  Two-dimensional hybrid perovskites are currently in the spotlight of
condensed matter and nanotechnology research due to their intriguing
optoelectronic and vibrational properties with emerging potential for
light-harvesting and -emitting applications. While it is known that these
natural quantum wells host tightly bound excitons, the mobilities of these
fundamental optical excitations at the heart of the optoelectronic applications
are still largely unexplored. Here, we directly monitor the diffusion of
excitons through ultrafast emission microscopy from liquid helium to room
temperature in hBN-encapsulated two-dimensional hybrid perovskites. We find
very fast diffusion with characteristic hallmarks of free exciton propagation
for all temperatures above 50 K. In the cryogenic regime we observe nonlinear,
anomalous behavior with an exceptionally rapid expansion of the exciton cloud
followed by a very slow and even negative effective diffusion. We discuss our
findings in view of efficient exciton-phonon coupling, highlighting
two-dimensional hybrids as promising platforms for many-body physics research
and optoelectronic applications on the nanoscale.
