Coherent control of wave-like phenomena via metamaterials is driving a technological revolution in fields ranging from electronics, photonics, to phononics.
Although temperature has been historically taken as the paradigmatic example of an incoherent field, undergoing diffusive as opposed to wave-like propagation, on short space and time scales Fourier law fails and the possibility for temperature wave propagation sets in .
Building on this rational we propose a new class of metamaterials allowing for coherent temperature control on the ultrafast time-scale. As a model example we propose and theoretically investigate the dispersion relation of a “Temperonic Crystal”, a periodicic structure made alternating two materials sustaining heat waves on short time-scales. For instance a Temperonic Crystal may act as a frequency filter for a temperature pulse triggered by an ultra-short laser pulse. The above concepts are then contextualized in the frame of Quantum Materials. The anisotropy inherent high temperatures superconductors makes them an ideal building block to engineer metamaterials encompassing coherent control capabilities of the wave-like nature of the temperature fields occurring on ultrafast time-scales [2,3]. The possibility of accessing these phenomena via ultra-fast time resolved optics is discussed.
 Tzou, “Macro- to Microscale Heat Transfer: the Lagging Behavior” (John Wiley & Sons, Inc., 2014)
 Gandolfi et al., in press on Physica Scripta
 Giannetti et al., Advances in Physics 65, 58-238 (2016)