## 1 Introduction  
Two dimensional (2D) materials are atomically thin sheets that exhibit unique properties with lots of potential for technological applications, and they possess an abundance of applications which remain unexplored by fundamental science. Two dimensional materials also serve as building blocks for a variety of the next generation layered and composite materials [1; 2]. Since the isolation of the first 2D material, graphene, from a bulk graphite, thousands of 2D materials have been developed. For example, graphene-like 2D materials such as the boron nitride (h-BN) monolayer [3; 4] and transition metal dichalcogenides (TMDs), e.g., MoS\({}_{2}\), WS\({}_{2}\), MoSe\({}_{2}\), and WSe\({}_{2}\)[5; 6], MXenes [7], mono-layered silicon carbides (Si\({}_{x}\)C\({}_{y}\)) [8], and monochalcogenides (GaSe) [9], etc.  
The reliable synthesis of 2D materials is an important first step towards characterizing the size-related changes in their properties, which provides ways to integrate them into many applications [10]. Synthesis strategies can be divided into top-down and bottom-up methods. In the bottom-up approach, nano-scale materials are constructed from atomic or molecular precursors which grow into complex structures [11; 12]. On the other hand, the top-down approach carves nano-scale structures by the removal of materials from bulk solids using various exfoliation methods [13; 14; 15]. Two dimensional materials synthesized using the methods described above have many unusual properties. For example, MoS\({}_{2}\) has a tunable bandgap, and it can be used as a hole transport layer in solar cells [16], and mono-layered titanium oxide (TiO\({}_{2}\)) can be used to enhance the dielectric properties of polyvinylidene fluoride [17], etc.  
However, it is difficult to carry out experimental studies on such thin materials due to experimental constraints, as the experiments are costly and time consuming. This means that theoretical and computational studies can be considered as an integral part of the research on 2D materials. At the moment, there are many theoretical methods for studying 2D materials such as machine learning-based approaches [18], first-principles calculations based on the density function theory [19], the Monte Carlo method [20], and finite element simulations [21], etc. More specifically, first-principles calculations have been found to be a powerful tool for predicting the structures and properties of materials due to their consistency with the experimental results. Using first-principles calculations, the structure and properties of various 2D materials such as the novel Dirac material TiZrB\({}_{\mu}\), with its negative Poisson ratio [22], V\({}_{2}\)O\({}_{3}\), with its quantum anomalous Hall effect [23], and hightemperature ferromagnetic Co\({}_{2}\)Ti\({}_{2}\)Sn\({}_{2}\)[24] and BiXenes [25] have been predicted. It is also notable that many 2D materials, in particular, hematene [26], Fe\({}_{2}\)O\({}_{3}\)[27] and FeTiO\({}_{3}\)[28], have been synthesized based on first-principles simulations results.  
In this work, a new material, the Cu\({}_{2}\)TeO\({}_{6}\) monolayer, which is 2D analog of bulk Cu\({}_{2}\)TeO\({}_{6}\)[29], is predicted using first-principles calculations. Its dynamic and thermal stability is studied. The comprehensive analysis on the properties of the predicted Cu\({}_{2}\)TeO\({}_{6}\) monolayer is also conducted. Particularly, its electronic and mechanical properties are investigated.