AN APPROACH BASED ON LANDAUER–BÜTTIKER FORMALISM TO COMPUTE THE ELECTRONIC LOCALIZED STATES AT SURFACE BOUNDARIES
Abstract
In this contribution, we provide a theoretical model to study the effect of different cutting edges on the appearance of localized electronic states. The system under study is a three-dimensional atomic chain that ends with an open cut forming a semi-infinite structured layer in the (1 0 0), (1 1 0) and (1 1 1) directions. We investigate the surface electronic characteristics of the monoatomic chain of a simple cube (sc), orthorhombic (orth), and tetragonal (tetr) structures. We have adopted in our approach the tight-binding approximation to build up the surface Hamiltonian matrix. Additionally, the number of secular equation, at the surface, has been determined by using phase field matching theory (FPMT). In fact, the Hamiltonian system obtained from different cutting orientations provides an inhomogeneous system. To solve the surface eigenvalue problem, we integrate the calculation of the scattering reflection probabilities as given in Landauer–Büttiker formalism. Next, based on the computed scattering probabilities, we build up the surface core states which provide the surface Hamiltonian matrix which can be solved numerically. Our model calculation has been applied to the following elements: (i) fluorite (F), manganese (Mn), polonium (Po), bromine (Br), indium (I), tin (Sn), and protactinium (Pa). The results emphasize the influence of cutting direction on the electronic characteristic of surface and on the scale of energy values. We report the appearance of new electronic curves that characterize the surface states. Those surface states are localized down, within, and above the bulk spectrum. They also provide different characteristic features, of the metals under study, in a given cutting orientation. Furthermore, we have integrated the calculation of non-structured cuts on the outer layers. The relaxation effect on the surface is a standard process which leads to stabilize the changes in the internal energy until the equilibrium. The spacing geometry caused by the relaxation on the surface could be determined by using the molecular dynamic algorithm. We account in this case the lift of degeneracy and the rise of additional localized branches within and outside the bulk range.
