  The semimetal MoTe$_2$ is studied by spin- and angle- resolved photoemission
spectroscopy to probe the detailed electronic structure underlying its broad
range of response behavior. A novel spin-texture is uncovered in the bulk Fermi
surface of the non-centrosymmetric structural phase that is consistent with
first-principles calculations. The spin-texture is three-dimensional, both in
terms of momentum dependence and spin-orientation, and is not completely
suppressed above the centrosymmetry-breaking transition temperature. Two types
of surface Fermi arc are found to persist well above the transition
temperature. The appearance of a large Fermi arc depends strongly on thermal
history, and the electron quasiparticle lifetimes are greatly enhanced in the
initial cooling. The results indicate that polar instability with strong
electron-lattice interactions exists near the surface when the bulk is largely
in a centrosymmetric phase.
