Giant dielectric constant in CaCu$_3$Ti$_4$O$_{12}$-MgB$_2$ composites near the percolation threshold

We have investigated the enhancement of the dielectric constant K in CaCu$_{3}$Ti$_{4}$O$_{12}$ (CCTO)-MgB$_{2}$ composite near the percolation threshold. To optimize the dielectric properties of pure CCTO we have sintered the samples at variuos temperatures. We will present the results of the measurements of $K$ in a broad frequency for pure CCTO for the samples sintered at 1100$^{\circ}$C and 500$^{\circ}$C. Commercially available MgB$_{2}$ powder was mixed with different weight fractions of CCTO and the pressure of 1GPa was applied to form composite pellets. Near the percolation threshold P$_{\mathrm{C}}$, CCTO/MgB$_{2}$ composite system exhibit a dramatic increase of the dielectric constant K by several orders of magnitude, compared to pure CCTO. We will also discuss the magnetic field dependence of the capacitance of CCTO composite powders.