Flat-band thermodynamics reveals enhanced performance across Otto, Carnot, and Stirling cycles

TL;DR

The paper investigates how magic-angle twisted bilayer graphene (MATBG) behaves as a quantum thermal machine across three cycles—Quantum Otto, Carnot, and Stirling—using a continuum eight-band model to capture flat-band effects and Landau-level structure. MATBG consistently exhibits superior heat-engine performance in the Stirling cycle, while achieving high efficiency with reduced work in the Otto cycle; it also shows notable refrigeration and Joule-pump features, especially under adiabatic constraints, and outperforms other graphene systems in select regimes. The study reveals that flat-band physics and tunable twist angles profoundly shape cycle performance, enabling high cooling power at Carnot limits and revealing unique reversible operation modes such as Joule pumping in MATBG. These insights position MATBG and related moiré systems as versatile platforms for quantum thermodynamics, with potential applications in nanoscale energy harvesting and low-temperature cooling, and motivate exploration of magic-angle multilayer graphene variants. Overall, the work demonstrates how engineered band structure and magnetic-field control can optimize quantum thermal machines in strongly correlated 2D materials.

Abstract

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., 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, AB-Bernal stacked bilayer graphene, and non-magic-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.

Figures (22)

• Figure 1: Renormalized Fermi velocity vs twist angle $\theta$, exact 8-band Hamiltonian results (solid red line) with the approximated 2-band model (dashed blue line). The normalized velocity tends to zero in both cases at the magic-angle ($\theta=1.05^o$)
• Figure 2: Operational regimes in any quantum thermodynamic cycle. The heat engine is present in the first quadrant, the refrigerator in the third quadrant, and the cold pump in the fourth quadrant. The Joule pump can appear in the third or fourth quadrant, depending on the relative magnitudes of heat exchanges. Any other heat and work relation violates the first or second law of thermodynamics (see, Appendix A).
• Figure 3: (a) Entropy–temperature (S–T) and (b) entropy–magnetic field (S–B) diagrams for the QOC. Strokes $\text{A} \rightarrow \text{B}$ and $\text{C} \rightarrow \text{D}$ are adiabatic, while $\text{B} \rightarrow \text{C}$ and $\text{D} \rightarrow \text{A}$ are isochoric.
• Figure 4: (a) Entropy–temperature (S–T) and (b) entropy–magnetic field (S–B) diagrams for the QCC. Strokes $\text{A} \rightarrow \text{B}$ and $\text{C} \rightarrow \text{D}$ are adiabatic, while $\text{B} \rightarrow \text{C}$ and $\text{D} \rightarrow \text{A}$ are isothermal.
• Figure 5: (a) Entropy–temperature (S–T) and (b) entropy–magnetic field (S–B) diagrams for the QSC. Strokes $\text{A} \rightarrow \text{B}$ and $\text{C} \rightarrow \text{D}$ are isothermal, while $\text{B} \rightarrow \text{C}$ and $\text{D} \rightarrow \text{A}$ are isochoric.