Graphene ElectroMechanical Resonators. Adrian Bachtold. ICN, CIN2, Barcelona

Transcription

1 Graphene ElectroMechanical Resonators Adrian Bachtold ICN, CIN2, Barcelona

2 Graphene Moser (Barcelona) 3 nm

3 Graphene Hall Bar

4 2nm

5 When going small F (nn) F = -kx x (nm) GRAPHENE F (nn) C Lee et al. Science 28;321: x (nm)

6 bending rigidity GRAPHENE Atalaya, Isacsson and Kinaret, Nano Letters (28)

7 Motivation : mass sensing mass resolution (g) 1E-9 1E-1 1E-11 1E-12 1E-13 1E-14 1E-15 1E-16 1E-17 1E-18 1E-19 1E-2 1E-21 1E-22 1E-23 1E-24 Cleveland. Poncharal Reulet Lavrik Ono Ekinci Yang Forsen Lassagne Jenssen Chiu year Lassagne, Garcia-Sanchez, Aguasca, Bachtold, Nano Letters 28 K. Jensen, K. Kim, and A. Zettl. Nature Nanotech 28 Chiu, Hung, Postma, Bockrath, Nano Letters 28

8 Motivation : quantum limit E ( n 1/ 2) x QL m O Connell, et al., Nature 21 1 m 6 m x QL ~ 1-11 m x QL ~ m

9 seeing is believing 31 MHz 31 MHz Garcia-Sanchez, van der Zande, San Paulo, Lassagne, McEuen, Bachtold Nano Letters 8, 1399 (28)

10 mixing technique frequency modulation V. Gouttenoire et al., Small 6, 16 (21) adapted from V. Sazonova et al., Nature 431, 284 (24)

11 mixing technique frequency modulation V. Gouttenoire et al., Small 6, 16 (21) adapted from V. Sazonova et al., Nature 431, 284 (24)

12 mixing technique frequency modulation mixing current frequency V. Gouttenoire et al., Small 6, 16 (21) adapted from V. Sazonova et al., Nature 431, 284 (24) I mix f Re(x)

13 resonance frequency f mixing current resonance width f f / Q frequency m 2 x 2 t x t kx F cos(2ft) 1 f k / m 2 Q 2mf

14 What a surprise! 5 K driving force m 2 x 2 t x t kx F cos(2ft) 1 f k / m 2 Q 2 mf strong deviation

15 2 x x m kx F cos(2 ft 2 t t ) 1 f k / 2 Q 2 mf frequency m width (Hz) shift (khz) strong deviation

16 Scott Bunch, et al. Science 27 width (Hz) shift (khz) frequency m 2 x 2 t x t kx F cos(2ft) 1 f k / m 2 Q 2 mf strong deviation

17 2 x x m kx F cos(2 ft 2 t t ) 1 f k / 2 Q 2 mf frequency m width (Hz) shift (khz) strong deviation

18 higher order terms width (Hz) shift (khz) m x kx xx 3 Duffing force

19 higher order terms width (Hz) shift (khz) m x kx xx 3 ax 2 bx x cxx 2 dx 2 x ex 3

20 higher order terms width (Hz) shift (khz) m x kx xx 3 x 2 x nonlinear damping Ron Lifshitz and M.C. Cross. Review of Nonlinear Dynamics and Complexity 1 (28) S. Zaitsev, O. Shtempluck, E. Buks, O. Gottlieb, arxiv:

21 NONLINEAR DAMPING width (Hz) 2 / ( V AC ) 3 shift (khz) m x kx xx 3 x 2 x A. Eichler, J. Moser, J. Chaste, M. Zdrojek, I. Wilson-Rae, A. Bachtold, arxiv:

22 hysteresis and nonlinear damping m x kx xx 3 x 2 x / 3 / 2f NO hysterisis / 3 / 2f hysterisis

23 DAMPING F damping x for mechanical resonators

24 2 F damping x x 1 m 1 mm 1 m 1 nm Ligo Paris Vienna Caltech Caltech F damping x

25 high quality factor 9 mk

26 Can we tune: m x kx x x 3 x 2 x? quantum dot F electro k electro x electro x Lassagne, Tarakanov, Kinaret, Garcia-Sanchez, Bachtold, Science (29) see also: Steele, Hüttel, Witkamp, Poot, Meerwaldt, Kouwenhoven, van der Zant, Science (29)

27 source drain oxide backgate Saturation current ~1microAmps per nm 2nm as fabricated I (micro Amps) 1 5 ultra-narrow constriction Vsd (V) ultra-narrow constriction

28 source drain oxide backgate Saturation current ~1microAmps per nm 2nm as fabricated I (micro Amps) 1 5 ultra-narrow constriction Vsd (V) ultra-narrow constriction

29 source drain oxide backgate Saturation current ~1microAmps per nm 2nm as fabricated I (micro Amps) 1 5 ultra-narrow constriction Vsd (V) ultra-narrow constriction

30 Stability diagrams di/dv ( S) source - drain bias (mv) backgate bias (V) source - drain bias (mv) di/dv ( S) E=25meV backgate bias (V) J. Moser and A. Bachtold, Appl. Phys. Lett. 95, (29)

31 Models for quantum dots in constrictions Gap between valence and conductance bands K. Todd, H.-T. Chou, S. Amasha, and D. Goldhaber- Gordon Nano. Lett. 9, 416 (29) C. Stampfer, J. Güttinger, S. Hellmüller, F. Molitor, K. Ensslin, and T. Ihn Phys. Rev. Lett. 12, 5643 (29) Xinglan Liu, J.B. Oostinga, A.F. Morpurgo, and L.M.K. Vandersypen PhysicalReviewB 8, (29) M.Y. Han, B. Oezyilmaz, Y. Zhang, and P. Kim Phys. Rev. Lett. 98, 2685 (27)

32 conclusion m x kx x x 3 x 2 x quantum dot F electro k electro x electro x

33 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 Quantum NanoElectronics group ICN MJ Esplandiu J Chaste A Eichler B Lassagne J Moser M Zdrojek A Barreiro D Garcia M Slezinska A Gruneis A Afshar I Tsioutsios EURYI, NMP RODIN, Spanish ministry Munich I Wilson-Rae Cornell A van der Zande P McEuen MIT P Jarillo-Herrero Paris M. Lazzeri F. Mauri Santa Barbara B Thibeault