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Graphene NEMS at the Chalmers Condensed Matter Theory Group

Graphene NEMS at the Chalmers Condensed Matter Theory Group. Isacsson RODIN Kick-off, Hindås. The Condensed Matter Theory Group. Chalmers 2 professors: J. Kinaret , P. Apell 1 Associate professor: L. Y. Gorelik 1 Assistant professor: A. Isacsson 2 Postdocs: D. Radic, W. Wang

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Graphene NEMS at the Chalmers Condensed Matter Theory Group

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  1. Graphene NEMS at the Chalmers Condensed Matter Theory Group Isacsson RODIN Kick-off, Hindås

  2. The Condensed Matter Theory Group Chalmers • 2 professors: J. Kinaret, P. Apell • 1 Associate professor: L. Y. Gorelik • 1 Assistant professor: A. Isacsson • 2 Postdocs: D. Radic, W. Wang • 5 Graduate students R. Rehammar, Y. Tarakanov, • J. Atalaya, A. Voje, D. Midtvedt, E. Helgee/2, D. Kadigrob/2 • Göteborg University • 2 Professors M. Jonson, R. I. Shekhter • 1 Post doc. H.-C. Park • 1 long term visitor A. M. Kadigrobov • 4 Graduate students G. Sonne, F. Santandrea, E. Pena, A. Nordenfeldt

  3. Main research directions • CNT NEMS Graphene NEMS • Graphene NEMS • Nonlinear dynamics of graphene membranes • Graphene mass-sensing • Noise and fluctuations in NEMS • Graphene Quantum NEMS • Coherent transport in NEMS

  4. Graphene NEMS, Mechanical properties and Non-linear dynamics Proper continuum elasticity theory is von-Karman theory. Microscopic parameters can be derived from MD-simulations von-Karman equations are complex ~ Can approximate with simpler PDE Expand in eigenmodes => Coupled Duffing oscillators

  5. Graphene Mass-Sensing Adding a point mass, lowers resonance frequency To know M we need position (x,y) Second parameter from nonlinear resp. splitting (x,y) Simple formula for responsivity Due to nonlinearity, all measurements can be done at the fundamental resonance frequency using multi-frequency excitation.

  6. Diffusion induced frequency noise and fluctuations in NEMS What if the particle on/in the resonator moves around? Fluctuating frequency. Diffusion: Resulting spectrum/response function, depend on (correlation time) x (rms-fluctuations)

  7. Quantum (FP7, QNEMS) Degenerate modes open new possibilities at Quantum limit Consider two lowest degenerate modes. Two harmonic oscillators with same frequency. Applying a gate pulse V(t) to asymmetric gate leads to well controlled mode coupling Applying a sudden pulse V(t) = q(t) to membrane in ground state leads to coherent oscillations between mode populations prop. to : sin2(W1-W2)t Linear Quantum Mechanical model ~ Classical behavior What quantum signatures appear if nonlinear terms are added, i.e. coupled Duffing .vs. Classical Duffing?

  8. Coherent transport in Graphene NEMS Sheet conductance changes due to: - carrier concentration modulation - tension changes band structure Coherent transport in nanoribbons. Conductance quantization 2. Length scale Although

  9. Planned/promised activities in RODIN (1/3) • Intrinsic Q-factor limitations graphene resonators • Theoretical study on limiting factors for Q. • SLG • FLG • Edge modes • Nonlinearities • Shape Associated deliverables D5.3 [M24]: Optimum resonator geometry from mechanical and electrical modelling Updates since proposal: A few theory papers on the topic of interlayer friction between graphene sheets in FLG. Not much done otherwise.

  10. Planned/promised activities in RODIN (2/3) • A further look at strain-fields .vs. Conductance in suspended graphene. • Strain induces synthetic gauge field • In the low T-limit this affects coherent transport • Can one find situations where effect in T>0 NEMS? • Can this effect be exploited? Read out? • Tool to study mechanical properties of FLG and SLG in AFM-push experiments? Associated deliverable: D4.2 [M30]: Model for piezo resistive response of SLG and FLG Updates since proposal: Piezo resistivity in graphene and strain-engineering in SLG has been studied a lot the past two years. In FLG less has been done. Interesting effects appear for disorder+strain and strain + ”engineered defects” in SLG.

  11. Planned/promised activities in RODIN (3/3) • Coupled graphene resonators • Single graphene resonator quickly show nonlinear behavior • Sculpting graphene allows for etching out coupled resonators with desired coupling properties • To what extent can one directly tailor the frequency response by making coupled resonators? • Coupled nonlinear resonators: How will the nonlinearities in the affect the spectrum? Associated Deliverable: D5.4 [M36]: Evaluation of the application potential for coupled resonators Updates since proposal: Not much has happened? No coupled graphene resonators shown. No realization of coupled nonlinear NEMS demonstrated.

  12. Other planned activities Paperwork, Report writing, Administration, Sending lots of email, …  Thank you for your attention 

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