# Entropy spikes as a signature of Lifshitz transitions in the Dirac materials

## TL;DR

This paper theoretically shows that entropy spikes occur at Lifshitz transitions in 2D Dirac materials, serving as a signature of topological changes, and provides a formula for entropy behavior related to these transitions.

## Contribution

It introduces a general expression for entropy per particle in gapped Dirac materials and links entropy spikes to Lifshitz topological transitions as a novel signature.

## Key findings

- Entropy per particle exhibits spikes of magnitude ±ln(2)/(J-1/2) at Lifshitz transitions.
- The entropy dependence on chemical potential shows a dip-and-peak structure near the Dirac point.
- Entropy spikes can be detected experimentally through transport measurements with temperature modulation.

## Abstract

We demonstrate theoretically that the characteristic feature of a 2D system undergoing $N$ consequent Lifshitz topological transitions is the occurrence of spikes of entropy per particle $s$ of a magnitude $\pm \ln 2/(J-1/2)$ with $2 \leq J \leq N$ at low temperatures. We derive a general expression for $s$ as a function of chemical potential, temperature and gap magnitude for the gapped Dirac materials. Inside the smallest gap, the dependence of $s$ on the chemical potential exhibits a dip-and-peak structure in the temperature vicinity of the Dirac point. The spikes of the entropy per particles can be considered as a signature of the Dirac materials. These distinctive characteristics of gapped Dirac materials can be detected in transport experiments where the temperature is modulated in gated structures.