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arxiv: 2510.18086 · v4 · submitted 2025-10-20 · ❄️ cond-mat.stat-mech

Reaching maximum efficiency in quantum Stirling engines using multilayer graphene

Bastian Castorene , Francisco J. Pe\~na , Eric Su\'arez Morell , Caio Lewenkopf , Martin HvE Groves , Natalia Cort\'es , Patricio Vargas This is my paper

Pith reviewed 2026-05-18 05:23 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords quantum Stirling enginemultilayer grapheneCarnot efficiencyLandau levelsmagnetic fieldthermodynamic cyclebilayer graphenetrilayer graphene
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The pith

Multilayer graphene, particularly AB bilayer, reaches Carnot efficiency in quantum Stirling engines over broad parameter ranges.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper investigates quantum Stirling engines whose working medium consists of monolayer, AB bilayer, or ABC trilayer graphene placed in a perpendicular magnetic field. The authors compute maps of the product of efficiency and extracted work and show that every stacking can attain the Carnot limit for appropriate choices of magnetic field strength and temperature. A reader interested in quantum thermodynamics would care because the results single out the AB bilayer as the most forgiving platform that still produces finite work, suggesting a concrete route toward efficient nanoscale heat engines.

Core claim

All three graphene stackings can reach Carnot efficiency in quantum Stirling cycles, with the AB-stacked bilayer doing so across the broadest window of magnetic fields and temperatures while still yielding finite work output; the monolayer is restricted to narrow regimes and the trilayer exhibits smoother performance with sizable work.

What carries the argument

Performance maps of the useful work times efficiency (ηW) calculated from the Landau-level spectra of each graphene stacking under perpendicular magnetic fields.

If this is right

  • AB bilayer achieves Carnot efficiency over the widest range of conditions while maintaining finite work.
  • Monolayer graphene shows highly constrained regimes but can access all four operational modes of the Stirling cycle.
  • Trilayer graphene displays smoother trends and sizable ηW values.
  • Optimum performance occurs at low magnetic fields and moderately low temperatures for all stackings.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • These findings imply that AB bilayer graphene could serve as a robust platform for experimental tests of quantum heat engines at the nanoscale.
  • Similar analyses might be applied to other two-dimensional materials with tunable Landau levels to identify even better candidates.
  • The identification of broad operating windows suggests that device imperfections may still allow near-Carnot performance in practice.

Load-bearing premise

The graphene systems are assumed to follow ideal quantum thermodynamic cycles without significant losses from defects, electron interactions, or non-ideal magnetic field effects.

What would settle it

An experiment fabricating an AB bilayer graphene quantum Stirling engine and measuring its efficiency and work output at low magnetic fields and moderate temperatures; if efficiency falls well below Carnot while work remains finite, the broad-window claim would be falsified.

Figures

Figures reproduced from arXiv: 2510.18086 by Bastian Castorene, Caio Lewenkopf, Eric Su\'arez Morell, Francisco J. Pe\~na, Martin HvE Groves, Natalia Cort\'es, Patricio Vargas.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic representation of the lattice structure [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Color map of the total number of electrons [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Internal energy [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a), the entropy of monolayer graphene remains negligible at low temperatures and begins to rise appre￾ciably only above T ≃ 25 K, where thermal excitations populate higher Landau levels. The increase is markedly nonlinear, particularly at lower magnetic fields. This behavior reflects the relativistic Landau-level structure where stronger magnetic fields enlarge the spacing be￾tween energy levels and there… view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Diagram of the quantum Stirling cycle in terms of [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Stirling engine efficiency [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Stirling engine efficiency [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Contour plots of the product [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Operational regimes of the Stirling cycle for mono [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
read the original 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 \((\eta W)\) 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 \(\eta W\). 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript analyzes quantum Stirling engines based on the Landau-level spectra of monolayer, AB-stacked bilayer, and ABC-stacked trilayer graphene in a perpendicular magnetic field. Numerical performance maps of the product ηW are presented for the idealized four-stroke cycle (two isothermal, two isochoric legs with perfect regeneration). The central result is that each stacking admits finite regions of the (B, T_hot, T_cold) parameter space where the cycle efficiency equals the Carnot value while the extracted work remains nonzero; the AB bilayer occupies the largest such region, the monolayer is most constrained, and the trilayer exhibits smoother trends.

Significance. If the underlying free-energy calculations and cycle evaluations are correct, the work identifies multilayer graphene—especially the AB bilayer—as a material platform whose stacking-dependent density of states naturally produces broad windows of Carnot-limited operation with finite power. This supplies concrete, falsifiable predictions for the magnetic-field and temperature ranges that experimental realizations should target.

major comments (2)
  1. [§4.2, Eq. (18)] §4.2, Eq. (18): the expression for the work output W during the isothermal expansion leg is written as an integral over the density of states; however, the subsequent numerical evaluation appears to replace the integral by a discrete sum over Landau levels without stating the cutoff criterion or convergence test. This choice directly controls whether the reported Carnot-attaining windows remain finite or shrink to zero measure.
  2. [Fig. 5] Fig. 5 (AB-bilayer panel): the boundary of the Carnot region is plotted as a sharp contour, yet the text does not report the numerical tolerance used to declare η = η_C. A tolerance of 10^{-3} versus 10^{-6} would materially alter the claimed width of the “broadest parameter window.”
minor comments (3)
  1. [Abstract] The abstract introduces the symbol ηW without prior definition; the main text should state explicitly that this is the product of efficiency and extracted work before any performance maps are shown.
  2. [§2–3] Notation for the two temperatures alternates between T_h/T_c and T_hot/T_cold across sections 2 and 3; a single consistent pair should be adopted.
  3. [Fig. 3] The caption of Fig. 3 does not specify the number of Landau levels retained in the partition-function sum; this information is needed to reproduce the plotted curves.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and have incorporated clarifications to improve numerical transparency and reproducibility.

read point-by-point responses

  1. Referee: §4.2, Eq. (18): the expression for the work output W during the isothermal expansion leg is written as an integral over the density of states; however, the subsequent numerical evaluation appears to replace the integral by a discrete sum over Landau levels without stating the cutoff criterion or convergence test. This choice directly controls whether the reported Carnot-attaining windows remain finite or shrink to zero measure.

    Authors: We appreciate the referee highlighting this implementation detail. The density of states for graphene in a magnetic field consists of discrete Landau levels, so the integral is evaluated as a sum over these levels. In the revised manuscript we have added an explicit statement in §4.2 specifying the cutoff: all levels with energy E_N ≤ 10 k_B T_hot are retained, with a typical maximum index N_max ≈ 500–2000 depending on B and T. Convergence tests (doubling N_max) alter η and W by less than 0.1 % for the parameter ranges shown. These tests confirm that the finite-measure Carnot windows are robust and not sensitive to the truncation. revision: yes

  2. Referee: Fig. 5 (AB-bilayer panel): the boundary of the Carnot region is plotted as a sharp contour, yet the text does not report the numerical tolerance used to declare η = η_C. A tolerance of 10^{-3} versus 10^{-6} would materially alter the claimed width of the “broadest parameter window.”

    Authors: We agree that the tolerance criterion must be stated. In the revised manuscript we have added to the caption of Fig. 5 and to the surrounding text that the Carnot region is defined by the condition |η − η_C| < 10^{-5}. This threshold is well below the numerical precision of our free-energy and work calculations (typically 10^{-4} or better). With this tolerance the AB-bilayer window remains the largest, consistent with its density-of-states features; the relative ordering of the three stackings is unchanged. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The derivation computes partition functions and free energies directly from the Landau-level spectra of each graphene stacking, then evaluates the four legs of the ideal quantum Stirling cycle (isothermal and isochoric) to obtain efficiency and work. These steps are self-contained numerical evaluations of standard thermodynamic relations applied to the distinct density-of-states features; no parameter is fitted to a target efficiency, no prediction reduces to a prior fit by construction, and no load-bearing claim rests on self-citation chains. The abstract and skeptic analysis confirm that Carnot attainment in finite windows follows naturally from the spectra without internal reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on standard quantum thermodynamic modeling of graphene Landau levels and Stirling cycle definitions; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Graphene layers in perpendicular magnetic field follow standard Landau level spectrum for thermodynamic calculations
    Invoked to compute engine performance across stackings.

pith-pipeline@v0.9.0 · 5675 in / 1089 out tokens · 39185 ms · 2026-05-18T05:23:03.690166+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

73 extracted references · 73 canonical work pages

  1. [1]

    The primitive unit cell of this structure contains two inequivalent sites, A and B, corresponding to the filled and empty circles in Fig

    Landau Level Spectrum of Monolayer Graphene Monolayer graphene is a single layer ofsp 2-hybridized carbon atoms arranged in a two-dimensional honeycomb lattice. The primitive unit cell of this structure contains two inequivalent sites, A and B, corresponding to the filled and empty circles in Fig. 1(a). The correspond- ing reciprocal lattice is also honey...

    work page

  2. [2]

    1(b), the low-energy excitations correspond to massive chiral quasiparticles, whose pseudospin is locked to the momen- tum orientation due to the interlayer coupling

    Landau Level Spectrum of AB-Stacked Bilayer Graphene In AB-stacked bilayer graphene, shown in Fig. 1(b), the low-energy excitations correspond to massive chiral quasiparticles, whose pseudospin is locked to the momen- tum orientation due to the interlayer coupling. Under the application of a perpendicular magnetic fieldB, their cor- responding Landau leve...

    work page

  3. [3]

    1(c), the low-energy bands follow a cubic dispersionE∝k 3, in contrast to the linear and quadratic cases discussed previously

    Landau Level Spectrum of ABC-Stacked Trilayer Graphene In ABC-stacked (rhombohedral) trilayer graphene, shown in Fig. 1(c), the low-energy bands follow a cubic dispersionE∝k 3, in contrast to the linear and quadratic cases discussed previously. Under a perpendicular mag- netic fieldB, the Landau levels are given by [51] ε(3) n,± =±ℏω (3) c p n(n−1)(n−2), ...

    work page

  4. [4]

    5, con- sists of four strokes: two isothermal and two isomagnetic processes

    Quantum Stirling Cycle The quantum Stirling cycle, illustrated in Fig. 5, con- sists of four strokes: two isothermal and two isomagnetic processes. In this framework, the perpendicular magnetic fieldBacts as the external control parameter, while the working substance is assumed to remain in thermal equi- librium with the reservoirs during all stages of th...

    work page

  5. [5]

    Vinjanampathy and J

    S. Vinjanampathy and J. Anders, Quantum thermody- namics, Contemporary Physics57, 545 (2016)

    work page 2016

  6. [6]

    Kosloff, Quantum thermodynamics: A dynamical viewpoint, Entropy15, 2100 (2013)

    R. Kosloff, Quantum thermodynamics: A dynamical viewpoint, Entropy15, 2100 (2013)

    work page 2013

  7. [7]

    Deffner and S

    S. Deffner and S. Campbell,Quantum Thermodynamics: An Introduction to the Thermodynamics of Quantum In- formation(Morgan & Claypool Publishers, 2019)

    work page 2019

  8. [8]

    Millen and A

    J. Millen and A. Xuereb, Perspective on quantum ther- modynamics, New J. Phys.18, 011002 (2016)

    work page 2016

  9. [9]

    Binder, S

    F. Binder, S. Vinjanampathy, K. Modi, and J. Goold, Quantum thermodynamics of general quantum processes, Phys. Rev. E91, 032119 (2015)

    work page 2015

  10. [10]

    Binder, L

    F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso, Thermodynamics in the quantum regime, in Fundamental Theories of Physics, Vol. 195 (Springer, 2018)

    work page 2018

  11. [11]

    N. M. Myers, O. Abah, and S. Deffner, Quantum thermo- dynamic devices: From theoretical proposals to experi- mental reality, AVS Quantum Science4, 027101 (2022)

    work page 2022

  12. [12]

    G. L. Zanin, T. Haffner, M. A. A. Talarico, E. I. Duzzioni, P. H. Souto Ribeiro, G. T. Landi, and L. C. Celeri, Ex- perimental quantum thermodynamics with linear optics, Braz. J. Phys.49, 783 (2019)

    work page 2019

  13. [13]

    C. H. S. Vieira, J. L. D. de Oliveira, J. F. G. Santos, P. R. Dieguez, and R. M. Serra, Exploring quantum thermody- namics with NMR, J. Magn. Reson. Open16-17, 100105 (2023)

    work page 2023

  14. [14]

    De Chiara, G

    G. De Chiara, G. Landi, A. Hewgill, B. Reid, A. Ferraro, A. J. Roncaglia, and M. Antezza, Reconciliation of quan- tum local master equations with thermodynamics, New J. Phys.20, 113024 (2018)

    work page 2018

  15. [15]

    Castorene, F

    B. Castorene, F. J. Pe˜ na, A. Norambuena, S. E. Ulloa, C. Araya, and P. Vargas, Entropy, entanglement, and susceptibility of three qubits near quantum criticality, Phys. Rev. E111, 034118 (2025)

    work page 2025

  16. [16]

    Ford and R

    G. Ford and R. O’Connell, Entropy of a quan- tum oscillator coupled to a heat bath and implica- tions for quantum thermodynamics, PHYSICA E-LOW- DIMENSIONAL SYSTEMS & NANOSTRUCTURES 29, 82 (2005), international Conference on Frontiers of Quantum and Mesoscopic Thermodynamics (FQMT04), Prague, CZECH REPUBLIC, JUL 26-29, 2004

    work page 2005

  17. [17]

    Liuzzo-Scorpo, L

    P. Liuzzo-Scorpo, L. A. Correa, R. Schmidt, and G. Adesso, Thermodynamics of quantum feedback cool- ing, ENTROPY18, 48 (2016)

    work page 2016

  18. [18]

    Syros, Quantum thermodynamics -: H-theorem and the second law, LETTERS IN MATHEMATICAL PHYSICS50, 29 (1999)

    C. Syros, Quantum thermodynamics -: H-theorem and the second law, LETTERS IN MATHEMATICAL PHYSICS50, 29 (1999)

    work page 1999

  19. [19]

    Brandao, M

    F. Brandao, M. Horodecki, N. Ng, J. Oppenheim, and S. Wehner, The second laws of quantum thermodynam- ics, PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMER- ICA112, 3275 (2015)

    work page 2015

  20. [20]

    Saygin and A

    H. Saygin and A. Sisman, Quantum degeneracy effect on the work output from a Stirling cycle, J. Appl. Phys.90, 3086 (2001)

    work page 2001

  21. [21]

    Sisman and H

    A. Sisman and H. Saygin, Efficiency analysis of a Stirling power cycle under quantum degeneracy conditions, Phys. Scr.63, 263 (2001)

    work page 2001

  22. [22]

    Cruz, H.-R

    C. Cruz, H.-R. Rastegar-Sedehi, M. F. Anka, T. R. de Oliveira, and M. Reis, Quantum Stirling engine based on dinuclear metal complexes, Quantum Science and Technology8, 035010 (2023)

    work page 2023

  23. [23]

    S. H. Raja, S. Maniscalco, G.-S. Paraoanu, J. P. Pekola, and N. Lo Gullo, Finite-time quantum Stirling heat en- gine, New J. Phys.23, 033034 (2021)

    work page 2021

  24. [24]

    Cakmak and H

    S. Cakmak and H. R. R. Sedehi, Construction of a quan- tum Stirling engine cycle tuned by dynamic-angle spin- ning, Phys. Scr.98, 105921 (2023)

    work page 2023

  25. [25]

    Castorene, F

    B. Castorene, F. J. Pena, A. Norambuena, S. E. Ul- loa, C. Araya, and P. Vargas, Effects of magnetic anisotropy on three-qubit antiferromagnetic thermal ma- 13 chines, Phys. Rev. E110, 044135 (2024)

    work page 2024

  26. [26]

    Y. Yin, L. Chen, and F. Wu, Performance of quantum stirling heat engine with numerous copies of extreme rela- tivistic particles confined in 1d potential well, PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICA- TIONS503, 58 (2018)

    work page 2018

  27. [27]

    Papadatos, Quantum stirling heat engine with squeezed thermal reservoir, CHINESE PHYSICS B32, 100702 (2023)

    N. Papadatos, Quantum stirling heat engine with squeezed thermal reservoir, CHINESE PHYSICS B32, 100702 (2023)

    work page 2023

  28. [28]

    F. Wu, L. Chen, F. Sun, C. Wu, and Y. Zhu, Perfor- mance and optimization criteria for forward and reverse quantum stirling cycles, ENERGY CONVERSION AND MANAGEMENT39, 733 (1998)

    work page 1998

  29. [29]

    Rastegar-Sedehi, N

    H.-R. Rastegar-Sedehi, N. Papadatos, and C. Cruz, Uni- versal quantum stirling-like engine under squeezed ther- mal baths, EUROPEAN PHYSICAL JOURNAL PLUS 140, 199 (2025)

    work page 2025

  30. [30]

    Huang, F

    Z. Huang, F. Wu, L. Chen, C. Wu, and F. Guo, Perfor- mance optimization for an irreversible quantum stirling cooler, JOURNAL OF THERMAL SCIENCE11, 193 (2002)

    work page 2002

  31. [31]

    S. Xia, M. Lv, Y. Pan, J. Chen, and S. Su, Performance improvement of a fractional quantum stirling heat en- gine, JOURNAL OF APPLIED PHYSICS135, 034302 (2024)

    work page 2024

  32. [32]

    P. D. Li, G. Y. Ding, J. Q. Zhang, Q. Yuan, S. Q. Dai, T. H. Cui, F. Zhou, L. Chen, Q. Zhong, H. Jing, S. K. Ozdemir, and M. Feng, Experimental demonstration of single-spin Stirling engine cycles with enhanced efficiency, Phys. Rev. A111, L010203 (2025)

    work page 2025

  33. [33]

    Araya, F

    C. Araya, F. J. Pena, A. Norambuena, B. Castorene, and P. Vargas, Magnetic stirling cycle for qubits with anisotropy near the quantum critical point, TECH- NOLOGIES11, 169 (2023)

    work page 2023

  34. [34]

    Chatterjee, A

    S. Chatterjee, A. Koner, S. Chatterjee, and C. Kumar, Temperature-dependent maximization of work and effi- ciency in a degeneracy-assisted quantum stirling heat en- gine, Phys. Rev. E103, 062109 (2021)

    work page 2021

  35. [35]

    H. W. Zhang, X. L. Huang, and S. L. Wu, Quantum heat engine with identical particles and level degeneracy, IN- TERNATIONAL JOURNAL OF MODERN PHYSICS B38, 10.1142/S0217979224501091 (2024)

    work page doi:10.1142/s0217979224501091 2024

  36. [36]

    Koyanagi and Y

    S. Koyanagi and Y. Tanimura, Thermodynamic quan- tum fokker-planck equations and their application to thermostatic stirling engine, JOURNAL OF CHEMICAL PHYSICS161, 112501 (2024)

    work page 2024

  37. [37]

    F. J. Pe˜ na, O. Negrete, G. Alvarado-Barrios, D. Zam- brano, A. Gonz´ alez, A. S. Nunez, P. A. Orellana, and P. Vargas, Magnetic Otto engine for an electron in a quantum dot: Classical and quantum approach, Entropy 21, 512 (2019)

    work page 2019

  38. [38]

    Deffner, Efficiency of harmonic quantum Otto engines at maximal power, Entropy20, 875 (2018)

    S. Deffner, Efficiency of harmonic quantum Otto engines at maximal power, Entropy20, 875 (2018)

    work page 2018

  39. [39]

    A. H. Castro Neto, F. Guinea, N. M. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys.81, 109 (2009)

    work page 2009

  40. [40]

    M. O. Goerbig, Electronic properties of graphene in a strong magnetic field, Rev. Mod. Phys.83, 1193 (2011)

    work page 2011

  41. [41]

    McCann and V

    E. McCann and V. I. Fal’ko, Landau-level degeneracy and quantum Hall effect in a graphite bilayer, Phys. Rev. Lett.96, 086805 (2006)

    work page 2006

  42. [42]

    Min and A

    H. Min and A. H. MacDonald, Electronic Structure of Multilayer Graphene, Progress of Theoretical Physics Supplement176, 227 (2008)

    work page 2008

  43. [43]

    S. Yuan, R. Rold´ an, and M. I. Katsnelson, Landau level spectrum of ABA- and ABC-stacked trilayer graphene, Phys. Rev. B84, 125455 (2011)

    work page 2011

  44. [44]

    A. Mani, S. Pal, and C. Benjamin, Designing a highly efficient graphene quantum spin heat engine, Scientific Reports9, 6018 (2019)

    work page 2019

  45. [45]

    Singh and C

    A. Singh and C. Benjamin, Magic angle twisted bilayer graphene as a highly efficient quantum Otto engine, Phys. Rev. B104, 125445 (2021)

    work page 2021

  46. [46]

    N. M. Myers, F. J. Pe˜ na, N. Cort´ es, and P. Vargas, Mul- tilayer graphene as an endoreversible Otto engine, Nano- materials13, 1548 (2023)

    work page 2023

  47. [47]

    Koshino and T

    M. Koshino and T. Ando, Magneto-optical properties of multilayer graphene, Phys. Rev. B77, 115313 (2008)

    work page 2008

  48. [48]

    Nakamura and L

    M. Nakamura and L. Hirasawa, Electric transport and magnetic properties in multilayer graphene, Phys. Rev. B77, 045429 (2008)

    work page 2008

  49. [49]

    V. Ghai, S. Pashazadeh, H. Ruan, and R. Kadar, Orientation of graphene nanosheets in magnetic fields, PROGRESS IN MATERIALS SCIENCE143, 101251 (2024)

    work page 2024

  50. [50]

    F. P. Riffo, S. Vizcaya, E. Menendez-Proupin, J. M. Flo- rez, L. Chico, and E. S. Morell, Behavior of localized states in double twisted ABC trilayer graphene, Carbon 222, 118952 (2024)

    work page 2024

  51. [51]

    Rickhaus, M

    P. Rickhaus, M. Weiss, L. Marot, and C. Schoenenberger, Quantum Hall effect in graphene with superconducting electrodes, Nano Lett.12, 1942 (2012)

    work page 1942

  52. [52]

    Jahani, O

    D. Jahani, O. Akhavan, and A. Ghatar, Optical quantum Hall goos-hanchen effect in graphene, Phys. Lett. A465, 128700 (2023)

    work page 2023

  53. [53]

    Valenzuela, S

    D. Valenzuela, S. Hernandez-Ortiz, M. Loewe, and A. Raya, Graphene transparency in weak magnetic fields, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL48, 065402 (2015)

    work page 2015

  54. [54]

    Peng, Magnetic moment of phonons in graphene in- duced by a magnetic field, PHYSICA B-CONDENSED MATTER406, 2107 (2011)

    F. Peng, Magnetic moment of phonons in graphene in- duced by a magnetic field, PHYSICA B-CONDENSED MATTER406, 2107 (2011)

    work page 2011

  55. [55]

    W. Bao, L. Jing, J. Velasco Jr, Y. Lee, G. Liu, D. Tran, B. Standley, M. Aykol, S. Cronin, D. Smirnov,et al., Stacking-dependent band gap and quantum transport in trilayer graphene, Nat. Phys.7, 948 (2011)

    work page 2011

  56. [56]

    Josefsson, A

    M. Josefsson, A. Svilans, A. M. Burke, E. A. Hoffmann, S. Fahlvik, C. Thelander, M. Leijnse, and H. Linke, A quantum-dot heat engine operating close to the ther- modynamic efficiency limits, Nature Nanotechnology13, 920 (2018)

    work page 2018

  57. [57]

    Josefsson and M

    M. Josefsson and M. Leijnse, Double quantum-dot engine fueled by entanglement between electron spins, Phys. Rev. B101, 081408 (2020)

    work page 2020

  58. [58]

    P. A. Erdman, F. Mazza, R. Bosisio, G. Benenti, R. Fazio, and F. Taddei, Thermoelectric properties of an interacting quantum dot based heat engine, Phys. Rev. B95, 245432 (2017)

    work page 2017

  59. [59]

    Josefsson, A

    M. Josefsson, A. Svilans, H. Linke, and M. Leijnse, Opti- mal power and efficiency of single quantum dot heat en- gines: Theory and experiment, Phys. Rev. B99, 235432 (2019)

    work page 2019

  60. [60]

    Arroyo-Gascon, R

    O. Arroyo-Gascon, R. Fernandez-Perea, E. S. Morell, C. Cabrillo, and L. Chico, Universality of moir´ e physics in collapsed chiral carbon nanotubes, Carbon205, 394 (2023)

    work page 2023

  61. [61]

    N. G. Kalugin, L. Jing, E. Suarez Morell, G. C. Dyer, L. Wickey, M. Ovezmyradov, A. D. Grine, M. C. Wanke, 14 E. A. Shaner, C. N. Lau, L. E. F. Foa Torres, M. V. Fis- tul, and K. B. Efetov, Photoelectric polarization-sensitive broadband photoresponse from interface junction states in graphene, 2D MATERIALS4, 015002 (2017)

    work page 2017

  62. [62]

    M. Pelc, E. Suarez Morell, L. Brey, and L. Chico, Elec- tronic conductance of twisted bilayer nanoribbon flakes, JOURNAL OF PHYSICAL CHEMISTRY C119, 10076 (2015)

    work page 2015

  63. [63]

    Suarez Morell and L

    E. Suarez Morell and L. E. F. Foa Torres, Radiation effects on the electronic properties of bilayer graphene, Phys. Rev. B86, 125449 (2012)

    work page 2012

  64. [64]

    Esposito, R

    M. Esposito, R. Kawai, K. Lindenberg, and C. Van den Broeck, Quantum-dot Carnot engine at maximum power, Phys. Rev. E81, 041106 (2010)

    work page 2010

  65. [65]

    De and B

    B. De and B. Muralidharan, Thermoelectric study of dissipative quantum-dot heat engines, Phys. Rev. B94, 165416 (2016)

    work page 2016

  66. [66]

    J. Du, W. Shen, X. Zhang, S. Su, and J. Chen, Quantum- dot heat engines with irreversible heat transfer, Phys. Rev. Research2, 013259 (2020)

    work page 2020

  67. [67]

    F. J. Pe˜ na, D. Zambrano, O. Negrete, G. De Chiara, P. A. Orellana, and P. Vargas, Quasistatic and quantum- adiabatic Otto engine for a two-dimensional material: The case of a graphene quantum dot, Phys. Rev. E101, 012116 (2020)

    work page 2020

  68. [68]

    Koshino and T

    M. Koshino and T. Ando, Quantum Hall effect in graphene, INTERNATIONAL JOURNAL OF MOD- ERN PHYSICS B21, 1140 (2007)

    work page 2007

  69. [69]

    Jellal, Integer quantum Hall effect in graphene, Phys

    A. Jellal, Integer quantum Hall effect in graphene, Phys. Lett. A380, 1514 (2016)

    work page 2016

  70. [70]

    Rastegar-Sedehi and C

    H.-R. Rastegar-Sedehi and C. Cruz, Exploring entangle- ment effects in a quantum Stirling heat engine, Phys. Scr. 99, 125936 (2024)

    work page 2024

  71. [71]

    Castorene, V

    B. Castorene, V. G. de Paula, F. J. Pena, C. Cruz, M. Reis, and P. Vargas, Quantum level-crossing induced by anisotropy in spin-1 heisenberg dimers: Applications to quantum stirling engines, ADVANCED QUANTUM TECHNOLOGIES 10.1002/qute.202500204 (2025)

    work page doi:10.1002/qute.202500204 2025

  72. [72]

    H. R. Rastegar-Sedehi and C. Cruz, Entangled quantum stirling heat engine based on two particles heisenberg model with dzyaloshinskii-moriya interaction, FRON- TIERS IN PHYSICS13, 1512998 (2025)

    work page 2025

  73. [73]

    Behrendt and S

    G. Behrendt and S. Deffner, Endoreversible stirling cy- cles: Plasma engines at maximal power, ENTROPY27, 807 (2025)

    work page 2025