Nernst effect in normal metals by 6xNrDX

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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
• 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
Nernst-Ettingshausen effect




                        Albert von Ettingshausen
                        (1850-1932) teacher of Nernst
Nernst effect in the semimetal Bi (compared to normal metals)




                  K. Behnia et al, Phys. Rev. Lett. 98, 166602 (2007)
Nernst effect in normal metals



In metals, the thermoelectric tensor    can be expressed as


                                 (Mott formula)




    Order of magnitude of the effect:
Oscillations of the Nernst constant vs magentic field
(in disagreement with the Sondheimer formula)
                                                        zinc
Strong Nernst effect
in superconductors
(Sondheimer theory
fails to explain)
    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
        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
  In metals:



The Varlamov formula         works remarkably well:




         In metals:




         we obtain


                       in full agreement with Sondheimer !
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)
Particular case 2: superconductors above Tc




   Estimation:




                               In agreement with Pourret et al, PRB76, 214504 (2007)
Graphene: 2D semimetal with Dirac fermions
How to describe oscillations?




We use the thermodynamical potential


                                               T , H      
 T , H ,    T  g   , H  ln 1  exp                    d
                                     
                                                    T          
                                                                  

                                 1
 d        
               2           2
                
 dT  T    2 T
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
                              Dirac fermions

Comparison with experiment:
graphene




                              Normal carriers
                                                                              PREDICTION: longitudinal NEE
        Graphene: Dirac fermions


       The drift current is limited to                                                 “sound velocity”




                                                Conventional (transverse) Nernst effect



Above

the thermal current cannot be
compensated by the drift current
induced by the crossed fields.                    Longitudinal Nernst effect
This results in the longitudinal
Nernst effect




  A.A. Varlamov and A.V. Kavokin, Nernst-Ettinsghausen effect in two-component electronic liquids, Europhysics Letters, 86, 47007 (2009).
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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