Formation of the density wave energy gap in Na$_2$Ti$_2$Sb$_2$O: an optical spectroscopy study

We performed optical spectroscopy measurement on single crystals of Na$_2$Ti$_2$Sb$_2$O, which is the parent compound for the newly discovered Ti-based superconductors. The study reveals significant spectral change across the phase transition at 114 K and formation of a density-wave type energy gap. The opening of the gap removes most part of the free carrier spectral weight and causes a dramatic reduction of the carrier scattering rate. The ratio of 2$\Delta/k_BT_s\approx$14 is considerably larger than the mean-field value based on the weak-coupling BCS theory. The study also reveals a weak correlation effect in the titanium oxypnictides.