Breakdown of continuum mechanics for nanometer-wavelength rippling of graphene

Abstract

Understanding how the mechanical behavior of materials deviates at the nanoscale from the macroscopically established concepts is a key challenge of particular importance for graphene, given the complex interplay between its nanoscale morphology and electronic properties. In this work, the (sub-) nanometer wavelength periodic rippling of suspended graphene nanomembranes has been realized by thermal strain-engineering and investigated using Scanning Tunneling Microscopy. This allows us to explore the rippling of a crystalline membrane with wavelengths comparable to its lattice constant. The observed nanorippling mode violates the predictions of the continuum model, and evidences the breakdown of the plate idealization of the graphene monolayer. Nevertheless, microscopic simulations based on a quantum mechanical description of the chemical binding accurately describe the observed rippling mode and elucidate the origin of the continuum model breakdown. Spatially resolved tunneling spectroscopy measurements indicate a substantial influence of the nanoripples on the local electronic structure of graphene and reveal the formation of one-dimensional electronic superlattices.

References in corpus (13)

• Ripple Texturing of Suspended Graphene Atomic Membranes
• Tailoring the atomic structure of graphene nanoribbons by STM lithography
• Anisotropic behaviors of massless Dirac fermions in graphene under periodic potential
• Periodically rippled graphene: growth and spatially resolved electronic structure
• Electron scattering on microscopic corrugations in graphene
• Finite temperature lattice properties of graphene beyond the quasiharmonic approximation
• Subjecting a graphene monolayer to tension and compression
• Graphene as an electronic membrane
• Spatially resolved spectroscopy of monolayer graphene on SiO2
• Quasi-Periodic Nanoripples in Graphene Grown by Chemical Vapor Deposition and Its Impact on Charge Transport
• Evidence for Strain-Induced Local Conductance Modulations in Single-Layer Graphene on SiO2
• Electronic superlattices in corrugated graphene
• Exchange induced charge inhomogeneities in rippled neutral graphene

Cited by in corpus (14)

• Creating One-dimensional Nanoscale Periodic Ripples in a Continuous Mosaic Graphene Monolayer
• Defects controlled hole doping and multi-valley transport in SnSe single crystals
• Evidence for Superlattice Dirac Points and Space-dependent Fermi Velocity in Corrugated Graphene Monolayer
• Generating nanoscale and atomically-sharp p-n junctions in graphene via monolayer-vacancy-island engineering of Cu surface
• Wrinkled few-layer graphene as highly efficient load bearer
• Direct Probing Stacking Order and Electronic Spectrum of Rhombohedral Trilayer Graphene with Scanning Tunneling Microscopy
• Graphene Cardboard: from Ripples to Tunable Metamaterial
• A new material property of graphene: the bending Poisson coefficient
• Determination of the STM tip-graphene repulsive forces by comparative STM and AFM measurements on suspended graphene
• Radiative decay effects influence the local electromagnetic response of the monolayer graphene with surface corrugations in terahertz range
• Apparent rippling with honeycomb symmetry and tunable periodicity observed by scanning tunneling microscopy on suspended graphene
• Nature of Spontaneous Curvature in Suspended Graphene
• Corrugation induced stacking solitons with topologically confined states in gapped bilayer graphene
• Magnetic-field-assisted electron confinement and valley splitting in strained graphene