  To investigate the role of long-range van der Waals interactions in static
friction, we derive an analytic expression for the coefficient of static
friction $\mu_s$ between two thin layers of polarizable materials under zero
load. For simplicity, we model the surface roughness with sinusoidal
corrugations and calculate the interaction energy perturbatively up to the
second order in corrugation amplitude. The ratio of corresponding maximum
lateral Casimir force to normal Casimir force is defined as the coefficient of
static friction, which is found to be independent of the dielectric properties
of the materials. It depends on the geometric properties, like interlayer
separation, corrugation amplitude, and wavelength of the corrugation. As a
proof of concept, our predicted values of $\mu_s$ for the 2D van der Waals
materials graphene and hexagonal boron nitride are in reasonable agreement with
previously reported values in the literature. This simplistic model could be
generalized by incorporating other forces, such as the frequency-dependent
contributions of van der Waals interactions and electrostatic interactions.
