Accurate tight-binding Hamiltonian matrices from ab-initio calculations: Minimal basis sets

TL;DR

This paper introduces an improved method for constructing highly accurate ab-initio tight-binding Hamiltonian matrices by removing spurious states caused by low projectability Bloch states, enhancing the reliability of the approach.

Contribution

The authors identify the cause of spurious states in tight-binding models and propose an analytical and practical scheme to eliminate them, improving accuracy.

Findings

Spurious states are due to low projectability Bloch states.

The new scheme effectively removes unphysical hybridizations.

Resulting Hamiltonians are more accurate and reliable.

Abstract

Projection of Bloch states obtained from quantum-mechanical calculations onto atomic orbitals is the fastest scheme to construct ab-initio tight-binding Hamiltonian matrices. However, the presence of spurious states and unphysical hybridizations of the tight-binding eigenstates has hindered the applicability of this construction. Here we demonstrate that those spurious effects are due to the inclusion of Bloch states with low projectability. The mechanism for the formation of those effects is derived analytically. We present an improved scheme for the removal of the spurious states which results in an efficient scheme for the construction of highly accurate ab-initio tight-binding Hamiltonians.