  Thin film of superfluid $^3$He on a corrugated graphene substrate represents
topological matter with a smooth disorder. It is possible that the atomically
smooth disorder produced by the corrugated graphene does not destroy the
superfluidity even in a very thin film, where the system can be considered as
quasi two-dimensional topological material. This will allow us to study the
effect of disorder on different classes of the $2+1$ topological materials: the
chiral $^3$He-A with intrinsic quantum Hall effect and the time reversal
invariant planar phase with intrinsic spin quantum Hall effect. In the limit of
smooth disorder, the system can be considered as a Chern mosaic -- a collection
of domains with different values of Chern numbers. In this limit, the
quantization of the Hall conductance is determined by the percolated domain,
while the density of the fermionic states is determined by the edge modes on
the boundaries of the finite domains. This system can be useful for the general
consideration of disorder in the topological matter.

Strongly Correlated Electrons;High Energy Physics - Phenomenology