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Thermoelectrics properties of two-dimensional materials with combination of linear and nonlinear band structures

We investigate thermoelectric (TE) properties of two-dimensional materials possessing two Dirac bands (a Dirac band) and a nonlinear band within the three-(two-)band model using linearized Boltzmann transport theory and relaxation time approximation. In the three-band model, we find that combinations of Dirac bands with a heavy nonlinear band, either a parabolic or a pudding-mold band, does not give much difference in their TE performance. The apparent difference only occurs in the position of the nonlinear band that leads to the maximum figure of merit ($ZT$). The optimum $ZT$ of the three-band model consisting of a nonlinear band is found when the nonlinear band intersects the Dirac bands near the Fermi level. By removing the linear conduction band, or, in other words, transforming the three-band model to the two-band model, we find better TE performance in the two-band model than in the three-band model, i.e., in terms of higher $ZT$ values