  We study analytically and numerically the thermoelectric properties of cold
ions placed in an optical lattice. Our results show that the transition from
sliding to pinned phase takes place at a certain critical amplitude of lattice
potential being similar to the Aubry transition for the Frenkel-Kontorova
model. We show that this critical amplitude is proportional to the cube of ion
density that allows to perform experimental realization of this system at
moderate lattice amplitudes. We show that the Aubry phase is characterized by
the dimensionless Seebeck coefficient about 50 and the figure of merit being
around 8. We propose possible experimental investigations of such system with
cold ions and argue that the experiments with electrons on liquid helium
surface can also help to understand its unusual properties. The obtained
results represent also a challenge for modern methods of quantum chemistry and
material science.
