Nernst-Ettingshausen effect in Nernst-Ettingshausen effect in graphenegraphene

Andrei Varlamov INFM-CNR, Tor Vergata, Italy

Igor Lukyanchuk Universite Jules Vernes, France

Alexey Kavokin University of Southampton, UK

PLMCN10

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 effectNernst-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 metalsNernst effect in normal metals

Order of magnitude of the effect:

In metals, the thermoelectric tensor can be expressed as

(Mott formula)

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

The amplitude of Nernst oscillations decreeses as a function of Fermi energy in contrast to their theory

Their theory: Mott formula

B=9T

Nernst effect & chemical potentialNernst 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

The Varlamov formula works remarkably well:

In metals:

we obtain

in full agreement with Sondheimer !

In metals:

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

12 2

2

T

d

dT T

We use the thermodynamical potential

,, , , ln 1 exp

T HT H T g H d

T

How to describe oscillations?

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

Comparison with experiment: graphene

Dirac fermions

Normal carriers

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

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