Thermoelectric properties of two-dimensional (2D) Dirac materials are calculated within linearized Boltzmann transport theory and relaxation time approximation. We find that the gapless 2D Dirac material exhibits poorer thermoelectric performance than the gapped one. This fact arises due to cancelation effect from electron-hole contributions to the transport quantities. Opening the band gap lifts this cancellation effect. Furthermore, there exists an optimal band gap for maximizing figure of merit (ZT ) in the gapped 2D Dirac material. The optimal band gap ranges from 6kBT to 18kBT , where kB is the Boltzmann constant and T is the operating temperature in kelvin. This result indicates the importance of having narrow gaps to achieve the best thermoelectrics in 2D systems. Larger maximum ZT s can also be obtained by suppressing the lattice thermal conductivity. In the most ideal case where the lattice thermal conductivity is very small, the maximum ZT in the gapped 2D Dirac material can be many times ZT of commercial thermoelectric materials. arXiv:1901.03999v2 [cond-mat.mes-hall]

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Materials with Mexican-hat electronic energy dispersions emerging from heterostructures, substrate effects, or spin-orbit couplings are believed to exhibit excellent thermoelectric properties due to its van Hove singularity of density of states in two-dimension. However, within a constant relaxation time approximation, we disprove this belief and we find that the singularity effect is cancelled down by the group velocity contribution in the thermoelectric transport distribution. Nevertheless, the band parameters can still be optimised to reach thermoelectric figure of merit larger than 2 in a wide bandwidth, thus keeping the potential of materials with Mexican-hat bands for thermoelectric applications.

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