@istria- While solid state reactions are not actually used by your solid state flash drives, solid state reactions are used to make most capacitor material in those drives and other electronics. Solid-state reactions are also used in a large number of power storage technologies. Lithium-ion batteries use solid-state reactions to store and transfer energy. Large renewable energy systems may also use solid-state reactions for molten thermal storage (i.e., liquid sodium energy storage). These are just a few of the roles solid-state reactions play in our everyday lives. They are very important roles that actually allow us to be as technologically advanced as we are.
As for who would study solid-state reactions, it could be both chemists and physicists. I have a friend who is a chemist and is in graduate school for chemical engineering. He is working on research to develop solid-state batteries and capacitors for use in efficient energy storage. Solid-state reactions are actually at the cusp of chemistry and physics, so either type of scientists may study these reactions.