  We have performed terahertz time-domain spectroscopy of carrier-doped
nanoporous crystal 12CaO7Al2O3 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 1ps in the
carrier-doped 12CaO7Al2O3.
