Post on 26-Aug-2020
Adrian Bachtold
Graphene ElectroMechanical Resonators
ICN, CIN2, Barcelona
Graphene
Moser (Barcelona)300 nm
Graphene Hall Bar
200nm
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
bending rigidity
GRAPHENE
Atalaya, Isacsson and Kinaret, Nano Letters (2008)
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
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
seeing is believing
Garcia-Sanchez, van der Zande, San Paulo, Lassagne, McEuen, BachtoldNano Letters 8, 1399 (2008)
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)
mixing technique – frequency modulation
V. Gouttenoire et al., Small 6, 1060 (2010)
adapted from V. Sazonova et al., Nature 431, 284 (2004)
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)
frequency
mixingcurren
t
resonance frequency
resonance width
Qff /0
0f
)2cos(02
2
ftFkxtx
txm
02 mfQ
mkf /21
0
What a surprise !
)2cos(02
2
ftFkxtx
txm
02 mfQ
mkf /21
0
driving force
strong devia
tion
5 K
)2cos(02
2
ftFkxtx
txm
02 mfQ
mkf /21
0
frequency
shift
(kHz)
width
(Hz)
strong devia
tion
)2cos(02
2
ftFkxtx
txm
02 mfQ
mkf /21
0
frequency
shift
(kHz)
width
(Hz)
strong devia
tion
Scott Bunch, et al. Science 2007
)2cos(02
2
ftFkxtx
txm
02 mfQ
mkf /21
0
frequency
shift
(kHz)
width
(Hz)
strong devia
tion
higher order terms
Duffing forceshift
(kHz)
width
(Hz)
3xxkxxm
3xxkxxm
3222 exxdxcxxxbxax
higher order terms
shift
(kHz)
width
(Hz)
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)
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
hysteresis and nonlinear damping
xx23xxkxxm
02/3/ f NO hysterisis
02/3/ f hysterisis
DAMPING
xFdamping
for mechanical resonators
xFdamping
1 m 1 mm 1 m 1 nm
Paris Vienna Caltech Caltech
xxFdamping2
Ligo
high quality factor
90 mK
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
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
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
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
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
• 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
conclusion
xxxxkxxm 23
xxkF electroelectroelectro quantum dot
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