Coherent control of thermoelectric performance via engineered transmission functions in multi-dot Aharonov-Bohm heat engine

We theoretically investigate strategies for harnessing quantum interference to optimize the figure of merit $ZT$, power output, and thermodynamic efficiency in multi-quantum-dot Aharonov-Bohm (AB) thermoelectric heat engines. Using the non-equilibrium Green function formalism, we show that interference effects such as Fano-type asymmetries, Dicke-like superradiant and subradiant modes, and multi-peaked transmission spectra can be tailored through device geometry, magnetic flux, and dot-lead coupling to produce hybrid transmission profiles that combine Lorentzian, boxcar, and Fano lineshapes. Such engineered profiles enable configurations that balance the high efficiency of sharp Lorentzian resonances with the high power output of boxcar-like spectra, yielding near-optimal power-efficiency trade-offs. For symmetric quantum-dot arrays in square, pentagonal, and hexagonal configurations, we identify an optimal regime, $t/γ\approx 2$, where the interdot tunneling amplitude $t$ and the dot-lead coupling $γ$ yield the best balance of power and efficiency. A hexagonal six-dot configuration achieves $ZT \sim 30$ at dilution temperatures, while the four-dot geometry reaches about $76\%$ of Carnot efficiency with output power $4.74$ fW. We also find a direct correspondence between the high-$ZT$ regime and maximal violation of the Wiedemann-Franz law. Introducing source-drain coupling asymmetry further enhances both efficiency and power. A scaling analysis reveals that efficiency systematically increases with the number of quantum dots, whereas power output is maximized at intermediate system sizes. These findings establish coherent control in multi-dot nanostructures as a promising pathway toward high-performance quantum thermoelectric heat engines for ultralow-power electronics applications.