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Nernst-Ettingshausen effect in graphene

PLMCN10. Nernst-Ettingshausen effect in graphene. Andrei Varlamov INFM-CNR, Tor Vergata, Italy Igor Lukyanchuk Universite Jules Vernes, France Alexey Kavokin University of Southampton, UK. Outline. Nernst-Ettingshausen effect: 124 years of studies

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Nernst-Ettingshausen effect in graphene

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  1. PLMCN10 Nernst-Ettingshausen effect in graphene Andrei Varlamov INFM-CNR, Tor Vergata, Italy Igor Lukyanchuk Universite Jules Vernes, France Alexey Kavokin University of Southampton, UK

  2. Outline • Nernst-Ettingshausen effect: 124 years of studies • In 2009 giant Nernst oscillations observed in graphene • Why the Nernst constant is so different in different systems? • Qualitative explanation in terms of thermodynamics • Dirac fermions vs normal carriers • Longitudinal Nernst effect in graphene • Comparison with experiment

  3. Nernst-Ettingshausen effect Albert von Ettingshausen (1850-1932) teacher of Nernst

  4. Nernst effect in the semimetal Bi (compared to normal metals) K. Behnia et al, Phys. Rev. Lett. 98, 166602 (2007)

  5. Nernst effect in normal metals In metals, the thermoelectric tensor can be expressed as (Mott formula) Order of magnitude of the effect:

  6. Oscillations of the Nernst constant vs magentic field (in disagreement with the Sondheimer formula) zinc

  7. Strong Nernst effect in superconductors (Sondheimer theory fails to explain)

  8. A giant oscialltory Nernst signal in graphene B=9T Their theory: Mott formula The amplitude of Nernst oscillations decreeses as a function of Fermi energy in contrast to their theory

  9. Nernst effect & chemical potential Varlamov formula M.N.Serbin, M.A. Skvortsov, A.A.Varlamov, V. Galitski,Phys. Rev. Lett. 102, 067001 (2009) Idea: Drift current of carriers in crossed electric and magnetic fields is compensated by the thermal diffusion current, which is proportional to the temperature gradient of the chemical potential

  10. In metals: The Varlamov formula works remarkably well: In metals: we obtain in full agreement with Sondheimer !

  11. Particular case 1: semimetals Shallow Fermi level (Bismuth) to be compared with (metals) Describes the experiment of Behnia et al Phys. Rev. Lett. 98, 166602 (2007)

  12. Particular case 2: superconductors above Tc Estimation: In agreement with Pourret et al, PRB76, 214504 (2007)

  13. Graphene: 2D semimetal with Dirac fermions How to describe oscillations? We use the thermodynamical potential

  14. Density of states (quasi 2D formula): T. Champel and V.P. Mineev, de Haas van Alphen effect in two- and quasi-two-dimensional metals and superconductors, Phylosophical Magasin B, 81, 55-74 (2001). Exact analytical result in the 2D case: Normal carriers: Dirac fermions: =1/2 =0

  15. Dirac fermions Comparison with experiment: graphene Normal carriers

  16. PREDICTION: longitudinal NEE Graphene: Dirac fermions “sound velocity” The drift current is limited to Conventional (transverse) Nernst effect Above the thermal current cannot be compensated by the drift current induced by the crossed fields. This results in the longitudinal Nernst effect Longitudinal Nernst effect A.A. Varlamov and A.V. Kavokin, Nernst-Ettinsghausen effect in two-component electronic liquids, Europhysics Letters, 86, 47007 (2009).

  17. CONCLUSIONS: • The simple model based on balancing of the drift and thermal currents allowed: • To treat very different systems within the same formalism • To explain strong variations of the Nernst constant in metals, semimetals, superconductors, graphene • To predict the longitudinal Nernst-Ettingshausen effect in graphene • To explain the decrease of the amplitude of oscillations vs Fermi energy in graphene

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