  Low-temperature specific-heat study has been performed on the insulating
giant dielectric constant material CaCu3Ti4O12 and two related compounds,
Bi2/3Cu3Ti4O12 and La0.5Na0.5Cu3Ti4O12, from 0.6 to 10 K. From analyzing the
specific heat data at very low-temperature range, 0.6 to 1.5 K, and moderately
low-temperature range, 1.5 to 5 K, in addition to the expected Debye terms, we
noticed significant contributions originated from the linear and Einstein
terms, which we attributed as the manifestation of low-lying elementary
excitations due to lattice vibrations occurred at the grain boundaries and
induced by local defects. Together with the findings on electronic and
mechanical properties, a phenomenological model is proposed to explain the high
dielectric constant behaviors at both low and high frequency regions.
