Supercollision cooling of electrons in graphenejonckhee/VietnamPresentations/Quy...PhD Andreas Betz...

Supercollision cooling of electrons in graphene

Meso‐group : A.C. Betz, E. Pallecchi, S‐H. Jhang, G. Fève, J‐M. Berroir, B. Plaçais Optic‐group : D. Drunel, F. Vialla, C. Voisin, R. Ferreira

Laboratoire Pierre Aigrain – Ecole Normale Supérieure24 rue Lhomond, 75231 Paris Cedex 05 France

www.lpa.ens.fr

h-BN

Drain

Si++ Gate SiO2

Source

1

Why studying cooling processes ?

2EDISON-18, Matsue, 25/7/2013

1. Hot carriers affect resolution detectors

2. Can be useful as bolometers

3. Graphene lab for electron‐phonon physics

4. Acoustic phonon bottleneck

Acoustic phonon bottleneck

F. Wu et al. , APL 97, 262115 (2010) (nanotube)A. Fay et al., PRB 84, 245427 (2011) (Bilayer)K.C. Fong, K. C. Schwab, PRX, 031006 (2012)A.C. Betz et al., PRL 109, 056805 (2012)A.C. Betz, et al. nphys 19, 109 (2013)

Optical absorption (2.3%)

N.M. Gabor et al., Science 334 , 648 (2011)S. Winnerl et al. PRL 107, 237401 (2011)J. Yan et al., nnano 7, 472 (2012)M. Freitag et al., nphoto 453 (2013)M.W. Graham et al., nphys 19, 103 (2013)

optical-phonons(200 meV)

Joule heating

photons

photo‐current or pump‐probe noise thermometry (this work)

acoustic-phonons

Electric field + scattering

3Nanophysics, Quy-Nhon, 7/8/2013

acoustic-phonons only

C = 3x108 m/sVF = 1x106 m/sS = 2x104 m/s

+ fast electron-electron

4

SI=4kB/R

VI

P=V2/R

W

L

Nanophysics, Quy-Nhon, 7/8/2013

noise thermometry

Steady state Heat conduction Joule heating phonon P=Tα

5

SI=4kB/R

VI

P=V2/R

W

L


noise thermometry

electron-electron

electron-impurity

Electron-p

Fano factor

α=5 in 3D metals (Wellstood, Urbina, Clarke, PRB 1994)α=3 in 1D CNTs (Wu, …, Hakonen, APL 2010)

α=d+2 => α=4 in 2D graphene ???

Steady state Heat conduction Joule heating phonon P=Tα

Outline


1. Introduction : the Bloch‐Grüneisen phonon resistivity

2. Relaxation by acoustic phonons Betz et al., PRL 109, 056805 (2012).

3. Disorder assisted relaxation : supercollisionsBetz et al., Nature Physics 9, 109 (2013)

Phonon resistivity

GR/BN

Chen-Fuhrer., Nat. Nano 2008 Efetov-Kim PRL 2010

OP‐phononsirrelevant

large AC‐phononsvelocity

(s = 2x104 m/s)

weakAC‐phonons

effect


Phonon resistivity in (2D) graphene

GR/BN

Chen-Fuhrer., Nat. Nano 2008 Efetov-Kim PRL 2010

OP‐phononsirrelevant

large AC‐phononsvelocity

(s = 2x104 m/s)

AC‐phononsweak effect

8

0.1Ω/K


Bloch-Gruneisencrossover

The Bloch‐Grüneisen crossover

Fermi surface Available phonon space

kFq

qmax α T2 kF >

T < TBG (cold)

qmax2 kF =

T = TBG=(2s/VF)TF

q=kT/s

(Efetov-Kim PRL2010)

2 kF qmax<

T > TBG(hot)

(Hwang-Das-Sarma PRB2008)

4%

9

Outline





acoustic‐phonon cooling (theory)

(Viljas-Heikkila PRB 2010) 11Nanophysics, Quy-Nhon, 7/8/2013

kF

q

T < TBG (cold phonons)

T > TBG (hot phonons)

(non-degenerate electrons)

Electron-Phonon conductance

Bloch-Gruneisencrossover

AC‐phonon cooling (principles)

phonon thermal conductance

12

phonon cooling power


Σph ~10 mW/m2/K4

KapitzaΣK ~ 10 W/m2/K4

phonon thermal conductance

13

T0 = 4 K

phonon cooling power

Tph ~ 40 K

Te ~ 400 K

AC‐phonon cooling (practicals)

P ~100 µW/µm2


Σph ~10 mW/m2/K4

KapitzaΣK ~ 10 W/m2/K4

Device fabrication

Gr/BN (diffusive) CVD (doped and diffusive)

Schneider et al., Nano Letters 2010 10 (5)

Wedging transfer: polymer CAB & water

CVD grown on Cu (A. Madouri, LPN)

Length (μm)

R (k

Ω)

14

Mitutoyo


Noise thermometry

SI=4kBTe(P)/R

15

P=V2/R

linear sub-linear linear

Te(x)

Relaxation by « cold AC phonons »

WF-dip

Agreement with T4 dependence for 2D acoustic phonons

Σ* =0.5-2 mW/m2K4 is disorder dependent and Σ* < Σ = 10mW/m2K4

ΣT4 plateaus


Sample GR/BN1kF

q

Tph < TBG (cold phonons)

Outline





Crossing the Bloch‐Gruneisen temperature

Fermi surface Available phonon space

kFq

qmax2 kF >

T > TBG

qmax2 kF =

T = TBG=(2s/VF)TF

q=kT/c

2 kF qmax<

T > TBG

4%

18

electrons Te

phonons Tph

substrate To

I I=V/R

P=ΣK Tph4P

decrease µ

Relaxation at the Charge Neutrality Point

0,0 -0,5 -1,0 -1,50,0

0,5

1,0

1,5

2,0

0 V

-20 V

-10 V

-32 V

+12 V (CNP)

T4 /

P (K

4 /mW

)Vds (V)

Sample GR/BN2

0

200

400

600

800

Tph

-55 V

-43 V-32 V

-20 V-10 V

0 VVg = +12 V (CNP)

T e (K

)

P (mW [m]-2)

-30 0 301

2

3

R (k

)

Vg (V)

0.00 0.05 0.10 0.15 0.20

ReplotSample GR/BN2


We measure PαT3 instead of PαT

1

4 47 56 62 67

TBG

0.200.150.100.050

0.5

43

2

40Tph (K)

-55 V-43 V-32 V

-20 V

-10 V0 V

Vg = +12 V (CNP)

P (mW [m]-2)

T e3 /

P (K

3 m2 /W

)

Replot

0,0 -0,5 -1,0 -1,50,0

0,5

1,0

1,5

2,0

0 V

-20 V

-10 V

-32 V

+12 V (CNP)

T4 /

P (K

4 /mW

)

Vds (V)

T2T4

T3


Supercollisions

2 kF qmax<

Tph > TBG

electron‐impurity

Theory : Song-Reizer-Levitov, PRL 109, 106602 (2012)


Ordinary collision

supercollisions

Theory : Song-Reizer-Levitov, PRL 109, 106602 (2012)


1

4 47 56 62 67

TBG

0.200.150.100.050

0.5

43

2

40Tph (K)

-55 V-43 V-32 V

-20 V

-10 V0 V

Vg = +12 V (CNP)

P (mW [m]-2)

T e3 /

P (K

3 m2 /W

)

supercollisions


1

4 47 56 62 67

TBG

0.200.150.100.050

0.5

43

2

40Tph (K)

-55 V-43 V-32 V

-20 V

-10 V0 V

Vg = +12 V (CNP)

P (mW [m]-2)

T e3 /

P (K

3 m2 /W

)

Experiment

Effect of disorder on relaxation


Te3

Te4

Theory clean ‐‐‐‐‐‐‐‐Exp. disorder _____

Electron-Phonon conductance

?

Conclusion

1

4 47 56 62 67

TBG

0.200.150.100.050

0.5

43

2

40Tph (K)

-55 V-43 V-32 V

-20 V

-10 V0 V

Vg = +12 V (CNP)

P (mW [m]-2)T e

3 / P

(K3 m

2 /W)

Te4

Te3

“ordinary collisions” rule momentum “Supercollisions” rule energy

25

Te2


Supercollision in the photocurrent(Graham et al. Nat Phys. 2013)


~µ2~µ ~100 ps

Conclusions and perspectives

27

• Ordinary phonon collisions observed at low temp (T4 law)

• Phonon bottelneck (T law) is overcomed by supercollisions (T3 law)

• Need for a theoretical approach for disorder

• Hot electrons useful for photodetection (from UV to THz)C. McKitterick et al., JAP 2013 and arXiv:1307.5012v1


Graphene teams at LPA‐ENS

Gwendal Fève Bernard PlaçaisJean-Marc BerroirPhD Andreas Betz(Hitachi Cambridge)

Emiliano Pallecchi(Assist-Prof, IEMN)

post‐doc positions at ENS‐LPA !!!!

Dr.Sung-Ho Jhang(Assist-Prof. Seoul)

PhD Fabien Viala Christophe VoisinDr David Brunel

Coherent and Non Linear Optics team

Mesoscopic physics team


Robson Ferreira

Supercollision cooling of electrons in graphenejonckhee/VietnamPresentations/Quy...PhD Andreas Betz...

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