关联无序材料中电子态的研究方法

The Study Methods of Electronic States in Correlated Disordered Materials

按照一般的无序理论,在非关联一维无序材料中不存在扩展态,在绝对零度下,电子的波函数是局域的,系统表现为绝缘体。在关联无序系统中,格点能量之间的长程关联,即对角关联,能导致扩展的波函数并由此导致系统的导电性。当关联强度于某一阈值,可以发现在热力学极限之下有存在于较宽能带范围内的扩展态,此阈值即为体系的金属-绝缘体转变临界点。考虑格点之间的长程相互作用势,即非对角关联时,在一维系统中通过使用传输矩阵方法,可以获得电子态的一些本质效应,长程跳跃可以改变系统的有效维度并能导出一维体系中存在有依赖于关联强度的金属-绝缘体转变。

According to traditional theories, no extended states can be found in 1D uncorrelated disordered materials. The electron wavefunctions are localized at T=OK and the system behaves as an insulator. But in correlated disordered systems, the long-range correlation of site energies（i. e. the diagonal correlations） can lead to extended wavefunctions and thus to conductivity. For correlations stronger than a certain threshold, one can find in the thermodynamic limit a bread energy band of extended states. We call the threshold the critical point at which a metal-insulator transition occurs. In addition, considering the long-range hoppings（i. e. the off-diagonal correlations）, we can obtain essential effect on properties of electron states in 1D systems by using the transfer matrix method. The long-range hoppings can change the effective dimensionality of the system and also lead to a metal-insulator transition.