The Hidden Order Gap and In-Gap Excitation Mode in URu$_2$Si$_2$ Revealed by Electronic Raman Scattering*

The heavy fermion compound URu$_2$Si$_2$ displays a phase transition into the so called ``hidden order'' state at $T_{HO}=17.5\,$K. Using polarized electronic Raman scattering, we show that the Raman response in the $A_{2g}$ symmetry channel ($D_{4h}$): (1)~at high temperatures can be described by a Drude-like continuum with the scattering rate decreasing from 46\,cm$^{-1}$ at 300\,K to 16\,cm$^{-1}$ at 70\,K; (2)~develops a low energy peak due to spectral weight transfer through Fano interference in the temperature range of 70-20\,K; (3)~below $T_{HO}$ develops a gap of about 55\,cm$^{-1}$ in the continuum, and a sharp in-gap mode centered at 14\,cm$^{-1}$. In addition, we show that the real part of the static Raman susceptibility in the $A_{2g}$ symmetry is proportional to the \textit{c}-axis static magnetic susceptibility above $T_{HO}$. The implication of these observations will be discussed in the talk.