Plasmonlike resonances in atomic chains: A time-dependent density-functional theory study

Abstract

We studied plasmonlike resonances in one-dimensional (1D) atomic chain systems by using time-dependent density-functional theory (TDDFT) and local density functional theory. Recent TDDFT studies have shown the coexistence of longitudinal and transverses collective plasmonlike resonances in the atomic chains of simple and noble metals. Such atomic chains contain only a few atoms. The induced polarization occurs along the atomic chain in longitudinal mode and perpendicular to the atomic chain in transverse mode. To understand the emergence of plasmonlike resonance in 1D atomic chains better, we studied carbon chains in which plasmonic resonances are not expected to occur. We used TDDFT to study the emergence of collective resonances in various forms of carbon chains, cumulenes ${\mathrm{C}}_{n}{\mathrm{H}}_{4}$, polyynes ${\mathrm{C}}_{n}{\mathrm{H}}_{2}$, and alkenes ${\mathrm{C}}_{n}{\mathrm{H}}_{n+2}$. The excitation energy and dipole oscillation strengths of these systems were determined through TDDFT by using the turbomole package. We determined how collective plasmonlike resonances arise from single-electron excitations when the number of electrons increases as the carbon chain lengthens. The collective excitation behavior is then compared with that of metallic atomic chains. Our TDDFT results showed longitudinal collective modes for cumulenes and polyynes, as well as for finite-length chains. These collective excitations exhibit the same behavior as that of longitudinal ``plasmon'' previously identified in sodium and silver chains, although polyynes are gapped in the long chain limit. Such longitudinal excitations are absent in alkenes. However, unlike metal atomic chains, carbon chains exhibited no transverse collective mode. The band structure of periodic atomic chains was calculated by using the standard local density functional method. These structures were used to interpret the results and to relate the single-electron excitation to the collective plasmonlike response. Within the one-particle quantum-well picture, the longitudinal mode in the linear atomic chain arises from intraband transition with $\ensuremath{\Delta}q=1$, where $q$ is the quantum number of quantum wells. $\ensuremath{\Delta}q=1$ intraband transitions can be found in metallic (e.g., Na) chains and in carbon chains (cumulenes and polyynes), such longitudinal collective mode is rather ``generic''. Meanwhile, the transverse modes of the sodium chains are attributed to interband transitions with an even $\ensuremath{\Delta}q$ (dominated by $\ensuremath{\Delta}q=0$), and such transverse collective excitations only form if the allowed $\ensuremath{\Delta}q=0$ transitions occur between bands that are parallel to each other. Such bands can be found in simple metals, but not in carbon chains.