graphene electromechanical resonators · atalaya, isacsson and kinaret, nano letters (2008) 1992...
TRANSCRIPT
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Adrian Bachtold
Graphene ElectroMechanical Resonators
ICN, CIN2, Barcelona
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Graphene
Moser (Barcelona)300 nm
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Graphene Hall Bar
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200nm
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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
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bending rigidity
GRAPHENE
Atalaya, Isacsson and Kinaret, Nano Letters (2008)
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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
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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
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seeing is believing
Garcia-Sanchez, van der Zande, San Paulo, Lassagne, McEuen, BachtoldNano Letters 8, 1399 (2008)
31 MHz
31 MHz
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mixing technique – frequency modulation
V. Gouttenoire et al., Small 6, 1060 (2010)
adapted from V. Sazonova et al., Nature 431, 284 (2004)
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mixing technique – frequency modulation
V. Gouttenoire et al., Small 6, 1060 (2010)
adapted from V. Sazonova et al., Nature 431, 284 (2004)
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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)
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frequency
mixingcurren
t
resonance frequency
resonance width
Qff /0
0f
)2cos(02
2
ftFkxtx
txm
02 mfQ
mkf /21
0
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What a surprise !
)2cos(02
2
ftFkxtx
txm
02 mfQ
mkf /21
0
driving force
strong devia
tion
5 K
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)2cos(02
2
ftFkxtx
txm
02 mfQ
mkf /21
0
frequency
shift
(kHz)
width
(Hz)
strong devia
tion
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)2cos(02
2
ftFkxtx
txm
02 mfQ
mkf /21
0
frequency
shift
(kHz)
width
(Hz)
strong devia
tion
Scott Bunch, et al. Science 2007
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)2cos(02
2
ftFkxtx
txm
02 mfQ
mkf /21
0
frequency
shift
(kHz)
width
(Hz)
strong devia
tion
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higher order terms
Duffing forceshift
(kHz)
width
(Hz)
3xxkxxm
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3xxkxxm
3222 exxdxcxxxbxax
higher order terms
shift
(kHz)
width
(Hz)
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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)
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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
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hysteresis and nonlinear damping
xx23xxkxxm
02/3/ f NO hysterisis
02/3/ f hysterisis
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DAMPING
xFdamping
for mechanical resonators
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xFdamping
1 m 1 mm 1 m 1 nm
Paris Vienna Caltech Caltech
xxFdamping2
Ligo
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high quality factor
90 mK
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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
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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
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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
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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
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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
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• 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
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conclusion
xxxxkxxm 23
xxkF electroelectroelectro quantum dot
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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