We have performed terahertz time-domain spectroscopy of carrier-doped nanoporous crystal $12\mathrm{Ca}\mathrm{O}\bullet 7{\mathrm{Al}}_2{\mathrm{O}}_3$ showing the Mott variable range hopping at room temperature. The real part of the dielectric constant clearly demonstrates the nature of localized carriers. The frequency dependence of both the real and imaginary parts of the dielectric constant can be simply explained by assuming two contributions: a dielectric response by the parent compound with no carriers and an ac hopping conduction with the Jonscher law generally reported up to GHz range. The possible obedience to the Jonscher law in the THz range suggests a relaxation time of the hopping carriers much faster than $1\mathrm{ps}$ in the carrier-doped $12\mathrm{Ca}\mathrm{O}\bullet 7{\mathrm{Al}}_2{\mathrm{O}}_3$.

• Received 21 May 2004

DOI:https://doi.org/10.1103/PhysRevB.70.193104