The temporal effects associated with surface plasmon polaritons (SPP) in a slab of conductive quantum material (metal, graphene, or semiconductor) are described as a quantum plasma. Exchange potentials associated with quantum degeneracy are included. We derive a new dispersion relation of SPP modes in a quantum plasma slab with finite size, which reduces to the previously known cases of a single plasma boundary and of a two-dimensional slab in the appropriate limits. A new SPP instability regime due to exchange quantum effects is demonstrated. The phenomenology of time refraction and time reflection is extended to SPP, and the frequency shifts and amplitude transformations due to a time boundary are derived. Finite time boundary effects and arbitrary temporal changes of the medium are also considered.
Mendonça et al. (2026) studied this question.