Localization 2011

Augutst 4-7, 2011; POSTECH

Department of Physics, POSTECH

Quantum Transport and Superconductivity Laboratory

Thermoelectric Transport in Bilayer Graphene

Seung-Geol Nam

Hu-Jong LeeDong-Keun Ki

Stefan Ketteman

POSTECHPOSTECHAMS, WCUJacobs Univ. Bremen

- Introduction Thermoelectric power (TEP)

TEP in monolayer graphene

TEP in bilayer graphene

- Results and Discussion – studies on bilayer Gate-voltage and temperature dependence

Deviation from Mott’s relation

Magneto-thermoelectric power

- Conclusion

Outline

f(E)

E

f(E)

E

Thermoelectric Power

V

EF

Th Tc

Mott relation

- Mott relation ; valid for TEP generated by diffusive carriers

Compare

Mott Relation of TEP

For weak e-p interaction in graphene; - TEP linearly depends on T- Phonon-drag component nonlinear T dependence

TEP details of EF(n),band structure of graphene near EF

TEP Meaurements on Monolayer Graphene

Checkelsky and Ong, PRB (2009)

- Gate dependent TEP and sign changes at CNP- Linear dispersion relation

P. Wei, et. al., PRL (2009)Zuev, Chang, and Kim,

PRL (2009)

- TEP increases linearly with T – weak e-p interaction1 1

thbg

Vn V

hole-like

electron-like

Bilayer Graphene

1

CNP

tight-binding model withinterlayer hopping (1)

How do thermoelectric properties change in bilayer graphene ?

1 ~ 0.39 eV (graphite)

A2 B2 A2 B2

A1 B1 B1

A1

v

v

Interlayer hopping energy

McCann and Fal’ko, PRL 96, 086805(2006)

1

- Introduction Thermoelectric effect

TEP in monolayer graphene

TEP in bilayer graphene

- Results and Discussion Gate-voltage and temperature dependence

Deviation from Mott’s relation

Magneto-thermoelectric effect

- Conclusion

Outline

Measurement Configuration

Ti/Au (3-17 nm)

Main Results

Resistance Thermoelectric power

- Resistance near the CNP is T-dependent - Sign changes in TEP @ CNP –ambipolar nature of carriers- Insulating behavior due to thermally excited

carriers

TEP > 0hole regime

TEP < 0electron regime

mobility = 2000 ∼ 4000 cm2/Vs

- Low e-p scattering rate in bilayer graphene

Comparison to Monolayer Graphene

R(T) changes

thermally activated carriers

Zuev et al. PRL 102, 096807 (2009)

general trends are similar

Monolayer graphene Bilayer graphene

Fit of TEP at Low Temperatures

TEP is consistent with the hyperbolic band structure of bilayer graphene.

T=30 K

Nam et al., PRB 82, 245416 (2010)

Fit at Different Temperatures

Fixed parameters;

At high T and low carrier density, a deviation appears.

P. Wei, et. al.PRL 102, 166808 (2009)

- For T up to 50 K; semiclassical Boltzmann theory valid- Deviation above 140 K – in contrast to monolayer graphene

Temperature Dependence for Different VBG

Y. M. Zuev, et. al., PRL 102, 096807 (2009)

guide line

Deviation from Mott’s Formula

E. H. Hwang, et. al., PRB 80, 235415 (2009)

(TF ~ 330 K at V = 10 V)

(V = VBG – VCNP)Bilayer

(TF ~ 1150 K at V = 10 V)

Monolayer

Mott’s relation; valid only at low T ≪ TF (~ 0.2TF)

Zuev et al. PRL 102, 096807 (2009) - Deviation from Mott’s relation at an onset temp. T*

(gate-dependent) – due to failure of Sommerfeld expansion at high T

- TEP saturates near the onset temp. T*

Temperature Dependence

guide line

consistent with theoretical prediction Hwang, et. al., PRB 2009

- upswing of T/TF potentially leads to new physics- further clarified with cleaner graphene by overcoming the effect of electron-hole puddles.

Nam et al., PRB 82, 245416 (2010)

T = 15 K, B = 7 T

Sxx in High Magnetic Field

Bilayergraphene

EF

DO

SE

8-fold degeneracy

Sxx in Magnetic Field

T = 15 K, B = 7 T

kBln2/e ~ 59.6 V/K

1 ln 2 11 2

Bnk

en

; monolayer

; bilayermax

,

0

ln 2 1

( )

x Bxx n n

mm

E kST e f E

- thermal broadening of Landau levels- disorder

1. Mott relation; valid in bilayer graphene at low temperatures

Conclusion

- Hyperbolic dispersion relation - Interlayer hopping term 1

2. Deviation from Mott’sbehavior;

- Saturation of TEP at high T- Saturation T is gate-dependent

- Validity of Mott’s formulaTF of bilayer ≪ TF of monolayer

~ Em

3. In high magnetic field, oscillatory behavior of TEP is observed

Reduction of maximum of Sxx - disorder effect?

Conclusion

T = 15 K, B = 7 T

Sxy in Magnetic Field – Nernst Effect

P. Wei, et. al.PRL 102, 166808 (2009) T = 15 K, B = 7 T

Z. Zhu, et. al., Nature Phys. 6, 26 (2010)

Two dimensional band

graphite 2D(graphene)

Sxy =−Ey/|∇T|

band dispersion along c axis

• (ln2)(kB/e) ~ 60 V/K• 1/(m+1/2) dependence를 보이지만 값은 작은데 disorder가있을 때 Sxx는 이론값보다 줄어

들 수 있습니다.

Increasing disorder

3. In high magnetic field, oscillatory behaviors of TEP and the Nernst signals are also observed

No anomalous sign change of TEP near CNP in bilayer graphene

Nernst signal points to 2D nature of the bilayer graphene

Conclusion

T = 15 K, B = 7 T

T = 15 K, B = 7 T

D.-K. Ki

S. Kettemann

H.-J. Lee S.-G. Nam

Collaborators

n=0 n=1 n=m

Monolayer Graphene

n=0+,0- n=1 n=m

Bilayer Graphene

n=0 n=1 n=m

2DEG

T = 15 K, B = 7 T

Sxx in High Magnetic Field Bilayer

graphene

EFD

OS

E

8-fold degeneracy

No anomalous sign change near the CNP

Checkelsky and Ong, PRB 80, 081413(R) (2009)

Zuev, Chang, & Kim, PRL 102, 096807 (2009)

Thermoelectric Power

Saturation of TEP

E. H. Hwang, et. al., PRB 80, 235415 (2009)

~ Emin monolayer graphene;

- Scattering due to unscreened charged impurities

Why is it saturated ?

- Further theoretical work is required

Zuev et al. PRL 102, 096807 (2009)

- Deviation from Mott’s relation at a certain onset T, (gate-dependent)

- TEP saturates near the onset T.

Comparison to Monolayer Graphene

Zuev et al. PRL 102, 096807 (2009)

Morozov et al. PRL 100, 0166027 (2008)

Finite DOS at CNP

Monolayer

Bilayer

~ 1012 cm-2 at RT

Due to the finite DOS in bilayer graphene at the CNP, TF of the system is almost an order of magnitude smaller than that of the monolayer graphene for a given charge carrier density.

M. F. Craciun, et. al., Nature Nanotech. 4,

383 (2009)

J. B. Oostinga, et. al., Nature Mater. 7, 151

(2007)

From Graphine to Graphite

Two dimension Three dimension

Bilayer Trilayer ·· ·· ·· ·· ··??

Z. Zhu, et. al., Nature Phys. 6, 26 (2010)

S. Ghosh, et. al., arXiv:1003.5247

(2010)

electron

hole

Manchester Univ.Columbia Univ.

Exfoliation

TEP

TEP measured TEP measured