  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.
