  In many high temperature superconductors, small orthorhombic distortions of
the lattice structure result in surprisingly large symmetry breaking of the
electronic states and macroscopic properties, an effect often referred to as
nematicity. To directly study the impact of symmetry-breaking lattice
distortions on the electronic states, using low-temperature scanning tunnelling
microscopy we image at the atomic scale the influence of strain-tuned lattice
distortions on the correlated electronic states in the iron-based
superconductor LiFeAs, a material which in its ground state is tetragonal, with
four-fold ($C_4$) symmetry. Our experiments uncover a new strain-stabilised
modulated phase which exhibits a smectic order in LiFeAs, an electronic state
which not only breaks rotational symmetry but also reduces translational
symmetry. We follow the evolution of the superconducting gap from the
unstrained material with $C_4$ symmetry through the new nematic phase with
two-fold ($C_2$) symmetry and charge-density-wave order to a state where
superconductivity is completely suppressed.
