A new technique to calculate the electronic structure of two-dimensional disordered systems

Abstract

The purpose of this work is to investigate the electronic structure of two-dimensional structurally disordered solids by means of a method based on multiple-scattering theory. The theoretical technique is applied to some two-dimensional models which can be varied from the limit of a perfect to a completely disordered structure. The models are continuous structural networks with different-fold coordinations of atoms in planar structures. The spectral density is determined through a self-consistent approach. Using the spectral density, the convergence of the technique is analysed through calculations of the density of electronic states, and the variation of the density of electronic states with respect to varying disorder in the structure is determined. In particular, the convergence of the technique for the calculation of the density of electronic states as a function of the size of the matrix representation used is confirmed and it is shown that the degree of disorder in two-dimensional systems significantly influences the density of electronic states.

Calculation of electronic states of a disordered binary alloy

“…However, it should be emphasized that the results do not depend on the potential in the extreme tightbinding limit because the total number of states in the band equals one per atom. We shall take appropriate values for atomic parameters such as the strength of the potential, as was done in the previous calculations [17,19]. For example, r = 0.5 (au) and the bond length between two atomic potential centres R = 2.0 (au), for which the ground state energy E 0 = −30 (au).…”

“…Hence, these calculations demonstrated that the approach can be used to calculate the DOS for systems having different hopping integrals and concentrations if the bandwidth is much greater than the spread of binding energies. In one sense such systems are also some kind of disordered system having different bond distances between atoms and consisting of sublattices like the Fibonacci lattice in two dimensions [19,26].…”

“…The technique used to evaluate the electronic states of disordered systems is based on multiplescattering theory and the calculated function is the total scattering function, the T -matrix, discussed in previous studies in [16,17,19] and given by…”

“…where M is the structural matrix of the system, and is due to the 12 different patterns, F is a block vector with blocks labelled by pattern type and elements of the blocks labelled by m. e is a block vector consisting of the identity matrix if m = 0, and zero elsewhere. In the present case the matrix M is a complex and non-symmetric block matrix, but it can be transformed to a real symmetric matrix as was done and discussed in detail in previous studies [17,19,20]. As a result, following the same way of symmetrization, equation ( 13) takes the form…”