Underlying Topological Dirac Nodal Line Mechanism of the Anomalously Large Electron-Phonon Coupling Strength on a Be (0001) Surface.

Beryllium has recently been discovered to harbor a Dirac nodal line (DNL) in its bulk phase and the DNL-induced nontrivial surface states (DNSSs) on its (0001) surface, rationalizing several already-existing historic puzzles [Phys. Rev. Lett. 117, 096401 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.096401]. However, to date the underlying mechanism as to why its (0001) surface exhibits an anomalously large electron-phonon coupling effect (λ_{e-ph}^{s}≈1.0) remains unresolved. Here, by means of first-principles calculations, we show that the coupling of the DNSSs with the phononic states mainly contributes to its novel surface e-ph enhancement. Besides the fact that the experimentally observed λ_{e-ph}^{s} and the main Eliashberg coupling function (ECF) peaks are reproduced well in our current calculations, we decompose the ECF α^{2}F(k,q;v) and the e-ph coupling strength λ(k,q;v) as a function of each electron momentum (k), each phonon momentum (q), and each phonon mode (v), evidencing the robust connection between the DNSSs and both α^{2}F(k,q;v) and λ(k,q;v). The results reveal the strong e-ph coupling between the DNSSs and the phonon modes, which contributes over 80% of the λ_{e-ph}^{s} coefficient on the Be (0001) surface. It highlights that the anomalously large e-ph coefficient on the Be (0001) surface can be attributed to the presence of its DNL-induced DNSSs, clarifying the long-debated mechanism.