Strain engineering of graphene takes advantage of one of the most dramatic responses of Dirac electrons enabling their manipulation via strain-induced pseudo-magnetic fields. Numerous theoretically proposed devices, such as resonant cavities and valley filters, as well as novel phenomena, such as snake states, could potentially be enabled via this effect. These proposals, however, require strong, spatially oscillating magnetic fields while to date only the generation and effects of pseudo-gauge fields which vary at a length scale much larger than the magnetic length have been reported. Here we create a periodic pseudo-gauge field profile using periodic strain that varies at the length scale comparable to the magnetic length and study its effects on Dirac electrons. A periodic strain profile is achieved by pulling on graphene with extreme (>10%) strain and forming nanoscale ripples, akin to a plastic wrap pulled taut at its edges. Combining scanning tunneling microscopy and atomistic calculations, we find that spatially oscillating strain results in a new quantization different from the familiar Landau quantization observed in previous studies. We also find that graphene ripples are characterized by large variations in carbon-carbon bond length, directly impacting the electronic coupling between atoms, which within a single ripple can be as different as in two different materials. The result is a single graphene sheet that effectively acts as an electronic superlattice. Our results thus also establish a novel approach to synthesize an effective 2D lateral heterostructure -by periodic modulation of lattice strain. Main Text:Due to its high electronic mobility, optical transparency, mechanical strength and flexibility, graphene is attractive for electronic applications 1,2 . However, several factors prevent the realization of common electronic applications. For example, the lack of a band gap prevents an effective off-state in graphene transistors. Furthermore, Klein tunneling 3 , in which electrons pass through an electrostatic barrier with perfect transmission, prevents electron confinement by traditional gating methods. Figure 1. Engineering periodic pseudo electric and magnetic fields at strained interfaces: (a)High(low) density of carbon atoms and hence electrons are created in regions marked by lightblue (yellow) regions due to a strain gradient. This inhomogeneous charge distribution results in an electric field (green arrows). (b) Stretching of bonds cause the Dirac cones at K and K' points to shift symmetrically (yellow) from their original unstrained positions (light-blue) in the reciprocal space. As a momentum shift can be interpreted as generating a pseudo-vector potential term eA/c 15 , (where is the electronic charge and is the velocity of light) this creates pseudo-magnetic fields with opposite signs at the two valleys. (c) The strain associated with rippling creates rare (yellow) and dense (turquoise) regions in the graphene, effectively acting as two different materials in a superlattice. (d) Pseudo...
Molecular insights into graphene-catalyst surface interactions can provide useful information for the efficient design of copper current collectors with graphitic anode interfaces. As graphene bending can affect the local electron density, it should reflect its local reactivity as well. Using ReaxFF reactive molecular simulations, we have investigated the possible bending of graphene in vacuum and near copper surfaces. We describe the energy cost for graphene bending and the binding energy with hydrogen and copper with two different ReaxFF parameter sets, demonstrating the relevance of using the more recently developed ReaxFF parameter sets for graphene properties. Moreover, the draping angle at copper step edges obtained from our atomistic simulations is in good agreement with the draping angle determined from experimental measurements, thus validating the ReaxFF results.
Ever since the discovery of graphene and subsequent explosion of interest in single-atom-thick materials, studying their mechanical properties has been an active area of research. Atomistic length scales often necessitate a rethinking of physical laws, making such studies crucial for understanding and ultimately utilizing material properties. Here, we report on the investigation of nanoscale periodic ripples in suspended, single-layer graphene sheets by scanning tunneling microscopy and atomistic scale simulations. Unlike the sinusoidal ripples found in classical fabrics, we find that graphene forms triangular ripples, where bending is limited to a narrow region on the order of a few unit cell dimensions at the apex of each ripple. This nonclassical bending profile results in graphene behaving like a bizarre fabric, which regardless of how it is draped, always buckles at the same angle. Investigating the origin of such nonclassical mechanical properties, we find that unlike a thin classical fabric, both in-plane and out-of-plane deformations occur in a graphene sheet. These two modes of deformation compete with each other, resulting in a strain-locked optimal buckling configuration when draped. Electronically, we see that this in-plane deformation generates pseudo electric fields creating a ∼3 nm wide pnp heterojunction purely by strain modulation.
The high sensitivity of scanning probe microscopes poses a barrier to their use in noisy environments. Vibrational noise, whether from structural or acoustic sources, can manifest as relative motion between the probe tip and sample, which then appears in the probe position ("Z") feedback as it tries to cancel this motion. Here we describe an active cancellation process that nullifies the appearance of this vibration by adding a drive signal into the existing Z-feedback loop. The drive is digitally calculated from accelerometer-based vibration measurements. By transferring the vibration cancellation effort to this drive signal, vibration-created noise is significantly reduced. This inexpensive and easy solution requires no major instrumental modifications and is ideal for those looking to place their microscopes in noisier environments, coupled, for example, to active refrigeration systems (e.g., pulse tube cryocoolers) or other high-vibration instruments.
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