自从被发现以来，石墨烯这种二维碳材料就不断受到物理学界和材料科学界的普遍关注。这是因为石墨烯的零隙能带结构，其费米点附近的电子服从相对论量子力学的Dirac方程。独特的电子行为引起了很多新奇的量子效应，如反常量子Hall效应、Klein隧穿、最小电导率等。本文在研究中分别采用了紧束缚近似理论，Dirac方程、Dyson方程及散射微扰理论，求得了描述体系的松原格林函数。利用费曼图技术以及Kubo公式，在T矩阵近似下研究了二维单层石墨烯的杂质散射效应。希望本文的研究能对电子波导纤维、石墨烯导体量子元件的设计和开发有一定的参考价值。现将本文的内容和结果简要归纳如下： （1）从石墨烯最近邻紧束缚模型出发，将原来非对角的哈密顿量经过玻戈留波夫变换对角化后，获得了准电子产生消灭算符的直接时间依赖关系，再将虚时格林函数经傅里叶变换后得到描绘体系的二分量自由松原格林函数。有掺杂时，自由格林函数会因为杂质散射而得以修正，从而产生松原函数的自能部分，根据Dyson方程得出有杂质散射的格林函数。在解析延拓得出推迟格林函数后，可计算体系的态密度，有掺杂时体系的态密度有限。 （2）定义通用的流算符形式，在谱表示下求出具有一般性的极化函数。取出推迟极化函数的虚部，这将适用于电导、热导、自旋导的计算。在研究杂质散射效应时，自由极化函数因杂质散射而对顶角产生修正，利用费曼阶梯图和T矩阵近似，得到了包含耦合参数g,速度(v_l ) ?,以及泡利矩阵τ ?_α的普适极化函数的虚部ImΠ ?_ret^glα。 （3）对于电导、热导、自旋导等输运系数的计算，每部分均由相应的流密度算符的推导开始，而流算符可由连续性方程、算符的运动方程以及对易关系计算得出。计算结果表明，电流、热流和自旋流均包含两项：平行费米面项和垂直费米面项。最后将关联函数的虚部代入Kubo公式可计算出石墨烯材料的微波电导率、热导率和自旋导。三个输运系数均有两个Bubble：垂直费米面项速度为(v_1 ) ?泡利矩阵为τ ?_1，平行费米面项速度为(v_2 ) ?泡利矩阵为τ ?_2，差别仅在于耦合参数。研究表明低温和弱掺杂的情况下，其电导率、热导率和自旋导的大小仍然符合Wiedemann-Franz定律。我们还发现，顶角关系对电导、热导、自旋导的修正也是一致的，并从数值分析的角度对顶角关系的意义进行了讨论：在杂质浓度趋近于零时，β_VC^(E,S,T)-1以[ln(P_0?Γ_0 )]^(-2)衰减。不论是玻恩极限还是在幺正极限下，γ因子可以视为是小量，因此对于低级掺杂浓度而言，顶角关系对各输运系数影响较小。

Graphene has attracted wide attention in the field of physics and materials science since it was discovered as a two-dimensional crystal. The main reason is that the conduction electrons of graphene near the Fermi surface are massless fermions. All of these electrons obey the Dirac equation of relativistic quantum mechanics. The behavior of these unique electrons exhibits many novel quantum effects. For example, quantum effects contain minimum conductivity, Klein tunneling, anomalous quantum Hall effect and so on. The appearance of graphene provides a broad space for the study of the properties of low-dimensional materials and their applications. In this study, tight-binding model，Dirac equation，Dyson equation and scattering perturbation theory were adopted accordingly. Using the technique of Feynman diagram and Kubo formula, we investigated the nonmagnetic impurity scattering effect of two-dimensional monolayer graphene under T-Matrix approximation. It is hoped that the research can shed some light on the design and development of single-layer graphene quantum devices and electronic waveguide fibers. The main contents and results of the present research are summarized as follows: (1) Under the tight-binding model for graphene，The original non-diagonal Hamiltonian was subjected to Bogoliubov transformation so that the creation and annihilation quasi-electron operators could be expressed in explicit time-dependent forms. Then the two-component Matsubara Green's function was obtained in frequency space via the Fourier transform. In the presence of impurities, the free Green's function is corrected due to impurity scattering. As a result, a Matsubara self-energy is generated. Then we obtained the Green's function with impurity scattering through Dyson's equation. After analytical continuation, we used retarded Green's function to calculate the doped system’s density of states which is a constant in the limit of zero frequency. (2) After introducing a generalized current operator, we found the general polarization functions neglecting all correction effects under spectral representation, and took the imaginary part of the generalized retarded polarization function. By specifying different input parameters, the imaginary part can be used to obtain the electrical, thermal, and spin conductivity. When studying the impurity scattering effect, we need to consider the renormalization of the generalized current caused by the contributions of vertex corrections. Because the scattering potential strengths between the intra- and inter-Fermi points are different, we need to establish Feyman Rules for nonmagnetic impurity scattering which include the ladder corrections. By evaluating the Feyman diagram and using T-Matrix approximation, we obtained an expression for a generalized retarded polarization function Π ?_ret^glα in which each of the vertices contributes a coupling parameter g, a velocity (v_l ) ?, Pauli matrix τ ?_α. (3) We made use of the generalized retarded polarization before calculating the electrical, thermal, and spin conductivity in the universal limit (Ω→0,T→0). Each of these sections began with a derivation of the appropriate current density operator. The current density operator can be calculated from the continuity equation which invokes the equation of motion of the operator and the commutation relation. The results show that electronic, thermal, and spin current all contain two items: parallel Fermi surface terms and vertical Fermi surface terms. Finally, the imaginary part of the polarization function is substituted into the Kubo formula to calculate all conductivities of the graphene material. All three transport coefficients have two bubble contributions separately: The term perpendicular to Fermi surface has velocity (v_1 ) ? and Pauli matrix τ ?_1, while the term parallel to Fermi surface has velocity (v_2 ) ? and Pauli matrix τ ?_2. The results suggest the transport coefficients still comply with Wiedemann-Franz's law in the case of low temperature and weak doping. The significance of the vertex corrections was discussed from the perspective of numerical analysis. It shows that β_VC^(E,S,T)-1 vanishes approximately as [ln(P_0?Γ_0 )]^(-2) in the small impurity density limit. Moreover, for all scattering strengths (from Born to unitary) vertex corrections have less influence on each transport coefficient in the small impurity density limit.