Journal of Experimental and Theoretical Physics

, Volume 127, Issue 5, pp 958–983 | Cite as

Entropy Signatures of Topological Phase Transitions

  • Y. M. Galperin
  • D. Grassano
  • V. P. Gusynin
  • A. V. Kavokin
  • O. Pulci
  • S. G. Sharapov
  • V. O. Shubnyi
  • A. A. VarlamovEmail author


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.



We thank A.O. Slobodeniuk for illuminating discussion. We acknowledge the support from the HORIZON 2020 RISE “CoExAN” project (GA644076). A. V. K. acknowledges support from the St. Petersburg State University for the research grant S. G. Sh. and V. P. G. acknowledge a partial support by the National Academy of Sciences of Ukraine (projects nos. 0117U000236 and 0116U003191) and by its Program of Fundamental Research of the Department of Physics and Astronomy (project no. 0117U000240).


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Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  • Y. M. Galperin
    • 1
    • 2
  • D. Grassano
    • 3
  • V. P. Gusynin
    • 4
  • A. V. Kavokin
    • 5
    • 6
  • O. Pulci
    • 3
  • S. G. Sharapov
    • 4
  • V. O. Shubnyi
    • 7
  • A. A. Varlamov
    • 5
    Email author
  1. 1.Department of Physics, University of Oslo, P. O. Box 1048 BlindernOsloNorway
  2. 2.Ioffe Physical–Technical Institute, Russian Academy of Sciences St. PetersburgRussia
  3. 3.Departments of Physics and INFN, University of Rome Tor VergataRomeItaly
  4. 4.Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of UkraineKievUkraine
  5. 5.SPIN-CNR, c/o Department of Civil Engineering and Computer Science, University “Tor Vergata,” Viale del Politecnico 1, RomeItaly
  6. 6.Spin Optics Laboratory, St. Petersburg State University, St. PeterbsurgRussia
  7. 7.Department of Physics, Taras Shevchenko National University of KievKievUkraine

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