Electronic properties of topological rough nanowires for thermoelectrical performance

We study the electronic states in topological nanowires of narrow-gap semiconductors, such as PbTe or SnTe, with rough surfaces, using a continuous two-band model. We calculate the subband structure and identify topological conducting states located at the surface of the nanowire. In addition, a novel approach to study a nanowire with rough surface demonstrates that the topological surface states are mostly confined in the widest areas of the nanowire. This effect leads to a flattening of the subbands, thus raising the effective mass of carriers. Finally, we analyze the thermoelectric properties of the topological nanowires. The reduction of the radius causes a noticeable enhancement of the thermoelectric efficiency due surface phonon scattering, as expected. However, we also observe that the appearance of topological surface states can play a detrimental role, reducing the thermoelectric efficiency. We conclude that, in addition to nanostructuring, the modulation of the radius of the nanowires, which partially suppress the conduction of the surface states, may be a potential strategy to improve the thermoelectric response of narrow-gap semiconductor nanowires.