Amplitude mode in a multi-gap superconductor MgB$_2$ investigated by terahertz two-dimensional coherent spectroscopy

Abstract

We have investigated the terahertz (THz) nonlinear response of the multigap superconductor MgB$_2$, using THz two-dimensional coherent spectroscopy (THz 2DCS). With broadband THz drive fields, we identified a nonlinear response at twice the lower superconducting gap energy $2\Delta_{\pi}$ at the lowest temperatures. Using narrow-band THz driving pulses, we observed first (FH) and third harmonic responses. The FH intensity shows a monotonic increase with decreasing temperature when properly normalized by the driving field strength. This is distinct from the single-gap superconductor NbN, where the FH signal exhibited a resonant enhancement at temperatures when twice the gap energy $2\Delta$ was resonant with the driving photon energy, which was interpreted to originate from the superconducting amplitude mode. Our results in MgB$_2$ are consistent with a well-defined amplitude mode only at the lowest temperatures and indicate strong damping as temperature increases. This likely indicates the importance of interband coupling in MgB$_2$ and its influence on the nature of the amplitude mode and its damping.