Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992...

33
Adrian Bachtold Graphene ElectroMechanical Resonators ICN, CIN2, Barcelona

Transcript of Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992...

Page 1: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

Adrian Bachtold

Graphene ElectroMechanical Resonators

ICN, CIN2, Barcelona

Page 2: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

Graphene

Moser (Barcelona)300 nm

Page 3: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

Graphene Hall Bar

Page 4: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

200nm

Page 5: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

When going small

F = -kx

x (nm)

F (n

N)

x (nm)

F (n

N)

C Lee et al. Science 2008;321:385-388

GRAPHENE

Page 6: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

bending rigidity

GRAPHENE

Atalaya, Isacsson and Kinaret, Nano Letters (2008)

Page 7: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

1992 1994 1996 1998 2000 2002 2004 2006 2008 20101E-241E-231E-221E-211E-201E-191E-181E-171E-161E-151E-141E-131E-121E-111E-101E-9

Reulet

ChiuJenssenLassagne

Yang

Ekinci

OnoForsen

LavrikPoncharal

mas

s re

solu

tion

(g)

year

Cleveland .

Motivation : mass sensing

Lassagne, Garcia-Sanchez, Aguasca, Bachtold, Nano Letters 2008K. Jensen, K. Kim, and A. Zettl. Nature Nanotech 2008 Chiu, Hung, Postma, Bockrath, Nano Letters 2008

Page 8: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

Motivation : quantum limit

mxQL

O’Connell, et al., Nature 2010

60 m

xQL ~ 2·10-17 mxQL ~ 10-11 m

1 m

)2/1( nE

Page 9: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

seeing is believing

Garcia-Sanchez, van der Zande, San Paulo, Lassagne, McEuen, BachtoldNano Letters 8, 1399 (2008)

31 MHz

31 MHz

Page 10: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

mixing technique – frequency modulation

V. Gouttenoire et al., Small 6, 1060 (2010)

adapted from V. Sazonova et al., Nature 431, 284 (2004)

Page 11: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

mixing technique – frequency modulation

V. Gouttenoire et al., Small 6, 1060 (2010)

adapted from V. Sazonova et al., Nature 431, 284 (2004)

Page 12: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

mixing technique – frequency modulation

frequency

mixingcurren

t

)Re(xfImix

V. Gouttenoire et al., Small 6, 1060 (2010)

adapted from V. Sazonova et al., Nature 431, 284 (2004)

Page 13: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

frequency

mixingcurren

t

resonance frequency

resonance width

Qff /0

0f

)2cos(02

2

ftFkxtx

txm

02 mfQ

mkf /21

0

Page 14: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

What a surprise !

)2cos(02

2

ftFkxtx

txm

02 mfQ

mkf /21

0

driving force

strong devia

tion

5 K

Page 15: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

)2cos(02

2

ftFkxtx

txm

02 mfQ

mkf /21

0

frequency

shift

(kHz)

width

(Hz)

strong devia

tion

Page 16: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

)2cos(02

2

ftFkxtx

txm

02 mfQ

mkf /21

0

frequency

shift

(kHz)

width

(Hz)

strong devia

tion

Scott Bunch, et al. Science 2007

Page 17: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

)2cos(02

2

ftFkxtx

txm

02 mfQ

mkf /21

0

frequency

shift

(kHz)

width

(Hz)

strong devia

tion

Page 18: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

higher order terms

Duffing forceshift

(kHz)

width

(Hz)

3xxkxxm

Page 19: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

3xxkxxm

3222 exxdxcxxxbxax

higher order terms

shift

(kHz)

width

(Hz)

Page 20: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

xx2

Ron Lifshitz and M.C. Cross. Review of Nonlinear Dynamics and Complexity 1 (2008) 1-52.S. Zaitsev, O. Shtempluck, E. Buks, O. Gottlieb, arXiv:0911.0833

nonlinear damping 

3xxkxxm

higher order terms

shift

(kHz)

width

(Hz)

Page 21: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

NONLINEAR DAMPING

3/2)( ACV shift

(kHz)

width

(Hz)

xx23xxkxxm

A. Eichler, J. Moser, J. Chaste, M. Zdrojek, I. Wilson-Rae, A. Bachtold, arXiv:1103.1788

Page 22: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

hysteresis and nonlinear damping

xx23xxkxxm

02/3/ f NO hysterisis

02/3/ f hysterisis

Page 23: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

DAMPING

xFdamping

for mechanical resonators

Page 24: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

xFdamping

1 m 1 mm 1 m 1 nm

Paris Vienna Caltech Caltech

xxFdamping2

Ligo

Page 25: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

high quality factor

90 mK

Page 26: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

xxxxkxxm 23 Can we tune:

?

xxkF electroelectroelectro

Lassagne, Tarakanov, Kinaret, Garcia-Sanchez, Bachtold, Science (2009)see also: Steele, Hüttel, Witkamp, Poot, Meerwaldt, Kouwenhoven, van der Zant, Science (2009)

quantum dot

Page 27: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

source drain

backgateoxide

as fabricated

200nm

ultra-narrow constriction

ultra-narrow constriction

0 1 2 3 40

50

100

I (m

icro

Am

ps)

Vsd (V)

Saturation current ~1microAmps per nm

Page 28: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

source drain

backgateoxide

as fabricated

200nm

ultra-narrow constriction

ultra-narrow constriction

0 1 2 3 40

50

100

I (m

icro

Am

ps)

Vsd (V)

Saturation current ~1microAmps per nm

Page 29: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

source drain

backgateoxide

as fabricated

200nm

ultra-narrow constriction

ultra-narrow constriction

0 1 2 3 40

50

100

I (m

icro

Am

ps)

Vsd (V)

Saturation current ~1microAmps per nm

Page 30: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

50

25

0

-25

-50

sour

ce -

drai

n bi

as (m

V)

-1 1-0.5 0backgate bias (V)

10-4

dI/dV ( S)10

-310

-210

-1

dI/dV ( S)0 5 10

150

50

100

0

-50

-100

-150so

urce

- dr

ain

bias

(mV

)0 1 2 3 4 5 6

backgate bias (V)

Stability diagrams

J. Moser and A. Bachtold, Appl. Phys. Lett. 95, 173506 (2009)

E=25meV

Page 31: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

• K. Todd, H.-T. Chou, S. Amasha, and D. Goldhaber-GordonNano. Lett. 9, 416 (2009)

• C. Stampfer, J. Güttinger, S. Hellmüller, F. Molitor, K. Ensslin, and T. IhnPhys. Rev. Lett. 102, 056403 (2009)

• Xinglan Liu, J.B. Oostinga, A.F. Morpurgo, and L.M.K. VandersypenPhysical Review B 80, 121407 (2009)

• M.Y. Han, B. Oezyilmaz, Y. Zhang, and P. KimPhys. Rev. Lett. 98, 206805 (2007)

Models for quantum dots in constrictions

Gap betweenvalence and

conductance bands

Page 32: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

conclusion

xxxxkxxm 23

xxkF electroelectroelectro quantum dot

Page 33: Graphene ElectroMechanical Resonators · Atalaya, Isacsson and Kinaret, Nano Letters (2008) 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 ... 31 MHz 31 MHz.

R RuraliE Hernandez A San PauloF PerezS ZippilliG MorigiF AlzinaC SotomayorS Roche

MJ EsplandiuJ ChasteA EichlerB LassagneJ MoserM Zdrojek

Quantum NanoElectronics group ICN

Barcelona

EURYI, NMP RODIN, Spanish ministry

CornellA van der ZandeP McEuen

A BarreiroD GarciaM SlezinskaA GruneisA AfsharI Tsioutsios

ChalmersY TarakanovJ Kinaret

ParisM. LazzeriF. Mauri

Santa BarbaraB Thibeault

MITP Jarillo-Herrero

MunichI Wilson-Rae


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