A convolution technique for the calculation of local densities of states

Abstract

A convolution technique is proposed for the calculation of local densities of states (LDOS) within the tight-binding (TB) model. It relies on the separability of the variables in the Hamiltonian. This technique allows one to carry out calculations for the two- and three-dimensional lattices if the one-dimensional LDOS is known. The approach avoids K-space integration as well as the processing of large clusters. The results are checked against known results produced by the straight TB model, and some new cases, such as that of the LDOS for a two-dimensional lattice in the presence of an external electric field, are also considered.

Local Density of States for Solids in an Electric Field

“…Conclusion Relying on a newly developed convolution technique [22], we have been able to treat within the semi-empirical TB model the effect of a constant electric field with arbitrary direction on the local densities of states (LDOSs) for some simple crystals. The proposed approach is sufficiently general as to be transposable to various other model Hamiltonians and different case studies.…”

“…The theoretical considerations of the Wannier-Stark ladder levels concern mainly 1D solids [3 to 6,22]; scarce information is available for the 2D case [7,22], and apparently the 3D system is not studied at all.…”

“…Model and Method We proposed in [22] a new technique of LDOS calculations in two or three dimensions for simple cubic crystals. The idea is to utilize the separability of the Hamiltonian, which allows to perform a convolution of the 1D result with the LDOS for one or two dimensions as to obtain the result for the case with a higher dimensionality.…”

Modelling Electronic Spectra of Crystals in Electric Fields with Various Orientations

“…Thus, it was possible to observe the effects of an electrical field at practically accessible values for its intensity [6]. Theoretical investigations most commonly envisage the effect of an electric field on the electronic spectrum of 1D crystals [18][19][20][21][22][23]. The 2D case has been considered by Nakanishi et al [3] and the authors have discussed the dependence of the LDOS on the electric field direction.…”

“…A new technique utilizing the separability of the Hamiltonian [22] allowed to treat easily a large array of cases. It was established that for a sufficiently high intensity along one of the axes of a 3D cubic crystal the LDOS becomes two-dimensional.…”