Optimal band gap for improved thermoelectric performance of two-dimensional Dirac materials

Abstract

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 the cancelation effect from electron-hole contributions to the transport quantities. Opening the bandgap lifts this cancelation effect. Furthermore, there exists an optimal bandgap for maximizing figure of merit (ZT) in the gapped 2D Dirac material. The optimal bandgap 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 ZTs 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 the ZT of commercial thermoelectric materials.