Citation: Dahal, D.; Gumbs, G.; Iurov, A.; Ting, C.-S. Plasmon Damping Rates in Coulomb-Coupled 2D Layers in a Heterostructure. Materials 2022, 15, 7964. https:// doi.org/10.3390/ma15227964 Academic Editors: Victoria Samanidou and Eleni Deliyanni Received: 9 October 2022 Accepted: 2 November 2022 Published: 11 November 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). materials Article Plasmon Damping Rates in Coulomb-Coupled 2D Layers in a Heterostructure Dipendra Dahal 1, *, Godfrey Gumbs 2 , Andrii Iurov 3 and Chin-Sen Ting 1 1 Texas Center for Superconductivity and Department of Physics, University of Houston, Houston, TX 77204, USA 2 Department of Physics and Astronomy, Hunter College, City University of New York, 695 Park Avenue, New York, NY 10065, USA 3 Department of Physics and Computer Science, Medgar Evers College, City University of New York, Brooklyn, NY 11225, USA * Correspondence: hn6565@wayne.edu Abstract: The Coulomb excitations of charge density oscillation are calculated for a double-layer heterostructure. Specifically, we consider two-dimensional (2D) layers of silicene and graphene on a substrate. From the obtained surface response function, we calculated the plasmon dispersion relations, which demonstrate how the Coulomb interaction renormalizes the plasmon frequencies. Most importantly, we have conducted a thorough investigation of how the decay rates of the plasmons in these heterostructures are affected by the Coulomb coupling between different types of two- dimensional materials whose separations could be varied. A novel effect of nullification of the silicene band gap is noticed when graphene is introduced into the system. To utilize these effects for experimental and industrial purposes, graphical results for the different parameters are presented. Keywords: plasmon; graphene; silicene; heterostructure 1. Introduction A huge number of researchers from various disciplines have been showing their inter- est in new materials, silicene especially, after the development of its fabrication process in 2012 [1]. Because of its exceptional potential applications in electronic and optoelectronic devices, many industries are making substantial investments to harness its properties. Additionally, before making investments for commercial gain, both theoreticians and experimentalists have been exploring this material for many years. A credit of foremost im- portance goes to Takeda and Shiraishi [2], who, in 1994, dealt with the atomic and electronic structure of the material for the first time. These authors calculated the band structure of silicon in the corrugated stage having optimized atomic geometry. This work, though very novel, did not receive the attention it deserves until 2004, when single-layer carbon atoms named graphene were fabricated in the laboratory from graphite by Novoselov et al. [3]. Their research not only validated the stability of two-dimensional (2D) material but also opened the door for new research on thin film materials, silicene being one of them. Both silicene and graphene were studied in parallel. The former has a buckled crystal geometry, whereas the latter has a honeycomb planar geometry. Due to this, differences arise between them. Ab initio calculations showed that the bandgap of silicene is electrically tunable [4–6], which is an advantageous property for designing a field effect transistor that works at room temperature. Another distinct difference between these two materials is the strength of the spin-orbital coupling (SOC), which is very weak in graphene. Consequently, the quantum spin Hall effect occurs at extremely low temperatures [7,8]. In contrast to this, silicene displays quantum spin Hall effect at temperature 18 K, far higher than that for graphene. Several investigations have been carried out on both graphene and silicene with respect to transport phenomena [9–16], as well as their magnetic and electric field Materials 2022, 15, 7964. https://doi.org/10.3390/ma15227964 https://www.mdpi.com/journal/materials