Enhanced performance across Otto, Carnot, and Stirling cycles revealed by flat-band thermodynamics

Magic-angle twisted bilayer graphene (MATBG) exhibits remarkable electronic properties under external magnetic fields, notably the emergence of flat Landau levels. In this study, we present a comprehensive analysis of MATBG's operational phase diagram under three distinct quantum thermodynamic cycles, i.e., the quantum Otto cycle (QOC), quantum Carnot cycle (QCC), and quantum Stirling cycle (QSC). Employing the continuum eight-band model, we evaluate the thermodynamic performance of MATBG across multiple operational modes---heat engine, refrigerator, cold pump, and Joule pump---and benchmark it against other graphene systems such as monolayer graphene, $\mathit{AB}$-Bernal stacked bilayer graphene, and nonmagic-angle twisted bilayer graphene. Our findings reveal that MATBG demonstrates superior heat engine performance in QSC, while achieving high efficiency albeit with reduced work output in QOC. Even though the performance of MATBG as a cold pump or refrigerator is modest in QOC and QSC, it shows notable improvement as a refrigerator in QCC. Additionally, we identify a highly reversible Joule pump mode in both QSC and QOC under strict adiabaticity, underscoring the unique thermodynamic behavior of MATBG.