  Full counting statistics of electron transport is a powerful diagnostic tool
for probing the nature of quantum transport beyond what is obtainable from the
average current or conductance measurement alone. In particular, the
non-Markovian dynamics of quantum dot molecule plays an important role in the
nonequilibrium electron tunneling processes. It is thus necessary to understand
the non-Markovian full counting statistics in a quantum dot molecule. Here we
study the non-Markovian full counting statistics in two typical quantum dot
molecules, namely, serially coupled and side-coupled double quantum dots with
high quantum coherence in a certain parameter regime. We demonstrate that the
non-Markovian effect manifests itself through the quantum coherence of the
quantum dot molecule system, and has a significant impact on the full counting
statistics in the high quantum-coherent quantum dot molecule system, which
depends on the coupling of the quantum dot molecule system with the source and
drain electrodes. The results indicated that the influence of the non-Markovian
effect on the full counting statistics of electron transport, which should be
considered in a high quantum-coherent quantum dot molecule system, can provide
a better understanding of electron transport through quantum dot molecules.
