Time-dependent density functional perturbation theory (TDDFPT) with Liouville-Lanczos recursion chains for large system-sizes: dispersion of the conventional and acoustic surface plasmons of high Miller-index vicinal surfaces of gold. Effect of spin-orbit coupling and of the surface geometry.*

Over a decade ago, a new type of surface plasmons has been both predicted theoretically for surfaces that support Shockley electronic surface states [1], and experimentally reported [2]. The so-called acoustic surface plasmon (ASP) exhibits a dispersion different from the behaviour of conventional surface plasmons. ASPs in gold have a twofold advantage for plasmonics applications: due to the linear dispersion, a signal consisting of several ASP waves can propagate without distortion; and vicinal Au surfaces have a step-terrace structure that provides the intrinsic grating on the atomic level, allowing, potentially, to couple the ASP to light.

I will present a new algorithm based on the Lanczos recursion within TDDFPT [3] that allows for accurate and efficient computations of the electron-energy loss spectra for arbitrary values of the transferred momentum q. The vicinal Au (455) surface could be modelled with 5 nm of gold (253 atoms) separated by 5 nm of vacuum. The effect of spin-orbit coupling on the ASP dispersion, as well as the role of intra- and inter-band transitions, have been examined. I show that the computation of plasmons on the quantum level is within reach for systems of unprecedented size.


[1] V. M. Silkin, A. García-Lekue, J. M. Pitarke, E. V. Chulkov, E. Zaremba, and P. M.
Echenique, Europhys. Lett. 66, 260, (2004).
[2] B. Diaconescu, K. Pohl, L. Vattuone, L. Savio, P. Hofmann, V.M. Silkin, J.M.
Pitarke, E.V. Chulkov, P.M. Echenique, D. Farias, and M. Rocca, Nature 448, 57, (2007).
[3] I. Timrov, N. Vast, R. Gebauer, S. Baroni, Phys. Rev. B88, 064301 (2013); Phys. Rev. B 91,139901 (2015); Computer Physics Communications 196, 460 (2015).