Entropy Signatures of Topological Phase Transitions

TL;DR

This paper reviews how the entropy per particle in two-dimensional electronic systems reveals topological phase transitions, showing quantized steps and spikes at critical points, thus providing insights into the electronic band structure.

Contribution

It links the entropy per particle to topological transitions in 2D materials and demonstrates how entropy signatures can identify phase changes and band structure features.

Findings

Entropy per particle shows quantized steps at Lifshitz transitions.

Characteristic spikes in entropy occur at band edges in Dirac materials.

Disappearance of zero-energy resonance indicates topological phase transition.

Abstract

We review the behavior of the entropy per particle in various two-dimensional electronic systems. The entropy per particle is an important characteristic of any many body system that tells how the entropy of the ensemble of electrons changes if one adds one more electron. Recently, it has been demonstrated how the entropy per particle of a two-dimensional electron gas can be extracted from the recharging current dynamics in a planar capacitor geometry. These experiments pave the way to the systematic studies of entropy in various crystal systems including novel two-dimensional crystals such as gapped graphene, germanene and silicene. Theoretically, the entropy per particle is linked to the temperature derivative of the chemical potential of the electron gas by the Maxwell relation. Using this relation, we calculate the entropy per particle in the vicinity of topological transitions in various two-dimensional electronic systems. We show that the entropy experiences quantized steps at the points of Lifshitz transitions in a two-dimensional electronic gas with a parabolic energy spectrum. In contrast, in doubled-gapped Dirac materials, the entropy per particles demonstrates characteristic spikes once the chemical potential passes through the band edges. The transition from a topological to trivial insulator phase in germanene is manifested by the disappearance of a strong zero-energy resonance in the entropy per particle dependence on the chemical potential. We conclude that studies of the entropy per particle shed light on multiple otherwise hidden peculiarities of the electronic band structure of novel two-dimensional crystals.