Optical matrix elements in tight-binding models with overlap

TL;DR

This paper examines how orbital overlap influences optical matrix elements in tight-binding models, revealing that non-orthogonality induces intra-atomic contributions and justifies certain spin-orbit interactions.

Contribution

It demonstrates that non-orthogonal bases in tight-binding models significantly affect optical matrix elements and provides a formal basis for including intra-atomic terms and spin-orbit interactions.

Findings

Non-orthogonality induces intra-atomic matrix elements.

Orthogonalization extends the effective Hamiltonian range.

Justifies the inclusion of spin-orbit interactions for Dresselhaus term.

Abstract

We investigate the effect of orbital overlap on optical matrix elements in empirical tight-binding models. Empirical tight-binding models assume an orthogonal basis of (atomiclike) states and a diagonal coordinate operator which neglects the intra-atomic part. It is shown that, starting with an atomic basis which is not orthogonal, the orthogonalization process induces intra-atomic matrix elements of the coordinate operator and extends the range of the effective Hamiltonian. We analyze simple tight-binding models and show that non-orthogonality plays an important role in optical matrix elements. In addition, the procedure gives formal justification to the nearest-neighbor spin-orbit interaction introduced by Boykin [Phys. Rev \textbf{B} 57, 1620 (1998)] in order to describe the Dresselahaus term which is neglected in empirical tight-binding models.