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Highly efficient quantum Stirling engine using multilayer Graphene

Bastian Castorene, Francisco J. Peña, Eric Suarez, Caio Lewenkopf, Martin HvE Groves, Natalia Cortés, Patricio Vargas

TL;DR

This work analyzes quantum Stirling cycles using monolayer, AB-stacked bilayer, and ABC-stacked trilayer graphene under perpendicular magnetic fields within a grand-canonical, fermionic framework that explicitly incorporates Landau level spectra and Fermi–Dirac statistics. The authors derive analytic LL spectra for each stacking, compute $U$, $S$, and $\langle N\rangle$, and implement a Stirling cycle by parametric variation of the magnetic field while enforcing particle-number conservation through a self-consistent chemical potential, obtaining $Q_{in}$, $Q_{out}$, and $\eta$ with $\eta = W / Q_{in}$. They find that AB bilayer graphene offers the broadest operational window and can reach Carnot efficiency with finite work, while monolayer shows highly constrained engine regimes and trilayer exhibits smoother but smaller-$\Delta$-scale performance; overall, multilayer graphene emerges as a versatile platform for efficient quantum heat engines controlled by $B$, with implications for quantum thermodynamics and nanoscale energy management. The study emphasizes the importance of LL degeneracies and the discrete spectrum in determining heat exchange and performance, making the approach relevant for experimental exploration under realistic doping and cooling conditions.

Abstract

In this work, quantum Stirling engines based on monolayer, AB-stacked bilayer, and ABC-stacked trilayer graphene under perpendicular magnetic fields are analyzed. Performance maps of the useful work \((ηW)\) reveal a robust optimum at low magnetic fields and moderately low temperatures, with all stackings capable of reaching Carnot efficiency under suitable configurations. The AB bilayer achieves this across the broadest parameter window while sustaining finite work, the monolayer exhibits highly constrained regimes, and the trilayer shows smoother trends with sizable \(ηW\). These results identify multilayer graphene, particularly the AB bilayer, as a promising platform for efficient Stirling engines, while also highlighting the versatility of the monolayer in realizing all four operational regimes of the Stirling cycle.

Highly efficient quantum Stirling engine using multilayer Graphene

TL;DR

This work analyzes quantum Stirling cycles using monolayer, AB-stacked bilayer, and ABC-stacked trilayer graphene under perpendicular magnetic fields within a grand-canonical, fermionic framework that explicitly incorporates Landau level spectra and Fermi–Dirac statistics. The authors derive analytic LL spectra for each stacking, compute , , and , and implement a Stirling cycle by parametric variation of the magnetic field while enforcing particle-number conservation through a self-consistent chemical potential, obtaining , , and with . They find that AB bilayer graphene offers the broadest operational window and can reach Carnot efficiency with finite work, while monolayer shows highly constrained engine regimes and trilayer exhibits smoother but smaller--scale performance; overall, multilayer graphene emerges as a versatile platform for efficient quantum heat engines controlled by , with implications for quantum thermodynamics and nanoscale energy management. The study emphasizes the importance of LL degeneracies and the discrete spectrum in determining heat exchange and performance, making the approach relevant for experimental exploration under realistic doping and cooling conditions.

Abstract

In this work, quantum Stirling engines based on monolayer, AB-stacked bilayer, and ABC-stacked trilayer graphene under perpendicular magnetic fields are analyzed. Performance maps of the useful work \((ηW)\) reveal a robust optimum at low magnetic fields and moderately low temperatures, with all stackings capable of reaching Carnot efficiency under suitable configurations. The AB bilayer achieves this across the broadest parameter window while sustaining finite work, the monolayer exhibits highly constrained regimes, and the trilayer shows smoother trends with sizable . These results identify multilayer graphene, particularly the AB bilayer, as a promising platform for efficient Stirling engines, while also highlighting the versatility of the monolayer in realizing all four operational regimes of the Stirling cycle.
Paper Structure (16 sections, 21 equations, 9 figures, 1 table)

This paper contains 16 sections, 21 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Theory and methods
  3. Landau Level Spectrum in Multilayer Graphene
  4. Landau Level Spectrum of Monolayer Graphene
  5. Landau Level Spectrum of AB-Stacked Bilayer Graphene
  6. Landau Level Spectrum of ABC-Stacked Trilayer Graphene
  7. Thermodynamic Description of Multilayer Graphene Systems Under Magnetic Field
  8. Grand canonical formalism
  9. Energy Scales and Parametrization of the Chemical Potential to Conserve Particle Number
  10. Thermodynamic Properties: Internal Energy and Entropy of Multilayer Graphene
  11. Quantum Stirling Cycle
  12. Results
  13. Stirling Engine Efficiency
  14. Stirling Maximum Gain
  15. Stirling Operational Regimes
  16. ...and 1 more sections

Figures (9)

  • Figure 1: Schematic representation of the lattice structure of graphene multilayer systems (under a perpendicular homogeneous magnetic field $B$). Panel (a) shows the monolayer, panel (b) the AB-stacked bilayer, and panel (c) the ABC-stacked trilayer.
  • Figure 2: Color map of the total number of electrons $\expval{N}$ as a function of magnetic field $B\, [T]$ and chemical potential $\mu\ $ [meV] for (a) monolayer, (b) bilayer and (c) trilayered graphene system under a fixed temperature $T =50$ K.
  • Figure 3: Internal energy $U(T,B)$ as a function of temperature for (a) monolayer, (b) bilayer, and (c) trilayer graphene at different magnetic fields, with the particle number fixed at $N_e = 15$.
  • Figure 4: Entropy $S(T,B)$ as a function of temperature for (a) monolayer, (b) bilayer, and (c) trilayer graphene at different magnetic fields, with the particle number fixed at $N_e = 15$.
  • Figure 5: Diagram of the quantum Stirling cycle in terms of entropy $S$ and the perpendicular magnetic field $B$. Curves AB and CD correspond to the isotherms at $T = T_H$ and $T = T_L$, respectively. As the magnetic field increases at fixed temperature, the entropy decreases, and vice versa.
  • ...and 4 more figures