberg function especially for low phonon frequencies. By using the Debye model relation between ⌫ e-ph and the characteristic Debye frequency D is obtained in good agreement with the experimental one. The e-e contribution to the lifetime broadening is evaluated from the imaginary part of the electron self-energy computed within a GW approximation.

Enhanced Tc and multiband superconductivity in the fully-gapped ReBe22 superconductor

“…The Coulomb pseudo-potential  m was fixed to 0.13, a typical value for metallic samples. From equation (5) we obtain λ ep =0.64(1) for ReBe 22 , almost three times larger than the reported value for elemental Be (0.21) [32]. By using this value, finally, the band-structure DOS N band (ò F ) can be estimated from the relation…”

Electron–Phonon Interaction at Interfaces

“…The theoretical value of l at E F was found to be 0.9 in good agreement with the available data. In any event, the coupling is much stronger than in bulk Be for which l ¼ 0:21À0:23 (theory, [67,68] The C surface states of Mg(0001) and Al(001) have a rather different character from those of the noble metal (111) surfaces and of Be(0001). Both reside in a narrow projected bandgap and penetrate deeply into the bulk.…”

“…Another important finding was that the low-and middle-energy phonons are more involved in the scattering processes of electrons than the high-energy phonon modes unlike the case of bulk Al, as well as other simple metals Be and Mg, where the lower energy part of the phonon spectrum is strongly suppressed by eÀph matrix elements [27,61,[68][69][70].…”

Electron-phonon coupling in surface electronic states on Be(101¯0)

“…1, 31 As regards the Be(1010) surface, a great deal of experimental information is now available on the e-ph coupling of two Shockley-type surface electronic states at the surface Brillouin zone (SBZ) boundary (the A point). Several experimental studies [19][20][21]24 using both the temperature dependence of the photoemission linewidth and the renormalization of the surface-state dispersion at F revealed that the strength of the e-ph interaction in these surface states was different.…”