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

在这项研究计划中，我们已经开发了一个计算机代码，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，表面区域被视为在表面法线方向上的局部缺陷，并且表面区域被视为在表面法线方向上的局部缺陷。用Inglesfield的嵌入技术计算了表面区的单电子绿色函数。本程序采用范数守恒赝势表示离子核，绿色函数采用类平面波基组展开。虽然真正的嵌入表面划分的基板和表面区域编织在一个复杂的方式，以避免交叉的离子核的电位是非本地的，我们已经发明了一种新的方法，取代这个弯曲的嵌入表面的等效平面表面。在这种方法中，在整个计算过程中根本不需要指定真曲面。我们的方法不仅可以评价绿色 ...更多信息 函数，但也适合于半无限表面几何形状的单电子波函数。目前，我们正在开发和测试一个计算机程序，用于使用增广平面波（APW）基组和线性化APW基组计算包含局域2p和过渡金属原子元素的三维周期系统的电子结构。有了这个代码，它成为可能，以产生嵌入潜在的半无限过渡金属基板。作为一个具体的主题，不能处理与标准的重复板为基础的计算方法，我们investigatedsurface resistivity所造成的弹性散射的导电电子在表面。为此，我们推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。我们对低折射率洁净Al表面的计算得出了一个明显违反直觉的结果，即紧密堆积的（111）表面的电阻率比更松散堆积的（001）表面的电阻率大近46倍。这两个表面之间的巨大差异可以归因于这样一个事实，即入射到聚焦晶体的（111）表面上的传导电子由于相对于（111）晶面缺乏反射而不能在镜面方向上反射。因此，所有传导电子在入射到（111）表面上时改变其在平面中的速度，从而对系统的电阻率有贡献。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