Non-orthogonal tight-binding models: Problems and possible remedies for realistic nano-scale devices

Abstract

Due to recent improvements in computing power, non-orthogonal tight-binding models have moved beyond their traditional applications in molecular electronics to nanoelectronics. These models are appealing due to their physical chemistry content and the availability of tabulated material parameterizations. There are, however, problems with them, related to their non-orthogonality, which are more serious in nanoelectronic vs molecular applications. First, the non-orthogonal basis leads to an inherent ambiguity in the charge density. More importantly, there are problems with the position matrix in a non-orthogonal basis. The position matrix must be compatible with the underlying translationally symmetric system, which is not guaranteed if it is calculated with explicit wavefunctions. In an orthogonal basis, the only way to guarantee compatibility and gauge invariance is to use diagonal position matrices, but transforming them to a non-orthogonal basis requires major computational effort in a device consisting of 103–105 atoms. We study the charge density, position matrix, and optical absorption using a non-orthogonal two-band one-dimensional model, comparing correct and approximate calculations. We find that a typical naïve calculation produces highly inaccurate results, while in contrast a first-order orthogonalized basis can represent a reasonable accuracy-efficiency trade-off.