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

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 Order of magnitude of the effect: In metals, the thermoelectric tensor can be expressed as (Mott formula)

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 The amplitude of Nernst oscillations decreeses as a function of Fermi energy in contrast to their theory Their theory: Mott formula B=9T

9. Nernst effect & chemical potential 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 Varlamov formula

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

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 We use the thermodynamical potential How to describe oscillations?

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. Comparison with experiment: graphene Dirac fermions Normal carriers

16. Graphene: Dirac fermions The drift current is limited to “sound velocity” Longitudinal 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 PREDICTION: longitudinal NEE A.A. Varlamov and A.V. Kavokin, Nernst-Ettinsghausen effect in two-component electronic liquids, Europhysics Letters, 86, 47007 (2009). Conventional (transverse) Nernst effect

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