We report the temperature-dependent optical conductivity and ARPES studies of the iron-based superconductor (SC) Sr$_{0.67}$Na$_{0.33}$Fe$_2$As$_2$ in the high-temperature tetragonal paramagnetic phase; below the structural and magnetic transitions at $T_{rm N}simeq$125 K in the orthorhombic spin-density-wave (SDW)-like phase, and $T_rsimeq$42 K in the reentrant tetragonal double-Q magnetic phase where both charge and SDW order exist; and below the SC transition at $T_csimeq$10 K. The free-carrier component in the optical conductivity is described by two Drude contributions; one strong and broad, the other weak and narrow. The broad Drude component decreases dramatically below $T_{rm N}$ and $T_r$, with much of its strength being transferred to a bound excitation in the mid-infrared, while the narrow Drude component shows no anomalies at either of the transitions, actually increasing in strength at low temperature while narrowing dramatically. The behavior of an infrared-active mode suggests zone-folding below $T_r$. Below $T_c$ the dramatic decrease in the low-frequency optical conductivity signals the formation of a SC energy gap. ARPES reveals hole-like bands at the center of the Brillouin zone (BZ), with both electron- and hole-like bands at the corners. Below $T_{rm N}$, the hole pockets at the center of the BZ decrease in size, consistent with the behavior of the broad Drude component; while below $T_r$ the electron-like bands shift and split, giving rise to a low-energy excitation in the optical conductivity at ~20 meV. The magnetic states, with resulting SDW and charge-SDW order, respectively, lead to a significant reconstruction of the Fermi surface that has profound implications for the transport originating from the electron and hole pockets, but appears to have relatively little impact on the SC in this material.
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