SLIDE 1
Adrian Bachtold Nanotube & Graphene ElectroMechanics
CIN2 (ICN-CSIC) Barcelona
1 m
Nanotube & Graphene ElectroMechanics Adrian Bachtold CIN2 - - PowerPoint PPT Presentation
Nanotube & Graphene ElectroMechanics Adrian Bachtold CIN2 - - PowerPoint PPT Presentation
Nanotube & Graphene ElectroMechanics Adrian Bachtold CIN2 (ICN-CSIC) Barcelona nanotube device 1 m 100 nm Eichler (Barcelona) Graphene 300 nm Moser (Barcelona) Graphene Hall Bar 200nm ultimate 1D and 2D NEMS When going small F
SLIDE 2
SLIDE 3
100 nm
Eichler (Barcelona)
SLIDE 4
Graphene
Moser (Barcelona)
300 nm
SLIDE 5
Graphene Hall Bar
SLIDE 6
200nm
SLIDE 7
ultimate 1D and 2D NEMS
SLIDE 8
When going small
F = -kx
x (nm) F (nN) x (nm) F (nN)
C Lee et al. Science 2008;321:385-388
GRAPHENE
SLIDE 9
bending rigidity
GRAPHENE
Atalaya, Isacsson and Kinaret, Nano Letters (2008)
SLIDE 10
1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 1E-21 1E-20 1E-19 1E-18 1E-17 1E-16 1E-15 1E-14 1E-13 1E-12 1E-11 1E-10 1E-9
Reulet Chiu Jenssen Lassagne Yang Ekinci Ono Forsen Lavrik Poncharal
mass resolution (g) year
Cleveland .
Motivation : mass sensing
Lassagne, Garcia-Sanchez, Aguasca, Bachtold, Nano Letters 2008
- K. Jensen, K. Kim, and A. Zettl. Nature Nanotech 2008
Chiu, Hung, Postma, Bockrath, Nano Letters 2008
SLIDE 11
1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 1E-24 1E-23 1E-22 1E-21 1E-20 1E-19 1E-18 1E-17 1E-16 1E-15 1E-14 1E-13 1E-12 1E-11 1E-10 1E-9
Reulet Chiu Jenssen Lassagne Yang Ekinci Ono Forsen Lavrik Poncharal
mass resolution (g) year
Cleveland .
Motivation : mass sensing
Lassagne, Garcia-Sanchez, Aguasca, Bachtold, Nano Letters 2008
- K. Jensen, K. Kim, and A. Zettl. Nature Nanotech 2008
Chiu, Hung, Postma, Bockrath, Nano Letters 2008
SLIDE 12
Motivation : quantum limit
m xQL
O’Connell, et al., Nature 2010 60 m
xQL ~ 2·10-17 m xQL ~ 10-11 m
1 m
) 2 / 1 ( n E
SLIDE 13
seeing is believing
Garcia-Sanchez, San Paulo, Esplandiu, Perez-Murano, Forro, Aguasca, Bachtold, PRL 2007
SLIDE 14
mixing technique – frequency modulation
- V. Gouttenoire et al., Small 6, 1060 (2010)
adapted from V. Sazonova et al., Nature 431, 284 (2004)
SLIDE 15
mixing technique – frequency modulation
- V. Gouttenoire et al., Small 6, 1060 (2010)
adapted from V. Sazonova et al., Nature 431, 284 (2004)
SLIDE 16
mixing technique – frequency modulation
frequency mixing current
) Re(x f I mix
- V. Gouttenoire et al., Small 6, 1060 (2010)
adapted from V. Sazonova et al., Nature 431, 284 (2004)
SLIDE 17
frequency mixing current
resonance frequency resonance width
Q f f / f
) 2 cos(
2 2
ft F kx t x t x m 2 mf Q m k f / 2 1
SLIDE 18
What a surprise !
) 2 cos(
2 2
ft F kx t x t x m 2 mf Q m k f / 2 1
driving force
strong deviation
5 K
SLIDE 19
) 2 cos(
2 2
ft F kx t x t x m 2 mf Q m k f / 2 1
frequency shift (kHz) width (Hz)
strong deviation
SLIDE 20
) 2 cos(
2 2
ft F kx t x t x m 2 mf Q m k f / 2 1
frequency shift (kHz) width (Hz)
strong deviation
Scott Bunch, et al. Science 2007
SLIDE 21
) 2 cos(
2 2
ft F kx t x t x m 2 mf Q m k f / 2 1
frequency shift (kHz) width (Hz)
strong deviation
SLIDE 22
higher order terms
Duffing force
shift (kHz) width (Hz) 3
x x kx x m
SLIDE 23
3
x x kx x m
3 2 2 2
ex x dx cxx x bx ax
higher order terms
shift (kHz) width (Hz)
SLIDE 24
x x2
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
Dykman, Krivoglaz, Phys. Stat. Sol. (b) (1975)
nonlinear damping
3
x x kx x m
higher order terms
shift (kHz) width (Hz)
SLIDE 25
NONLINEAR DAMPING
3 / 2
) (
AC
V
shift (kHz) width (Hz)
x x2
3
x x kx x m
- A. Eichler, J. Moser, J. Chaste, M. Zdrojek, I. Wilson-Rae, A. Bachtold, Nature Nano (published online)
SLIDE 26
hysteresis and nonlinear damping
x x2
3
x x kx x m
2 / 3 / f
NO hysterisis
2 / 3 / f
hysterisis
SLIDE 27
DAMPING
x Fdamping
for mechanical resonators
SLIDE 28
x Fdamping
1 m 1 mm 1 m 1 nm
Paris Vienna Caltech Caltech
x x Fdamping
2
Ligo
SLIDE 29
high quality factor
90 mK
SLIDE 30
x x x x kx x m
2 3
Can we tune:
?
parametric excitation
) cos( t k k k
SLIDE 31
parametric excitation
) cos( t k k k
1.25e+007 2.50e+007 3.75e+007 5.00e+007 6.25e+007 7.50e+007 8.75e+007 1.00e+0 3.75 2.50 1.25 0.00- 1.25
- 2.50
- 3.75
- 3.75e-010
- 2.50e-010
- 1.25e-010
- 2.78e-017
f0 (MHz) 4
- 4
Vg (V) 10 100
2
f k
2 f
Eichler, Chaste, Moser, Bachtold, Nano Letters (ASAP)
SLIDE 32
parametric excitation
) cos( t k k k
2 f
Eichler, Chaste, Moser, Bachtold, Nano Letters (ASAP)
x x x x kx x m
2 3
SLIDE 33
x x x x kx x m
2 3
Can we tune:
?
SLIDE 34
coupling mechanics and electron transport
Lassagne, Tarakanov, Kinaret, Garcia-Sanchez, Bachtold, Science (2009) see also: Steele, Hüttel, Witkamp, Poot, Meerwaldt, Kouwenhoven, van der Zant, Science (2009)
mechanics mechanics electronics 4K
SLIDE 35
Tuning the motion
linear nonlinear
x x k F
electro electro electro
becomes nontrivial
electro
F
SLIDE 36
nonlinear dynamics of the nanotube
Lassagne, Tarakanov, Kinaret, Garcia-Sanchez, Bachtold, Science (2009) linear
driving force
nonlinear
SLIDE 37
conclusion
x x x x kx x m
2 3
Eichler, et al., Nature Nano (online) Lassagne et al., Science (2009)
x x k F
electro electro electro
Eichler, et al., Nano Letters (ASAP)
SLIDE 38
R Rurali E Hernandez A San Paulo F Perez S Zippilli G Morigi F Alzina C Sotomayor S Roche
MJ Esplandiu J Chaste A Eichler B Lassagne J Moser M Zdrojek Quantum NanoElectronics group ICN
Barcelona
EURYI, NMP RODIN, Spanish ministry
Cornell A van der Zande P McEuen
A Barreiro D Garcia M Slezinska A Gruneis A Afshar I Tsioutsios
Chalmers Y Tarakanov J Kinaret Paris
- M. Lazzeri
- F. Mauri
Santa Barbara B Thibeault MIT P Jarillo-Herrero Munich I Wilson-Rae