Fermi-Pasta-Ulam physics with nanomechanical graphene resonators: intrinsic relaxation and thermalization from flexural mode coupling.

Thermalization in nonlinear systems is a central concept in statistical mechanics and has been extensively studied theoretically since the seminal work of Fermi, Pasta, and Ulam. Using molecular dynamics and continuum modeling of a ring-down setup, we show that thermalization due to nonlinear mode coupling intrinsically limits the quality factor of nanomechanical graphene drums and turns them into potential test beds for Fermi-Pasta-Ulam physics. We find the thermalization rate Γ to be independent of radius and scaling as Γ∼T*/εpre2, where T* and εpre are effective resonator temperature and prestrain.

[1]  N. Zabusky,et al.  Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States , 1965 .

[2]  M. Cross,et al.  Elastic Wave Transmission at an Abrupt Junction in a Thin Plate, with Application to Heat Transport and Vibrations in Mesoscopic Systems , 2000, cond-mat/0011501.

[3]  A. Croy,et al.  Nonlinear Damping in Graphene Resonators , 2012, 1204.0911.

[4]  Matthias Imboden,et al.  Dissipation in nanoelectromechanical systems , 2014 .

[5]  Tiziano Penati,et al.  Tail resonances of Fermi-Pasta-Ulam q-breathers and their impact on the pathway to equipartition. , 2006, Chaos.

[6]  B. Camarota,et al.  Approaching the Quantum Limit of a Nanomechanical Resonator , 2004, Science.

[7]  A. M. van der Zande,et al.  Fluctuation broadening in carbon nanotube resonators , 2011, Proceedings of the National Academy of Sciences.

[8]  M. Blencowe,et al.  Damping and decoherence of a nanomechanical resonator due to a few two-level systems , 2009, 0907.0431.

[9]  Shin'ichi Warisawa,et al.  High Quality Factor Graphene Resonator Fabrication Using Resist Shrinkage-Induced Strain , 2012 .

[10]  Scott S. Verbridge,et al.  Electromechanical Resonators from Graphene Sheets , 2007, Science.

[11]  Dae Sung Yoon,et al.  Nanomechanical resonators and their applications in biological/chemical detection: Nanomechanics pri , 2011 .

[12]  A molecular simulation analysis of producing monatomic carbon chains by stretching ultranarrow graphene nanoribbons. , 2010, Nanotechnology.

[13]  J. Kysar,et al.  Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene , 2008, Science.

[14]  S. Stuart,et al.  A reactive potential for hydrocarbons with intermolecular interactions , 2000 .

[15]  L. Galgani,et al.  The Fermi-Pasta-Ulam Problem , 2002 .

[16]  Simone Paleari,et al.  Exponentially long times to equipartition in the thermodynamic limit , 2004 .

[17]  Harold G. Craighead,et al.  Virus detection using nanoelectromechanical devices , 2004 .

[18]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .

[19]  S. Ulam,et al.  Studies of nonlinear problems i , 1955 .

[20]  Andrew G. Glen,et al.  APPL , 2001 .

[21]  Giovanni Gallavotti,et al.  The Fermi-Pasta-Ulam Problem , 2008 .

[22]  J. Chaste,et al.  Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene. , 2011, Nature nanotechnology.

[23]  I. Wilson-Rae,et al.  Intrinsic dissipation in nanomechanical resonators due to phonon tunneling , 2007, 0710.0200.

[24]  G. Berman,et al.  The Fermi-Pasta-Ulam problem: fifty years of progress. , 2004, Chaos.

[25]  A. Croy,et al.  Frequency tuning, nonlinearities and mode coupling in circular mechanical graphene resonators , 2013, Nanotechnology.

[26]  G. Benettin,et al.  The Fermi—Pasta—Ulam Problem and the Metastability Perspective , 2007 .

[27]  Robert A. Barton,et al.  High, size-dependent quality factor in an array of graphene mechanical resonators. , 2011, Nano letters.

[28]  N. Aluru,et al.  Size and chirality dependent elastic properties of graphene nanoribbons under uniaxial tension. , 2009, Nano letters.

[29]  David K Campbell,et al.  Introduction: The Fermi-Pasta-Ulam problem--the first fifty years. , 2005, Chaos.

[30]  A. Isacsson,et al.  Direct transmission detection of tunable mechanical resonance in an individual carbon nanofiber relay. , 2008, Nano letters.

[31]  M. Roukes,et al.  Nonlinear mode-coupling in nanomechanical systems. , 2013, Nano letters.

[32]  Zenan Qi,et al.  Intrinsic energy dissipation in CVD-grown graphene nanoresonators. , 2012, Nanoscale.

[33]  Robert A. Barton,et al.  Large-scale arrays of single-layer graphene resonators. , 2010, Nano letters.

[34]  M. Roukes,et al.  Thermoelastic damping in micro- and nanomechanical systems , 1999, cond-mat/9909271.

[35]  M. Pettini,et al.  Relaxation properties and ergodicity breaking in nonlinear Hamiltonian dynamics. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[36]  G. Benettin,et al.  Boltzmann's ultraviolet cutoff and Nekhoroshev's theorem on Arnold diffusion , 1984, Nature.

[37]  L. Peliti,et al.  Approach to equilibrium in a chain of nonlinear oscillators , 1982 .

[38]  P. Kim,et al.  Performance of monolayer graphene nanomechanical resonators with electrical readout. , 2009, Nature nanotechnology.

[39]  M. Ivanchenko,et al.  q-Breathers and the Fermi-Pasta-Ulam problem. , 2005, Physical review letters.