Giant density-of-states van Hove singularities in the face-centered cubic lattice

TL;DR

This paper systematically classifies all van Hove singularities in the DOS of face-centered cubic lattices, revealing giant singularities at specific hopping ratios and proposing an efficient DOS calculation method.

Contribution

It provides a comprehensive classification of van Hove singularities in FCC lattices, including higher-order ones, and introduces an exact DOS formula suitable for numerical analysis.

Findings

Giant DOS singularities occur at specific hopping ratios.

Standard tetrahedron method is inadequate near singularities.

Comparison with infinite-dimensional models highlights unique features.

Abstract

All van Hove singularities in the density of states (DOS) of face-centered cubic lattice in the nearest and next-nearest neighbour approximation, focusing on higher-order ones, are found and classified. At special values of the ratio $\tau$ of nearest and next-nearest neighbour hopping integrals, $t$ and $t'$, giant DOS singularities, caused by van Hove lines or surfaces, are formed. An exact formula for DOS which provides efficient numerical implementation is proposed. The standard tetrahedron method is demonstrated to be inapplicable due to its poor convergence in the vicinity of kinks caused by van Hove singularities. A comparison with the case of large space dimensionality (infinite coordination number) including next-nearest neighbours is performed.