Accurate $ab~initio$ tight-binding Hamiltonians: effective tools for electronic transport and optical spectroscopy from first principles

TL;DR

This paper introduces an efficient first-principles tight-binding method for calculating electronic transport and optical properties, overcoming computational challenges and accurately capturing band structure details.

Contribution

It develops a pseudo-atomic orbital projection technique to produce exact tight-binding Hamiltonians for first-principles electronic structures, enabling efficient transport and optical calculations.

Findings

Validated on CoSb3, revealing multiple band minima affecting thermoelectric properties.

Analyzed a large nanowire, identifying mechanisms for photo-current and protected transport channels.

Enabled calculations for systems with hundreds of atoms using the tight-binding approach.

Abstract

The calculations of electronic transport coefficients and optical properties require a very dense interpolation of the electronic band structure in reciprocal space that is computationally expensive and may have issues with band crossing and degeneracies. Capitalizing on a recently developed pseudo-atomic orbital projection technique, we exploit the exact tight-binding representation of the first principles electronic structure for the purposes of (1) providing an efficient strategy to explore the full band structure $E_n({\bf k})$, (2) computing the momentum operator differentiating directly the Hamiltonian, and (3) calculating the imaginary part of the dielectric function. This enables us to determine the Boltzmann transport coefficients and the optical properties within the independent particle approximation. In addition, the local nature of the tight-binding representation facilitates the calculation of the ballistic transport within the Landauer theory for systems with hundreds of atoms. In order to validate our approach we study the multi-valley band structure of CoSb$_3$ and a large core-shell nanowire using the ACBN0 functional. In CoSb$_3$ we point the many band minima contributing to the electronic transport that enhance the thermoelectric properties; for the core-shell nanowire we identify possible mechanisms for photo-current generation and justify the presence of protected transport channels in the wire.