Enhanced thermoelectricity in nanowires with inhomogeneous helical states

Semiconductor nanowires (NWs) with strong Rashba spin-orbit coupling (RSOC), when exposed to a suitably applied Zeeman field, exhibit one-dimensional helical channels with a spin orientation locked to the propagation direction within the magnetic energy gap. Here, by adopting a scattering-matrix approach applied to a tight-binding model of the NW, we demonstrate that the thermoelectric (TE) properties can be widely controlled by tuning the misalignment angle <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>ϕ</a:mi> </a:math> between the spin-orbit directions of two NW segments. In particular, when the RSOC vectors are antiparallel (Dirac-paradox configuration), we predict a significant violation of the Wiedemann-Franz law, and a strong enhancement of the Seebeck coefficient and the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>Z</b:mi> <b:mi>T</b:mi> </b:mrow> </b:math> figure of merit. We also show that the Zeeman gap determines the optimal energy window for doping and temperatures. These results suggest that controlling the spin-orbit field direction, which can be achieved with suitably applied wrap gates, is a promising alternative for tuning and optimizing the TE response in quantum-coherent semiconducting NW devices.