Fundamental aspects of Aharonov-Bohm quantum machines: thermoelectric heat engines and diodes.

The study of heat-to-work conversion has garnered significant attention in recent years, underscoring the potential of nanoscale systems to achieve energy conversion in steady-state devices without the involvement of macroscopic moving parts. The operation of these devices relies on the steady-state flows of quantum particles, including electrons, photons, and phonons. This review explores the theoretical frameworks that govern these steady-state flows within various mesoscopic or nanoscale devices, such as thermoelectric heat engines, with a particular focus on quantum dot (QD) Aharonov-Bohm (AB) interferometric configurations. Quantum interference effects, in particular, show great promise for enhancing the thermoelectric transport properties of these quantum devices. By enabling precise control over energy levels and transport pathways, such effects can significantly improve heat-to-work conversion efficiency. Driven QD AB networks provide an ideal platform for studying these engines due to their ability to maintain quantum coherence and offer precise experimental control. Unlike bulk systems, nanoscale systems such as QDs exhibit unique quantum interference phenomena, including sharp features in transmission spectra and Fano resonances. This review highlights the distinction between optimization methods that produce boxcar functions and coherent control methods that yield complex interference patterns. It demonstrates that the effective design of thermoelectric heat engines requires the careful tailoring of quantum interference and magnetic field-induced effects to enhance performance. Additionally, it addresses fundamental questions regarding the bounds of these thermoelectric machines, with particular emphasis on how magnetic fields can alter the limits of power or efficiency and the interplay between quantum transport theories and the laws of thermodynamics. Thermoelectric devices with broken time-reversal symmetry provide valuable insights into directional dependencies and asymmetries in quantum transport. This review offers a comprehensive overview of past and present research on quantum thermoelectric heat engines utilizing the AB effect. Special attention is given to three-terminal AB heat engines, where broken time-reversal symmetry can induce a coherent diode effect. Furthermore, the review examines bounds on power and efficiency in systems with broken time-reversal symmetry. We conclude by presenting open questions, summarizing key findings, and offering insights into future directions in the field of quantum thermoelectric heat engines.