title: Graphene kirigami.
abstract: For centuries, practitioners of origami ('ori', fold; 'kami', paper) and kirigami ('kiru', cut) have fashioned sheets of paper into beautiful and complex three-dimensional structures. Both techniques are scalable, and scientists and engineers are adapting them to different two-dimensional starting materials to create structures from the macro- to the microscale. Here we show that graphene is well suited for kirigami, allowing us to build robust microscale structures with tunable mechanical properties. The material parameter crucial for kirigami is the Föppl-von Kármán number γ: an indication of the ratio between in-plane stiffness and out-of-plane bending stiffness, with high numbers corresponding to membranes that more easily bend and crumple than they stretch and shear. To determine γ, we measure the bending stiffness of graphene monolayers that are 10-100 micrometres in size and obtain a value that is thousands of times higher than the predicted atomic-scale bending stiffness. Interferometric imaging attributes this finding to ripples in the membrane that stiffen the graphene sheets considerably, to the extent that γ is comparable to that of a standard piece of paper. We may therefore apply ideas from kirigami to graphene sheets to build mechanical metamaterials such as stretchable electrodes, springs, and hinges. These results establish graphene kirigami as a simple yet powerful and customizable approach for fashioning one-atom-thick graphene sheets into resilient and movable parts with microscale dimensions.
authors.affiliation: Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA.
authors.forename: Melina K
authors.initials: MK
authors.lastname: Blees
authors.affiliation: School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA.
authors.forename: Arthur W
authors.initials: AW
authors.lastname: Barnard
authors.affiliation: Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA.
authors.forename: Peter A
authors.initials: PA
authors.lastname: Rose
authors.affiliation: Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA.
authors.forename: Samantha P
authors.initials: SP
authors.lastname: Roberts
authors.affiliation: Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA.
authors.forename: Kathryn L
authors.initials: KL
authors.lastname: McGill
authors.affiliation: School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA.
authors.forename: Pinshane Y
authors.initials: PY
authors.lastname: Huang
authors.affiliation: School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA.
authors.forename: Alexander R
authors.initials: AR
authors.lastname: Ruyack
authors.affiliation: Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA.
authors.forename: Joshua W
authors.initials: JW
authors.lastname: Kevek
authors.affiliation: Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA.
authors.forename: Bryce
authors.initials: B
authors.lastname: Kobrin
authors.affiliation: 1] School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA [2] Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, New York 14853, USA.
authors.forename: David A
authors.initials: DA
authors.lastname: Muller
authors.affiliation: 1] Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA [2] Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, New York 14853, USA.
authors.forename: Paul L
authors.initials: PL
authors.lastname: McEuen