以碳纳米管和石墨为代表的一维和二维结构材料展现出许多同种成分的体材料所不具备的光、电、磁和力学性质，同时由于自身的轻巧灵便在以后的电子器件方面拥有良好的应用前景。但是目前对低维材料的研究还远远不够，很多具备潜力的低维材料还等待着我们去发现。理论上预言能够稳定存在一种二维结构的Ag2Te（这里我们简称η结构）。这种二维结构的Ag2Te是拓扑绝缘体，在较大应力范围内仍能处于拓扑绝缘相。本文运用第一性原理计算研究了由η结构卷曲形成的纳米管，同时探究了是否还有可能存在其他的Ag2Te二维结构。与η结构相比，我们发现有的结构会使体系能量上升，但有的结构会使体系能量降低，同时由于原子位置的进一步移动，体系的电子结构也发生了变化。我们发现这些体系有的是半金属，也有窄隙半导体。我们仔细分析了ζ结构（总能最低的结构）和η结构的电子结构，发现结构不一样自旋轨道耦合强度也发生了变化。从理论上分析如果体系能量降低，体系应该更加稳定了，于是我们去计算了能量较低的结构体系声子谱，遗憾的是发现声子谱存在虚频，表明这些结构动力学性质并不稳定。同时我们计算了由η 结构组成的扶手型结构纳米管(2,2)～(7,7)和锯齿型纳米管(3,0)～(8,0)。我们发现不同于其他纳米管（如碳纳米管，BN纳米管等）正的卷曲能,Ag2Te除了锯齿型(3,0) 时卷曲能为正，其他的这些结构都是曲率能为负。负的卷曲能意味着卷曲可以使体系能量降低，这对实验上合成Ag2Te纳米管是很有帮助的，显示出一种“ 自组装”特性。此外这些纳米管都是能隙在0.05ev～0.36ev 范围内的半导体。我们计算了这类纳米管的杨氏模量，发现Ag2Te纳米管的杨氏模量是碳纳米管的杨氏模量的七分之一左右，是一种非常软的材料，十分容易拉伸，并且杨氏模量随着半径的变化没有发生很大变化。后面我们计算了Ag2Te纳米管(2,2)和(4,4) 结构的声子谱，发现在半径较小(2,2) 结构时的声子谱存在虚频，代表不能稳定的存在，而对于半径较大的(4, 4)结构我们发现声子谱是稳定的，只不过声子谱对真空层选取的距离特别的敏感。

Low-dimensional materials, such as one-dimensional graphene nanotubes and twodimensional graphene sheets, exhibit many outstanding optical, electrical, magnetic and mechanical properties distinguished from their bulk materials, which have great prospects in the field of electronic devices.However, the current research on low-dimensional materials is far from enough, and many potential low-dimensional materials are still waiting for us to discover. It has been predicted that there is a two-dimensional structure of Ag2T e(here we call it η structure) can be stabilized,whose topological insulating phase is robust even undergo a large stress. In this paper, we systemically study the properties of Ag2T e nanotubes via the first principle calculation, and then concentrate on some other possible two-dimensional structures of Ag2T e. Our calculations show that the total energy of Ag2T e with different structures can be either increased or decreased when comparing to η-Ag2T e. At the same time, the electronic structure of the system will change due to the displacements of atoms, exhibiting a semi-metallic or narrow-gap semiconducting state. By carefully comparing the electronic properties of η-Ag2T e and ζ-Ag2T e (the structure with the lowest total energy), we find out that the strength of spin-orbit coupling in these two systems are quite different.Theoretically, the system with lower energy prefers to be more stable. So we calculate the phonon spectrum of the lower-energy structure system . Unfortunately, we find that there is imaginary frequency in the phonon spectrum, which indicates that the kinetic properties of these structures are not stable.Moreover, we calculated the the curvature energy of armchair nanotubes (2, 2) ∼ (7, 7) and zigzag nanotubes (3, 0) ∼ (8, 0). Unlike other nanotubes such as carbon nanotubes and BN nanotubes that has a positive curvature energy, almost all the structures of Ag2T e have a negative curvature energy except for the zigzag nanotube (3, 0).Negative curvature energy means that crimping can reduce the energy of the system, which showing a “self-assemble” characteristic is helpful for the experimental synthesis of Ag2T e nanotubes. In addition, these nanotubes are all semiconductors with energy gaps in the range of 0.05ev ∼ 0.36eV.Moreover,We calculated the Young’s modulus of these nanotubes and found that they are very soft and easy-stretch materials with the Young’s modulus only about one seventh of that in the carbon nanotubes, which is almost unchanged under the various radius. Furthermore,we calculated the phonon spectra of (2, 2) and (4, 4) Ag2T e nanotubes . We found that the phonon spectra of the (2, 2) structures with a small radius have imaginary frequencies, implying the instability of this structure. As for the structure with a larger radius of (4, 4), the phonon spectra are stable in this system, but the phonon spectra are particularly sensitive to the distance of vacuum layers. The innovations of this paper are as follows: ∙A new type of nanotubes with negative curvature energy were found. The electronic structures of Ag2T e armchair and zigzag nanotubes were calculated. The phonon spectrum calculation showed that Ag2T e nanotube could exist stably. ∙Several possible two-dimensional structures of Ag2T e were calculated,their electronic structure and phonon spectrum properties also have been studied.It is found that these structures are not stable even with a lower energy