Fundamental aspects of Aharonov-Bohm quantum machines: Thermoelectric heatengines and diodes

Abstract The study of heat-to-work conversion has gained considerable attention in recent years, highlighting
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 is predicated on the
steady-state flows of quantum particles, including electrons, photons, and phonons. This review
examines the theoretical frameworks governing these steady-state flows within various mesoscopic
or nanoscale devices, such as thermoelectric heat engines, particularly in the context of quantum dot
Aharonov-Bohm interferometric configurations. Naturally, quantum interference effects hold great
promise for enhancing the thermoelectric transport properties of these quantum devices by allowing
more precise control over energy levels and transport pathways, thus improving heat-to-work conversion.
Driven quantum dot Aharonov-Bohm networks offer an ideal platform for studying these
engines, thanks to their ability to maintain quantum coherence and provide precise experimental
control. Unlike bulk systems, nanoscale systems such as quantum dots reveal distinct 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 result in complex interference patterns. This review reveals that the
effective design of thermoelectric heat engines requires careful tailoring of quantum interference and
the magnetic field-induced effects to enhance performance. In addition, We focus on the fundamental
questions about the bounds of these thermoelectric machines. Particular emphasis is given to how
magnetic fields can change the bounds of power or efficiency and the relationship between quantum
theories of transport and the laws of thermodynamics. These machines with broken time-reversal
symmetry provides insights into directional dependencies and asymmetries in quantum transport.
We offer a thorough overview of past and current research on quantum thermoelectric heat engines
using the Aharonov-Bohm effect and present a detailed review of three-terminal Aharonov-Bohm
heat engines, where broken time-reversal symmetry can induce a coherent diode effect. Our review
also covers bounds on power and efficiency in systems with broken time-reversal symmetry. We
close the review by presenting open questions, summaries, and conclusions.