Collective modes in superconductors and their coupling to near field THz probes*

We theoretically investigate methods to observe the phase (Anderson-Bogoliubov-Goldstone), amplitude (Higgs) and Carlson-Goldman modes using THz near field techniques. In a quasi-two-dimensional superconductor, we show that the Carlson-Goldman mode appears in the near field reflection coefficient as a weak feature in the sub-Terahertz frequency range. In a system of two superconductor layers separated by nanometer scale, the gapless phase mode reappears due to the mutual screening between the layers, as the antisymmetric plasmon mode of the system. This mode leads to a well defined resonance peak in the near-field THz response. Close to zero temperature, its speed contains the information of the original Goldstone mode. The amplitude mode could appear in the near field third harmonic generation for particle-hole asymmetric superconductors and we also discuss its observability in the linear response.