  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. Furthermore, there exists an
optimal band gap for maximizing the 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,
which is similar to that for bulk semiconductors, indicates the importance of
having narrow gaps to achieve the best thermoelectrics in 2D systems. Larger
maximum ZTs can also be obtained by suppressing the lattice thermal
conductivity. In the most ideal case where the lattice thermal conductivity is
zero (leaving the electron thermal conductivity alone), the maximum ZT in the
gapped 2D Dirac material is many times ZT of commercial thermoelectric
materials.
