Thermoelectric effects in semiconductor nanostructures
Ionel Tifrea, Department of Physics, California State University Fullerton, Fullerton, CA 92831, USA Low-dimensional systems, and in particular nanoscale systems based on quantum dots or single-molecule junctions coupled to thermal reservoirs at different temperatures and chemical potentials, have recently emerged as ideal configurations for enhanced thermoelectric transport properties, providing interesting solutions for efficient energy-harvesting devices [1,2,3]. I will present a brief review of recent advances in theoretical and experimental studies of thermoelectricity in nanostructured materials. In the case of semiconductor nanoscale devices, I will provide theoretical evidence that the general thermoelectric response must be considered beyond the standard linear-response approximation. I will present general theoretical expressions for the charge and heat currents, enabling us to calculate the power output of a nanoscale system in the nonlinear regime. The formulae for the charge and heat currents are analytical and can be expressed in terms of dimensionless kinetic transport coefficients [4]. As an example, I will 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 shows that terms beyond the standard linear approximation must be considered when investigating the thermoelectric response of a nanoscale device. These results enable optimization of the system's thermoelectric transport efficiency in the nonlinear regime. [1] L. D. Hicks and M. S. Dresselhaus, "Effect of quantum-well structures on the thermoelectric figure of merit," Phys. Rev. B 47, 12727–12731 (1993). [2] Y. Dubi and M. Di Ventra, "Colloquium: Heat flow and thermoelectricity in atomic and molecular junctions," Rev. Mod. Phys. 83, 131–155 (2011). [3] D. Sanchez and H. Linke, "Focus on thermoelectric effects in nanostructures," New Journal of Physics 16,110201 (2014). [4] R. J. Hartig, I. Grosu, and I. Tifrea, "Thermoelectric response of nanoscale devices in the nonlinear regime," Physica E 171, 1162236 (2025).