## 1 Introduction  
Several plasmonic metal nanoparticle-graphene systems have been reported in the literature for applications in surface-enhanced Raman spectroscopy (SERS) [1; 2], photodetection [3], enhanced biosensing, and photocatalysis, among others. Indeed, in analyzing this literature, the use of pristine graphene (G) or graphene oxide (GO) should also be noted [4; 5], the latter always presenting some defects and some oxygen functional groups such as COOH, COH, and COH at the reduced graphene oxide surface. Different oxidizing agents lead to various carbon-to-oxygen ratios and chemical compositions in GO and, consequently, to a different surface energy of graphene and GO, which contributes to the hydrophobic character of graphene and to the hydrophilic character of GO, thereby differently affecting the anchoring and coupling to plasmonic metal nanoparticles (NPs). Furthermore, most of these systems rely on noble plasmonic metals such as gold (Au) and silver (Ag), and again, in comparing literature in the field of graphene-plasmonic Au NPs, attention should be paid to whether Au NPs are pure or stabilized/decorated by surfactant and functionalizing agents, which also affects the graphene/NP interface and coupling [6]. Indeed, the use of Au and Ag metals on pristine graphene entails some problems. For instance, when Au film is in physical contact with graphene, delamination can easily occur at the contact interface. Furthermore, \(d\)-valence electrons of noble metals exhibit covalent bonding on the top (T) site of the graphene structure with strong hybridization of the adatom and graphene electronic states, which leads to a strong distortion and changes the graphene \(sp^{2}\)-like C to a more covalent reactive \(sp^{3}\)-like C [3; 7]. This strong interaction has also been reported to significantly modify the band structure and Dirac cones of graphene [8]. For example, in Ag NP/G/Ag systems the appearance of the D band in the Raman spectra of graphene has been reported due to the defects caused by the graphene-Ag interaction [2]. On the contrary, research on finding non-noble plasmonic metals is expanding [9], and among these, elements from groups XIII (i.e., Ga) are interesting since calculations predict [7] that Ga adsorbs on the hollow (H) site of graphene and does not distort the graphene sheet, so the C-C bonds near the adatom retain their \(sp^{2}\) character. Therefore, the use of this type of plasmonic metals presents advantages with respect to the widely used noble metals. Moreover, the plasmonic properties of Ga have been demonstrated to be superior to those of Ag, Au, or Cu due to its chemical stability (Ga forms a \(1\) nm oxide shell thickness that protects and keeps the NPs stable for years [10]) and the spectral tunability of the plasmon peak from the near-IR to the UV [11] (Ag, Au, and Cu have an interband transition in UV that inhibit a plasmonic response in this spectral region [12]). Furthermore, among the various configurations, the metal/graphene/metal sandwich coupling system has gained interest for using the graphene layer as a controlled nano-spacer [1; 2; 13; 14]. The reason for this is the strong local field enhancement achieved by the multiple couplings produced, including the NP-NP coupling and NP-metal film coupling through the graphene that further strengthens the electromagnetic field [1; 2]. Examples of this sandwich plasmonic graphene system are the all-Ag Ag NP/G/Ag [2] and all-Cu Cu NP/G/Cu [1] sandwich systems, which can be considered almost symmetric configurations in the sense that the metals on the two sides of graphene have the same work function. In this work, we analyze the Ga NP/graphene/Cu and the Ga NP/graphene/Ni sandwich structures.