Thermoelectric response of nanoscale devices in the nonlinear regime

We consider the thermoelectric transport through a two-terminal nanoscale device whose terminals are subject to a temperature ($\Delta T=T_L-T_R$) and voltage difference ($\Delta \mu ={\mu }_L-{\mu }_R;\Delta \mu =-e\Delta V$). We present general expressions for the charge and heat currents that allow us to calculate the power output in the nonlinear regime. The formulae for the charge and heat currents are analytical, and can be expressed using dimensionless kinetic transport coefficients $K_n^p(\mu ,T)$. As an example, we consider the cases of Breit–Wigner, antiresonance, and Fano line-shape electronic transmission functions. In these cases, the dimensionless kinetic coefficients can be calculated in terms of Hurwitz zeta functions and Bernoulli numbers. Our analysis proves that terms beyond the standard linear approximation have to be considered when one investigates the thermoelectric response of a nanoscale device. These results allow for the optimization of the system’s thermoelectric transport efficiency in the nonlinear regime.