Selective excitation of collective modes in multiband superconductor MgB2

Recent developments in nonequilibrium and nonlinear terahertz (THz) spectroscopies have significantly advanced our understanding of collective excitations in superconductors. However, there is still debate surrounding the identification of Higgs or Leggett modes, as well as BCS charge fluctuations, in the well-known two-band superconductor MgB$_2$. Here, we utilized both multi-cycle and single-cycle THz pump-broadband THz probe techniques to investigate the THz nonlinear response of MgB$_2$. Through multicycle THz pump-THz probe experiments on MgB$_2$, we observed distinct nonlinear signals at both the fundamental frequency ($\omega$) and the second harmonic frequency (2$\omega$) of the pump pulses, which exhibited resonant enhancement at temperatures where their frequencies respectively match 2$\Delta_{\pi}(T)$. They are mainly attributed to the $\pi$-band Higgs mode. By adjusting the THz pump pulse to a single-cycle waveform that satisfies non-adiabatic excitation criteria, we observed an over-damped oscillation corresponding to the Leggett mode. Our findings contribute to solving the ongoing debates and demonstrate the selective excitation of collective modes in multiband superconductors, offering new insights into the interaction between Higgs and Leggett modes.