Development of the computational method for determining the electronic structure of semi-infinite crystal surfaces

在这个研究项目中，我们开发了一种计算机代码，可以从第一性原理确定半无限晶体表面的基态电子结构。在这样做时，表面区域被视为表面法线方向上的局部缺陷，并且。利用英格尔斯菲尔德嵌入技术计算了表面区域的单电子格林函数。目前的计算机代码采用保范的伪势来表示离子核，用类平面波基集展开格林函数。虽然划分基板和表面区域的真正嵌入面以复杂的方式编织，以避免在非局域电位的离子核中交叉，但我们发明了一种新的方法，用等效的平面表面代替这种弯曲的嵌入面。该方法在整个计算过程中不需要指定真正的曲面。我们的方法不仅可以求出Green…More函数，还可以求出适合于半无限曲面几何的单电子波函数。目前，我们正在开发和测试一个计算机程序，用于利用增广平面波（APW）基集和线性化APW基集计算包含局域化2p和过渡金属原子元素的三维周期系统的电子结构。利用该代码，可以生成半无限过渡金属衬底的嵌入势。作为一个不能用标准的基于重复板的计算方法处理的具体课题，我们研究了导电电子在表面的弹性散射引起的表面电阻率。为此，我们导出了适用于任意半无限金属晶体表面的表面电阻率的一般表达式。我们对低指数清洁Al表面的计算得出了一个明显违反直觉的结果，即致密（111）表面的电阻率几乎是松散（001）表面的46倍。这两种表面之间的巨大差异可归因于这样一个事实，即由于（111）晶体平面缺乏反射对称性，入射到foc晶体（111）表面的传导电子不能在镜面方向上反射。因此，当所有的传导电子入射到（111）表面时，它们在平面内的速度会发生变化，从而有助于系统的电阻率。少

In this research program, we have developed a computer code that determines the ground-state electronic structure of semi-infinite crystal surfaces from first-principles. In doing so, the surface region is treated as a localized defect in the surface-normal direction, and the. one-electron Green function in the surface region is calculated with the use of the embedding technique of Inglesfield. The present computer code adopts norm-conserving pseudo-potentials to represent ion cores, and the Green function is expanded by a plane-wave-like basis set. Although the true embedding surface dividing the substrate and surface regions weaves in a complex way in order to avoid crossing the ion-cores where the potential is non-local, we have invented a new method that replaces this curvy embedding surface by an equivalent plane surface. In this method, there is no need to specify' the true curvy surface throughout all the computational procedure at all. Our method can evaluate not only the Green … More function but also one-electron wavefunctions appropriate for the semi-infinite surface geometry. At present, we aredeveloping and testing a computer code for calculating the electronic structure of three-dimensional periodic systems containing localized 2p and transition-metal atomic elements using the augmented plane wave (APW) basis set and also usingthe linearized APW basis set. With this code, it becomes possible to generate the embedding potential of semi-infinite transition metal substrates. As a concrete subject that cannot be treated with the standard repeating-slab-based computational methods, we investigatedsurface resistivity caused by the elastic scattering of conducting electrons at the surface. For this purpose, we derived a general expression of the surface resistivity that can be applicable to arbitrary semi-infinite metallic crystal surfaces. Our calculation for the low-index clean Al surfaces led to an apparently counter-intuitive result that the resistivity of the close-packed (111) surface is nearly 46 times larger than that of the more loosely packed (001) surface. The large difference between the two surfaces.can be attributed to the fact thatthe conduction electrons impinging on the (111) surface of foc crystals cannot be reflected in specular direction because of the lack of the reflection symmetrywith respect to the (111) crystalplane. Thus, all the conduction electrons change their velocity in the plane when they are incident on the (111) surface, thus contributing to the resistivity of the system. Less