Experimental Studies of the Giant Dielectric Constant Materials CaCu$_{3}$Ti$_{4}$O$_{12}$

We present results of four different experimental studies, namely (1) scanning electron microscopy, (2) dielectric measurements, (3) \textit{in-situ} high-pressure and X-ray and (4) low-temperature specific heat, on the insulating giant dielectric constant material CaCu$_{3}$Ti$_{4}$O$_{12}$. From analyzing the results, we first deduce the electronic and mechanical properties of the samples and conclude that the mechanism for high-dielectric constant phenomena is mostly extrinsic. In addition we propose a phenomenological model to explain the high dielectric constant behaviors at both low and high frequency regions.