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Optical study of hybridization and hidden order in URu$_2$Si$_2$

We summarize existing optical data of URu$_2$Si$_2$ to clarify the nature of the hidden order transition in this heavy fermion metal. Hybridization develops between 50 K and 17.5 K, and a coherent Drude peak emerges which mirrors the changes in the dc resistivity. The Drude weight indicates that there is little change in the effective mass of these carriers in this temperature range. In addition, there is a flat background conductivity that develops a partial hybridization gap at 10 meV as the temperature is lowered, shifting spectral weight to higher frequencies above 300 meV. Below 30 K the carriers become increasingly coherent and Fermi-liquid-like as the hidden order transition is approached. The hidden order state in URu$_2$Si$_2$ is characterized by multiple anisotropic gaps. The gap parameter $Δ_a=3.2$ meV in the {\it ab}-plane. In the {\it c}-direction, there are two distinct gaps with magnitudes of $Δ_{c1}=2.7$ meV and $Δ_{c2}=1.8$ meV. These observations are in good agreement with other spectroscopic measurements. Overall, the spectrum can be fit by a Dynes-type density of states model to extract values of the hidden order gap. The transfer of spectral weight strongly resembles what one sees in density wave transitions.