Temperature-dependent excitonic superfluid plasma frequency evolution in excitonic insulator, Ta$_2$NiSe$_5$

We investigate an excitonic insulate, Ta$_{2}$NiSe$_{5}$, using optical spectroscopy. Ta$_{2}$NiSe$_{5}$ has quasi-one dimensional chains along the $a$-axis. We have obtained anisotropic optical properties of a single crystal Ta$_{2}$NiSe$_{5}$ along the $a$- and $c$-axes. The measured $a$- and $c$-axis optical conductivities exhibit large anisotropic electronic and phononic properties. With regard to the $a$-axis optical conductivity, a sharp peak near 3050 cm$^{-1}$ at 9 K, with a well-defined optical gap ($\Delta^{EI} \simeq$ 1800 cm$^{-1}$) and a strong temperature-dependence, is observed. With an increase in temperature, this peak broadens and the optical energy gap closes around $\sim$325 K($T_c^{EI}$). The spectral weight redistribution with respect to the frequency and temperature indicates that the normalized optical energy gap ($\Delta^{EI}(T)/\Delta^{EI}(0)$) is $1-(T/T_c^{EI})^2$. The temperature-dependent superfluid plasma frequency of the excitonic condensation in Ta$_{2}$NiSe$_{5}$ has been determined from measured optical data.