Collective modes in the hot spot model of cuprates

We study the collective modes of the possible order parameters of cuprate high-temperature superconductors. Observing and analyzing these modes provide insights into the nature of the ordered state. Using the hot spot model of cuprates, we explore the amplitude oscillations of both charge density wave (CDW) and superconducting states. Especially interesting is the region, in which CDW and superconductivity coexist, and in which the two amplitude oscillations become mixed in a single mode with energy inside the single-particle gap. We compare these results with the recent data extracted from reflectivity measurements.