Entropy Signatures of Topological Phase Transitions
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ontribution for the JETP special issue in honor of L.P. Pitaevskii’s 85th birthday
Entropy Signatures of Topological Phase Transitions1 Y. M. Galperina,b, D. Grassanoc, V. P. Gusynind, A. V. Kavokine,f, O. Pulcic, S. G. Sharapovd, V. O. Shubnyig, and A. A. Varlamove,* a Department
of Physics, University of Oslo, P. O. Box 1048 Blindern, Oslo, 0316 Norway Physical–Technical Institute, Russian Academy of Sciences, St. Petersburg, 194021 Russia c Departments of Physics and INFN, University of Rome Tor Vergata, Rome, I-00133 Italy d Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, 03680 Ukraine e SPIN-CNR, c/o Department of Civil Engineering and Computer Science, University “Tor Vergata,” Viale del Politecnico 1, Rome, I-00133 Italy f Spin Optics Laboratory, St. Petersburg State University, St. Peterbsurg, 198504 Russia g Department of Physics, Taras Shevchenko National University of Kiev, Kiev, 03680 Ukraine * e-mail: [email protected] b Ioffe
Received April 1, 2018
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 electron gas with a parabolic energy spectrum. In contrast, in doubled-gapped Dirac materials, the entropy per particle 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. DOI: 10.1134/S1063776118110134
1. INTRODUCTION This review article is dedicated to Lev Petrovich Pitaevskii whose outstanding role in development of theoretical physics is well known. All the authors of this review had studied physics by the famous “Course of Theoretical Physics” written by Landau and Lifshitz with pronounced contribution of Lev Petrovich. This course, as w
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