High-Efficiency Three-Stroke Quantum Isochoric Heat Engine: From Infinite Potential Wells to Magic Angle Twisted Bilayer Graphene

Abstract

We introduce a three-stroke quantum isochoric cycle that functions as a heat engine operating between two thermal reservoirs. Implemented for a particle confined in a one-dimensional infinite potential well, the cycle's performance is benchmarked against the classical three-stroke triangular and isochoric engines. We find that the quantum isochoric cycle achieves a higher efficiency than both classical counterparts and also surpasses the efficiency of the recently proposed three-stroke quantum isoenergetic cycle. Owing to its reduced number of strokes, the design substantially lowers control complexity in nanoscale thermodynamic devices, offering a more feasible route to experimental realization compared to conventional four-stroke architectures. We further evaluate the cycle in graphene-based systems under an external magnetic field, including monolayer graphene (MLG), AB-stacked bilayer graphene (BLG), and twisted bilayer graphene (TBG) at both magic and non-magic twist angles. Among these platforms, magic-angle twisted bilayer graphene (MATBG) attains the highest efficiency at fixed work output, highlighting its promise for quantum thermodynamic applications.

Figures (12)

• Figure 1: Entropy - Temperature (T-S) diagrams for three thermodynamic cycles. Shown are: the classical triangular cycle $A \to B \xrightarrow{\text{Blue}} C \to A$rau2017statistical, the classical isochoric cycle $A \to B \xrightarrow{\text{Yellow}} C \to A$, the quantum isochoric cycle $A \to B \xrightarrow{\text{Green}} C \to A$, and the quantum isoenergetic cycle $A \to B \xrightarrow{\text{Purple}} C \to A$ou2016exotic. The classical triangular, classical isochoric and quantum isochoric cycles operate between two baths at fixed temperatures $T_h$ and $T_c$, while the quantum isoenergetic cycle operates with a single bath at $T_h$, where the effective cold temperature $T_c$ is not fixed but is determined by other parameters.
• Figure 2: Volume - Temperature diagram of ideal gas during a three-stroke classical isochoric cycle. Stroke $A\xrightarrow{}B$ is the isothermal stroke, $B\xrightarrow{\text{Yellow}}C$ is the isochoric stroke, and $C\xrightarrow{}A$ is the adiabatic stroke.
• Figure 3: Length - Temperature diagram of the particle in an IPW during a three-stroke quantum isochoric cycle. Stroke $A\xrightarrow{}B$ is the isothermal stroke, $B\xrightarrow{\text{Green}}C$ is the quantum isochoric stroke, and $C\xrightarrow{}A$ is the adiabatic stroke.
• Figure 4: (a) Efficiency in units of $\eta/\eta_c$ and (b) Work output (in meV) for a particle in an IPW undergoing a three-stroke quantum isochoric cycle working as a heat engine at different hot bath temperatures. In (a), the black dashed line corresponds to $\eta_\text{CT}/\eta_c$ from Eq. \ref{['eq:trianeta']} (classical triangular cycle), while the dotted-dashed line shows $\eta_\text{CI}/\eta_c$ from Eq. \ref{['eq:classical isocho eta']} (classical isochoric cycle). In (b), the dashed and dotted-dashed lines indicate the work outputs $W_\text{CT}$ (Eq. \ref{['eq:workmonoatomic']}) and $W_\text{CI}$ (Eq. \ref{['classical isochor work']}) for a monoatomic ideal gas undergoing the classical triangular and classical isochoric cycles, respectively. $L_B$ is the length of the well during the quantum isochoric process and $T_c=1 \text{K}$.
• Figure 5: Length - Temperature diagram of the IPW for a three-stroke quantum isoenergetic cycle. Stroke $A\xrightarrow{}B$ is the isothermal stroke, $B\xrightarrow{\text{Purple}}C$ is the isoenergetic stroke, and $C\xrightarrow{}A$ is the adiabatic stroke.