Electromechanical Properties of Graphene Drumheads

Abstract

We determined the electromechanical properties of a suspended graphene layer by scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) measurements, as well as computational simulations of the graphene-membrane mechanics and morphology. A graphene membrane was continuously deformed by controlling the competing interactions with a STM probe tip and the electric field from a back-gate electrode. The probe tip-induced deformation created a localized strain field in the graphene lattice. STS measurements on the deformed suspended graphene display an electronic spectrum completely different from that of graphene supported by a substrate. The spectrum indicates the formation of a spatially confined quantum dot, in agreement with recent predictions of confinement by strain-induced pseudomagnetic fields.

Analytic approach to magneto-strain tuning of electronic transport through a graphene nanobubble: perspectives for a strain sensor

“…More recently, Bahamon et al [32] studied the conductance induced by different strain nanobubles numerically using molecular dynamics and tight-binding simulations. However, STEM experiments reveal that the magnitude of the pseudomagnetic field due to local strain patterns is nearly uniform within a region with a characteristic radius on the order of 15 − 25 nm [18][19][20]26].…”

“…Experimentally, STEM measurements [18][19][20] reveal that when graphene is submitted to local strain patterns, the resulting pseudomagnetic fields possess a well defined compact support in the spatial domain. A number of attempts have been published in the literature to model such patterns by a gaussian distributed field, and the corresponding models for the associated Dirac single-particle eigenstates and energy eigenvalues can only be studied numerically [24].…”

“…As a model for a nanobubble, we shall assume that a circular region of radius a is submitted to a perpendicular uniform magnetic field (ê 3 B 0 ) and to mechanical strain as well. Typical experimental values for the characteristic diameter of graphene bubbles are a ∼ 15 − 25nm [18][19][20]26], while a graphene ribbon will have typical widths W ∼ 10µm . Therefore, under realistic experimental conditions a/W ≪ 1, and hence any influence of the edges of the ribbon over the carrier dynamics at the nanobubble becomes negligible.…”

“…Theoretical models to represent nanobubbles in graphene are mainly based on a gaussian approximation for the strain field, that leads to a non-uniform pseudo-magnetic field possessing a well defined compact support in the spatial domain [24,25]. On the other hand, experimental STEM measurements [18][19][20] are consistent with a nearly uniform pseudomagnetic field over a circular region with a radius commensurate to the size of the nanobubble [19] (15 -25 nm typically), or the width of a ridge [20]. Ab-initio calculations support these experimental findings as well [26].…”

“…Within the Dirac approximation, strain enters as a gauge field whose curl represents a pseudo-magnetic field that reverses sign at each Dirac point, thus breaking the valley symmetry [10][11][12][13][14][15][16][17]. Conductance experiments have shown the emergence of pseudo-relativistic Landau levels in the presence of strain solely, thus suggesting that the magnitude of the associated pseudo-magnetic fields can reach over 100 Tesla for a small nano-bubble [18,19] or ridge [20] in graphene. From the theoretical perspective, strain-induced gauge fields have been incorporated into extended Dirac Hamiltonians that involve the simultaneous description of both non-equivalent Dirac cones [10,14,16,17,21,22].…”