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 (nN) F = -kx x (nm) GRAPHENE F (nN) x (nm) C Lee et al. Science 2008;321:385-388

bending rigidity GRAPHENE Atalaya, Isacsson and Kinaret, Nano Letters (2008)

Motivation : mass sensing 1E-9 Cleveland . 1E-10 1E-11 1E-12 1E-13 mass resolution (g) 1E-14 Poncharal Lavrik 1E-15 1E-16 Forsen Reulet 1E-17 Ono 1E-18 Ekinci 1E-19 1E-20 Yang 1E-21 Lassagne 1E-22 Jenssen 1E-23 Chiu 1E-24 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 year 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

Motivation : mass sensing 1E-9 Cleveland . 1E-10 1E-11 1E-12 1E-13 mass resolution (g) 1E-14 Poncharal Lavrik 1E-15 1E-16 Forsen Reulet 1E-17 Ono 1E-18 Ekinci 1E-19 1E-20 Yang 1E-21 Lassagne 1E-22 Jenssen 1E-23 Chiu 1E-24 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 year 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

Motivation : quantum limit   (    E n 1 / 2 )   x QL  m O’Connell, et al., Nature 2010 1  m 60  m  x QL ~ 10 -11 m  x QL ~ 2 · 10 -17 m

seeing is believing Garcia-Sanchez, San Paulo, Esplandiu, Perez-Murano, Forro, Aguasca, Bachtold, PRL 2007

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 mixing current frequency   I mix Re( x )  f V. Gouttenoire et al ., Small 6 , 1060 (2010) adapted from V. Sazonova et al ., Nature 431 , 284 (2004)

resonance frequency f 0 mixing current resonance width   f f / Q 0 frequency 1  f k / m  0 2   2 x x      m kx F cos( 2 ft )    0 2 t t 2 mf Q  0 

What a surprise ! 5 K driving force strong deviation 1  f k / m  0 2   2 x x      m kx F cos( 2 ft )    0 2 t t 2 mf Q  0 

frequency width (Hz) shift (kHz) strong deviation 1  f k / m  0 2   2 x x      m kx F cos( 2 ft )    0 2 t t 2 mf Q  0 

Scott Bunch, et al. Science 2007 frequency width (Hz) shift (kHz) strong deviation 1  f k / m  0 2   2 x x      m kx F cos( 2 ft )    0 2 t t 2 mf Q  0 

frequency width (Hz) shift (kHz) strong deviation 1  f k / m  0 2   2 x x      m kx F cos( 2 ft )    0 2 t t 2 mf Q  0 

higher order terms width (Hz) shift (kHz)          3 m x kx x x Duffing force

higher order terms width (Hz) shift (kHz)          3 m x kx x x      2 2 2 3 ax bx x cxx dx x ex

higher order terms width (Hz) shift (kHz)            3 x 2 m x kx x x x nonlinear damping 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 width (Hz) shift (kHz)  2 / 3 ( V ) AC            3 x 2 m x kx x x x A. Eichler, J. Moser, J. Chaste, M. Zdrojek, I. Wilson-Rae, A. Bachtold, Nature Nano (published online)

hysteresis and nonlinear damping            3 x 2 m x kx x x x     / 3 / 2 f NO hysterisis 0     / 3 / 2 f hysterisis 0

DAMPING    F damping x for mechanical resonators

    2 F damping x x 1  m 1 m 1 mm 1 nm Ligo Paris Vienna Caltech Caltech     F damping x

high quality factor 90 mK

Can we tune:     3         ? 2 m x kx x x x x     k k k cos( t ) parametric excitation

f 0 (MHz) 100 10 -4 3.75 Eichler, Chaste, Moser, Bachtold, Nano Letters (ASAP) 2.50 1.25 V g (V) 0 row 0.00 parametric excitation -1.25 k k   -2.50 -3.75 4 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 f col  0 2 -3.75e-010 -2.50e-010 -1.25e-010 -2.78e-017 1.25e-010 2.50e-010 3.75e-010  RF_9_treated k cos( t  )   2 f 0

parametric excitation     k k k cos( t )   2 f 0     3         2 m x kx x x x x Eichler, Chaste, Moser, Bachtold, Nano Letters (ASAP)

Can we tune:     3         ? 2 m x kx x x x x

coupling mechanics and electron transport electronics mechanics 4K mechanics Lassagne, Tarakanov, Kinaret, Garcia-Sanchez, Bachtold, Science (2009) see also: Steele, Hüttel, Witkamp, Poot, Meerwaldt, Kouwenhoven, van der Zant, Science (2009)

Tuning the motion nonlinear linear      F k x x F becomes nontrivial electro electro electro electro

nonlinear dynamics of the nanotube nonlinear linear driving force Lassagne, Tarakanov, Kinaret, Garcia-Sanchez, Bachtold, Science (2009)

conclusion     3         Eichler, et al., Nature Nano (online) 2 m x kx x x x x Eichler, et al., Nano Letters (ASAP) Lassagne et al., Science (2009)      F k x x electro electro electro

Barcelona R Rurali E Hernandez A San Paulo F Perez S Zippilli G Morigi F Alzina C Sotomayor S Roche Chalmers Y Tarakanov J Kinaret Munich Quantum NanoElectronics group ICN I Wilson-Rae MJ Esplandiu A Barreiro Cornell A van der Zande J Chaste D Garcia P McEuen A Eichler M Slezinska MIT B Lassagne A Gruneis P Jarillo-Herrero J Moser A Afshar Paris M. Lazzeri M Zdrojek I Tsioutsios F. Mauri Santa Barbara EURYI, NMP RODIN, Spanish ministry B Thibeault