中文摘要：

采用基于密度泛函理论的第一原理方法研究了T型石墨烯及其衍生物-n（n=1—5）的结构稳定性和电子结构性质.T型石墨烯是一种拥有四角形环的二维碳材料同素异构体,通过改变连接四角形环的碳链上的碳原子个数n,可以得到一系列的sp-sp2杂化结构,称其为T型石墨烯衍生物-n.计算结果表明：这些材料的结构稳定性、化学键类型和电子结构性质都依存于n的奇偶性.其中T型石墨烯（n=0）的结构最稳定,并形成一个由8个碳原子构成的大环.声子谱计算的结果表明,n为偶数时的体系具有动力学稳定性,而n为奇数时的体系则是不稳定的.n为偶数时体系四角形环之间的碳链上的化学键呈单、三键交叉排列,体系显示为金属性特征,且随着n的增大,体系的金属性加强.n为奇数时体系四角形环之间的碳链上的化学键则为双键连续排列,体系呈金属性且具有磁性（n=1除外）.研究表明该系列材料作为一种新的二维碳材料同素异构体,具有独特的结构和丰富的电子结构特性,很可能在纳米器件中得到广泛应用.

英文摘要：

Recent years there has been aroused a growing interest in designing two-dimensional （2D） structures of carbon allotropes, owing to the great success in graphene. The T-graphene is a newly proposed 2D carbon allotrope possessing tetragonal symmetry other than hexagonal symmetry of graphene. Also, the energetic and dynamical stabilities of T-graphene have been revealed. So motivated, we investigate the structural stabilities and electronic properties of T-graphene and especially its derivatives-n（n=1–5） by using the first-principle calculation based on the density function theory. By changing the atomic number （n） of the linear carbon chains connecting the two tetragon rings of T-graphene, a series of sp-sp2 hybrid structures can be formed, which is named T-graphene derivatives-n. The calculation results show that the structural stabilities, chemical bond types and electronic structures of these materials depend greatly on the parity of n. Owing to a strongπ-bond formed by eight carbon atoms in T-graphene, it becomes the one with the lowest energy in all these materials studied in this work. An interesting phenomenon is found that the T-graphene derivatives-n with even n are dynamically stable as witnessed by the calculated phonon spectra without imaginary modes, while those with odd n are dynamically unstable. The metallic behaviors are present in the T-graphene derivatives-n with even carbon atoms in the linear carbon chains, showing an alternating single and triple C—C bonds. Besides, we observe that the metallicity of the T-graphene derivatives-n with even n becomes stronger as n increases. On the other hand, the linear carbon chains with odd carbon atoms are comprised of continuous C=C double bonds. These T-graphene derivatives-n with odd n also show metallic behaviors, but turn into magnetic materials （except for n=1）, the magnetic moments are about 0.961μB （n=3） and 0.863μB （n=5） respectively, and ferromagnetic ordering is the only possibility for the magnetism, which rarely oc