Entropy Signatures of Topological Phase Transitions

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.

arXiv comment33 pages,15 figures. Accepted for publication in JETP. arXiv admin note: text overlap with arXiv:1803.02083, arXiv:1712.09118, arXiv:1703.08962, arXiv:1512.08450

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• Evidence of Lifshitz transition in thermoelectric power of ultrahigh mobility bilayer graphene
• The Nernst effect in Corbino geometry
• Differential entropy per particle as a probe of van Hove singularities and flat bands
• Entropy and Seebeck signals meet on the edges
• Enhanced interaction effects in the vicinity of the topological transition