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
• 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 
T


1
d        

 2 
dT  T    T
2
2

 d
 
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:
=1/2
Dirac fermions:
=0
Dirac fermions
Comparison with experiment:
graphene
Normal carriers
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).
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