Differential entropy per particle as a probe of van Hove singularities and flat bands

TL;DR

This paper derives expressions for differential entropy per particle near van Hove singularities and flat bands, providing a tool to analyze the density of states and band flatness in materials.

Contribution

It introduces a general analytical framework for differential entropy near van Hove singularities, linking entropy behavior to band structure features and validating with numerical models.

Findings

Analytic expressions accurately describe differential entropy near vHs.

Entropy behavior distinguishes different types of van Hove singularities.

The method tests band flatness experimentally.

Abstract

In the present paper we derive the general expressions for the differential entropy per particle near van Hove singularities (vHs) in the density of states. The dependence of entropy per particle on chemical potential and temperature demonstrates different behavior depending on the type of vHs, and distinguishes high-order vHs with different divergence exponents and flat bands. In addition, it allows one to test the ``flatness" of the band in experiment. We compare the analytic predictions with the numerical calculation of the differential entropy for tight-binding models of graphene, Lieb lattice and square-octagon lattice. Our results show that the obtained analytic expressions capture the main features of the differential entropy, thus serving as a good probe for details of the density of states structure.