## 3 Results
Figure 2: Total energy fluctuation obtained from AIMD simulations conducted at 300 K (**a**) and 320 K (**c**) for the time of 4 ps for the Cu\({}_{2}\)TeO\({}_{6}\) monolayer. The atomic structure of the Cu\({}_{2}\)TeO\({}_{6}\) monolayer at 300 K (**b**) and 320 K (**d**) after 4 ps. in line with the fact that an ionic type of bond is characteristic of the bonded metal and non-metal, the difference in the electronegativity of which is higher than 1.5. Particularly, the electronegativity of O (3.5) and Cu (1.9) is higher 1.5, and the electronegativity of Te (2.1) is lower the electronegativity of O (3.5) by 1.4. The work function (WF) is a critical parameter to characterize a material [40]. It is defined as follows:  
\[\text{WF}=E_{\text{vac}}-E_{\text{Fermi}} \tag{2}\]  
where Evac is the energy level of a stationary electron in the vacuum, and \(E_{\text{Fermi}}\) corresponds to the Fermi level of the system. The calculated WF of the Cu\({}_{2}\)TeO\({}_{6}\) monolayer is found to be 7.76 eV, as shown in Figure 3b, which is much higher than it is for the most of the 2D materials such as graphene (4.60 eV) [41] and borophene (5.31 eV) [38] and 2D metal chlorides [35] and bulk metals [41] such as Ni (5.23 eV) and Pt (5.65 eV). Importantly, the materials with such a high WF value can be efficiently integrated, for instance, in photovoltaic devices based on a high-WF material/low-WF material hybrid junctions [42]. The calculated band structure and the local density of states (LDOS) of the Cu\({}_{2}\)TeO\({}_{6}\) monolayer are shown in Figure 4. It is predicted that the Cu\({}_{2}\)TeO\({}_{6}\) monolayer is a direct band gap semiconductor with the conduction band minimum (CBM) and valence band maximum (VBM) located at the Y and M points, and its band gap size is found to be 0.20 eV (Figure 4a). According to the LDOS plot in Figure 4b, both the CBM and VBM of the Cu\({}_{2}\)TeO\({}_{6}\) monolayer are formed of the Cu \(d\) states and O \(p\) states. Such a narrow band gap monolayer semiconductors can be used in infrared nanodetectors [43]. The mechanical stability of the Cu\({}_{2}\)TeO\({}_{6}\) monolayer is also evaluated using the conditions presented by [PERSON] [44]. As the elastic tensor is calculated based on the periodic boundary conditions, an arbitrary vacuum is presented in the out-of-plane direction when one is dealing with the monolayer. Therefore, the output values of the calculated elastic constants should be correct by eliminating the arbitrariness of the vacuum padding. Particularly, the C\({}_{ij}\) components (\(i,j\
eq 3\)) should be adjusted by multiplying them by the length of the vacuum padding [45]. For the considered Cu\({}_{2}\)TeO\({}_{6}\) monolayer elastic constants matrix is further calculated, the values of the obtained elastic constants \(C_{ij}\) are collected in Table 2. According to [44], the mechanical stability criteria for the oblique Bravais lattice are the following:  
\[ \begin{split} C_{11}>0\\ C_{11}C_{22}>\ C_{12}^{2}\\ \text{det}\ (C_{ij})\ >\ 0\end{split}  \tag{3}\]  
Figure 3: ELF with the isosurface value of 0.70 for the Cu\({}_{2}\)TeO\({}_{6}\) monolayer (**a**) and WF for the Cu\({}_{2}\)TeO\({}_{6}\) monolayer (**b**). Based on the data presented in Table 2, the Cu\({}_{2}\)TeO\({}_{6}\) monolayer is found to be mechanically stable as it satisfies the criteria in Equation (3). In addition, the mechanical properties of the Cu\({}_{2}\)TeO\({}_{6}\) monolayer such as Young's modulus, Poisson's ratio, and the shear modulus are calculated.