  Recent experiments have shown surprisingly large thermal time constants in
suspended graphene ranging from 10 to 100 ns in drums with a diameter ranging
from 2 to 7 microns. The large time constants and their scaling with diameter
points towards a thermal resistance at the edge of the drum. However, an
explanation of the microscopic origin of this resistance is lacking. Here, we
show how phonon scattering at a kink in the graphene, e.g. formed by sidewall
adhesion at the edge of the suspended membrane, can cause a large thermal time
constant. This kink strongly limits the fraction of flexural phonons that cross
the suspended graphene edge, which causes a thermal interface resistance at its
boundary. Our model predicts thermal time constants that are of the same order
of magnitude as experimental data, and shows a similar dependence on the
circumference. Furthermore, the model predicts the relative in-plane and
out-of-plane phonon contributions to graphene's thermal expansion force, in
agreement with experiments. We thus show, that in contrast to conventional
thermal (Kapitza) resistance which occurs between two different materials, in
2D materials another type of thermal interface resistance can be geometrically
induced in a single material.
