  In a material prone to a nematic instability, anisotropic strain in principle
provides a preferred symmetry-breaking direction for the electronic nematic
state to follow. This is consistent with experimental observations, where
electronic nematicity and structural anisotropy typically appear hand-in-hand.
In this work, we discover that electronic nematicity can be locally decoupled
from the underlying structural anisotropy in strain-engineered iron-selenide
(FeSe) thin films. We use heteroepitaxial molecular beam epitaxy to grow FeSe
with a nanoscale network of modulations that give rise to spatially varying
strain. We map local anisotropic strain by analyzing scanning tunneling
microscopy topographs, and visualize electronic nematic domains from
concomitant spectroscopic maps. While the domains form so that the energy of
nemato-elastic coupling is minimized, we observe distinct regions where
electronic nematic ordering fails to flip direction, even though the underlying
structural anisotropy is locally reversed. The findings point towards a
nanometer-scale stiffness of the nematic order parameter.
