Computing the surface electronic states on the (100), (110) and (111) surfaces of FCC monatomic crystals

• Published in: International journal of modern physics. B, Condensed matter physics, statistical physics, applied physics Vol. 35; no. 5; p. 2150066
• Main Authors: Bourahla, Boualem, Belayadi, Adel
• Format: Journal Article
• Language: English
• Published: Singapore World Scientific Publishing Company 20.02.2021; World Scientific Publishing Co. Pte., Ltd
• Subjects: Crystals; Eigenvalues; Electron states; Face centered cubic lattice; Internal energy; Mathematical analysis; Orbitals; Phase matching; Scattering coefficient; Wave functions; tight-binding approach; crystallographic directions; Localized electronic states; phase field matching method
• ISSN: 0217-9792; 1793-6578
• DOI: 10.1142/S0217979221500661

In this study, we carry out a simulation of the surface band structures for face-centered cubic (fcc) leads that end up in (100), (110) and (111) surfaces. The surface Hamiltonian matrix is constructed from tight-binding approach and the secular equations of the surface eigenvalue problem. The solution of the problem is performed by integrating the Landauer–Büttiker formalism (LBF) in the phase field matching approach (PFMA). The LBF provides the quantum scattering properties and the PFMA connects the bulk modes to those of the surface based on the quantum scattering coefficients. The combination of these methods allows calculating the electronic bands in the three directions mentioned above. We report the results of ordered slabs for Ag, described as s -like orbital and Ni given as d -type orbitals. To show the impact of expanding the crystal wavefunction, we reveal the calculation of the localized states for Rh, Cu, Pt given as d -type orbitals as first calculation then d 9 . 5 s 1 . 5 -coupling orbitals as second calculation. The results of the nonordered slabs are applied to Pd and Ir. Cutting the crystals affects the internal energy of the surface atoms, which will be subject to a relaxation effect until equilibrium is achieved.