Small polaron behavior in a two dimensional honeycomb net is studied by applying the strong coupling perturbative method to the Holstein molecular crystal model. We find that small optical polarons can be mobile also if the electrons are strongly coupled to the lattice. Before the polarons localize and become very heavy, there is infact a window of e-ph couplings in which the polarons are small and have masses of order ≃ 5−50 times the bare band mass according to the value of the adiabaticity parameter. The 2D honeycomb net favors the mobility of small optical polarons in comparison with the square lattice
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