Thermoelectricity of Wigner crystal in a periodic potential

We study numerically the thermoelectricity of the classical Wigner crystal placed in a periodic potential and being in contact with a thermal bath modeled by the Langevin dynamics. At low temperatures the system has sliding and pinned phases with the Aubry transition between them. We show that in the Aubry pinned phase the dimensionless Seebeck coefficient can reach very high values of several hundreds. At the same time the charge and thermal conductivity of crystal drop significantly inside this phase. Still we find that the largest values of $ZT$ factor are reached in the Aubry phase and for the studied parameter range we obtain $ZT \leq 4.5$. We argue that this system can provide an optimal regime for reaching high $ZT$ factors and realistic modeling of thermoelecriticy. Possible experimental realizations of this model are discussed.