TY - JOUR

T1 - Linking interlayer twist angle to geometrical parameters of self-assembled folded graphene structures

AU - Rode, Johannes C.

AU - Zhai, Dawei

AU - Belke, Christopher

AU - Hong, Sung Ju

AU - Schmidt, Hennrik

AU - Sandler, Nancy

AU - Haug, Rolf J.

N1 - Funding information: The authors acknowledge financial support from the DFG within the priority program SPP 1459, the School for Contacts in Nanosystems, the ‘Fundamentals of Physics and Metrology’ initiative (JCR, CB, SJH, HS, and RJH), and NSF-DMR 1508325 (DZ and NS). This work was partially performed at the Aspen Center for Physics, which is supported by NSF grant PHY-1607611 (NS). JC Rode acknowledges support from the Hannover School for Nanotechnology. The authors thank Peter Behrens and Hadar Steinberg for helpful discussion.

PY - 2019/1

Y1 - 2019/1

N2 - Thin adhesive films can be removed from substrates, torn, and folded in distinct geometries under external driving forces. In two-dimensional materials, however, these processes can be self-driven as shown in previous studies on folded twisted bilayer graphene nanoribbons produced by spontaneous tearing and peeling from a substrate. Here, we use atomic force microscopy techniques to generate and characterize the geometrical structure of naturally self-grown folded nanoribbon structures. Measurements of nanoribbon width and interlayer separation reveal similar twist-angle dependences possibly caused by the anisotropy in the bilayer potential. In addition, analysis of the data shows an unexpected correlation between the height of the folded arc edge - parameterized by a radius R - , and the ribbon width, suggestive of a self-growth process driven by a variable cross-sectional shape. These observations are well described by an energy minimization model that includes the bilayer adhesion energy density as represented by a distance dependent Morse potential. We obtain an analytical expression for the radius R versus the ribbon width that predicts a renormalized bending rigidity and stands in good agreement with experimental observations. The newly found relation between these geometrical parameters suggests a mechanism for tailored growth of folded twisted bilayer graphene- a platform for many intriguing physics phenomena.

AB - Thin adhesive films can be removed from substrates, torn, and folded in distinct geometries under external driving forces. In two-dimensional materials, however, these processes can be self-driven as shown in previous studies on folded twisted bilayer graphene nanoribbons produced by spontaneous tearing and peeling from a substrate. Here, we use atomic force microscopy techniques to generate and characterize the geometrical structure of naturally self-grown folded nanoribbon structures. Measurements of nanoribbon width and interlayer separation reveal similar twist-angle dependences possibly caused by the anisotropy in the bilayer potential. In addition, analysis of the data shows an unexpected correlation between the height of the folded arc edge - parameterized by a radius R - , and the ribbon width, suggestive of a self-growth process driven by a variable cross-sectional shape. These observations are well described by an energy minimization model that includes the bilayer adhesion energy density as represented by a distance dependent Morse potential. We obtain an analytical expression for the radius R versus the ribbon width that predicts a renormalized bending rigidity and stands in good agreement with experimental observations. The newly found relation between these geometrical parameters suggests a mechanism for tailored growth of folded twisted bilayer graphene- a platform for many intriguing physics phenomena.

KW - graphene folds

KW - graphene ribbons

KW - twisted bilayer grapheme

UR - http://www.scopus.com/inward/record.url?scp=85059246162&partnerID=8YFLogxK

U2 - 10.1088/2053-1583/aaf1e7

DO - 10.1088/2053-1583/aaf1e7

M3 - Article

AN - SCOPUS:85059246162

VL - 6

JO - 2D Materials

JF - 2D Materials

SN - 2053-1583

IS - 1

M1 - 015021

ER -