  Lead halide perovskites such as methylammonium lead triiodide (MAPI) have
outstanding optical and electronic properties for photovoltaic applications,
yet a full understanding of how this solution processable material works so
well is currently missing. Previous research has revealed that MAPI possesses
multiple forms of static disorder regardless of preparation method, which is
surprising in light of its excellent performance. Using high energy resolution
inelastic X-ray (HERIX) scattering, we measure phonon dispersions in MAPI and
find direct evidence for another form of disorder in single crystals: large
amplitude anharmonic zone-edge rotational instabilities of the PbI_6 octahedra
that persist to room temperature and above, left over from structural phase
transitions that take place tens to hundreds of degrees below. Phonon
calculations show that the orientations of the methylammonium couple strongly
and cooperatively to these modes. The result is a non-centrosymmetric,
instantaneous local structure, which we observe in atomic pair distribution
function (PDF) measurements. This local symmetry breaking is unobservable by
Bragg diffraction, but can explain key material properties such as the
structural phase sequence, ultra low thermal transport, and large minority
charge carrier lifetimes despite moderate carrier mobility.
