Abstract
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)]. However, to date the underlying mechanism as to why its (0001) surface exhibits an anomalously large electron-phonon coupling effect () 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 -ph enhancement. Besides the fact that the experimentally observed and the main Eliashberg coupling function (ECF) peaks are reproduced well in our current calculations, we decompose the ECF and the -ph coupling strength as a function of each electron momentum (), each phonon momentum (), and each phonon mode (), evidencing the robust connection between the DNSSs and both and . The results reveal the strong -ph coupling between the DNSSs and the phonon modes, which contributes over 80% of the coefficient on the Be (0001) surface. It highlights that the anomalously large -ph coefficient on the Be (0001) surface can be attributed to the presence of its DNL-induced DNSSs, clarifying the long-debated mechanism.
- Received 20 December 2018
- Revised 8 August 2019
DOI:https://doi.org/10.1103/PhysRevLett.123.136802
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