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arxiv: 2604.07504 · v1 · submitted 2026-04-08 · ❄️ cond-mat.mes-hall

Mode-Resolved Multiband Ballistic Transport and Conductance Thresholds in Bilayer Graphene Junctions

Dan-Na Liu , Jun Zheng , Pierre A. Pantaleon This is my paper

Pith reviewed 2026-05-10 17:11 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords bilayer grapheneballistic transportconductance thresholdmultiband transportinterlayer biasstraintransmission suppression
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The pith

A distinct conductance threshold in bilayer graphene junctions marks the onset of upper-band propagation inside the barrier.

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

The paper examines ballistic electron transport through bilayer graphene junctions under electrostatic gating, interlayer bias, and strain. Symmetry constraints normally suppress transmission at certain angles despite available states, but an interlayer bias mixes modes to lift the suppression and open a tunable gap. Using the full four-band model, the authors identify a conductance threshold tied to the upper band starting to propagate inside the barrier region, which changes the slope of conductance versus gate voltage and acts as a direct fingerprint of multiband effects and interlayer coupling. Strain then offers geometric control by reshaping momentum space and shifting the angular transmission window, suppressing conductance without adding disorder while keeping the underlying symmetry decoupling intact. These mechanisms together allow band-structure features to be read out from transport measurements in a clean system.

Core claim

Within a full four-band description, we identify a distinct conductance threshold that marks the onset of propagation of the upper band inside the barrier. This produces a clear change in the slope of the conductance and serves as an experimentally accessible transport fingerprint of the multiband structure and interlayer coupling. In the absence of strain, transport is governed by symmetry constraints that suppress transmission at specific incidence angles despite the availability of states. An interlayer bias lifts this suppression through mode mixing and opens a tunable transport gap. Homogeneous in-plane strain acts as a geometric control mechanism by reshaping the band structure in k-m,

What carries the argument

The four-band tight-binding model of bilayer graphene, which resolves both lower and upper bands plus interlayer coupling to locate the conductance threshold for upper-band propagation inside the electrostatic barrier.

Load-bearing premise

The system is assumed to remain in the ballistic regime with no disorder or scattering, and the standard four-band tight-binding model is taken to be sufficient to capture all relevant interlayer coupling and strain effects.

What would settle it

A plot of differential conductance versus gate voltage in a clean bilayer graphene junction should display an abrupt change in slope at the specific voltage where the upper band energy aligns with the barrier height.

Figures

Figures reproduced from arXiv: 2604.07504 by Dan-Na Liu, Jun Zheng, Pierre A. Pantaleon.

Figure 1
Figure 1. Figure 1: (a) The deformed AB-stacked BG lattice, and inset [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Electronic structure of bilayer graphene for (a) the unstrained case, (b) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Variation of four-band tunneling transmission probabilities with energy [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Transmission and reflection coefficients in strained BG as functions of energy [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) and (b) isoenergetic contours of the strained [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Transmission probability in the channel T + + through a single uniform electrostatic barrier with height V0 = 0.6 eV and zero interlayer bias (V1 = 0) as a function of the incident angle. Panels a)-d) correspond to incident energies E = 0.1, 0.3, 0.5, and 1.1 eV, respectively. Solid lines show the unstrained case (ϵ = 0), while dashed lines correspond to homogeneous strain with magnitude ϵ = 2% and directi… view at source ↗
Figure 7
Figure 7. Figure 7: Transmission in the channel T+ + with: (a1) ϵ = 0, (a2) ϵ = 2% and ϕ = 0π, (a3) ϵ = 2% and ϕ = 0.1π and (a4) ϵ = 2% and ϕ = 0.2π. The transmission for normal incidence ky = 0 is shown in (b1) and (b2) for the panels (a2) and (a3), respectively. In all figures we set V0=0.6 eV and V1 = 0. Red dashed lines in (a3) and (a4) roughly illustrate the shift of the zero transmission cloaked points. 0 1 2 0. 0 0. 6 … view at source ↗
Figure 8
Figure 8. Figure 8: Normalized conductance G/G0 as a function of the incident energy for different structural and strain con￾figurations. (a) Variation with strain magnitude: V0 = 0.6 eV, V1 = 0, θ = 0.2π, and ϵ = 2%, 4%, 6%; (b) Varia￾tion with strain direction: V0 = 0.6 eV, V1 = 0, ϵ = 2%, and θ = π/7, 3π/7, 5π/7; (c) Variation with barrier height: ϵ = 2%, θ = 0.2π, and V0 = 0.4, 0.6, 0.8 eV; (d) Variation with bias potenti… view at source ↗
read the original abstract

We study ballistic transport in bilayer graphene junctions and show how electrostatic gating, interlayer bias, and homogeneous strain provide complementary control over electron transmission. In the absence of strain, transport is governed by symmetry constraints that suppress transmission at specific incidence angles despite the availability of states. An interlayer bias lifts this suppression through mode mixing and opens a tunable transport gap. Within a full four-band description, we identify a distinct conductance threshold that marks the onset of propagation of the upper band inside the barrier. This produces a clear change in the slope of the conductance and serves as an experimentally accessible transport fingerprint of the multiband structure and interlayer coupling. Homogeneous in-plane strain acts as a geometric control mechanism. By reshaping the band structure in momentum space, it redistributes the angular transmission window and suppresses conductance without introducing disorder. Importantly, strain preserves the underlying symmetry-based decoupling responsible for transmission suppression while shifting its condition away from normal incidence. These results provide a unified framework for interpreting angle-resolved transport in bilayer graphene and establish multiband ballistic transport as a practical probe of band-structure geometry.

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 examines ballistic transport through bilayer graphene junctions, showing that electrostatic gating, interlayer bias, and homogeneous in-plane strain offer complementary control over transmission. Symmetry constraints in the unbiased case suppress transmission at specific angles despite available states; an interlayer bias lifts this via mode mixing and opens a tunable gap. Within the four-band tight-binding model the authors identify a distinct conductance threshold corresponding to the onset of upper-band propagation inside the barrier, which produces an observable change in the slope of the conductance versus gate voltage. Homogeneous strain is shown to reshape the momentum-space band structure, redistributing the angular transmission window and suppressing overall conductance while preserving the underlying symmetry-based decoupling (now shifted away from normal incidence). The work frames these effects as experimentally accessible fingerprints of multiband structure and interlayer coupling.

Significance. If substantiated by the full calculations, the identification of a clear conductance-threshold signature tied to upper-band onset supplies a practical, falsifiable probe of multiband effects and interlayer coupling that is directly measurable in angle-resolved or gate-dependent transport experiments. The demonstration that strain can suppress conductance geometrically without introducing disorder, while still respecting the symmetry decoupling, adds a useful control knob. The framework unifies gating, bias, and strain effects within the standard four-band Hamiltonian and Landauer-Büttiker formalism, which is appropriate for the ballistic regime. No machine-checked proofs or open code are mentioned, but the predictions are testable and could influence device modeling in bilayer-graphene mesoscopic physics.

major comments (2)
  1. [four-band transport section] The central claim that a distinct conductance threshold marks upper-band onset and produces a measurable slope change rests on the four-band dispersion inside the barrier. The manuscript should explicitly show (e.g., in the section deriving the transmission probabilities) how the threshold energy is obtained from the biased four-band Hamiltonian and confirm that the slope discontinuity survives after integration over angle and mode summation; without this step the experimental fingerprint remains plausible but not yet load-bearing.
  2. [methods or discussion of approximations] The assumption that the system remains strictly ballistic with no disorder or intervalley scattering is load-bearing for the symmetry-suppression and strain-redistribution results. The paper should quantify the mean-free-path or disorder-strength regime in which the predicted slope change and angular-window shift remain observable, perhaps via a brief estimate or reference to typical experimental values in bilayer graphene.
minor comments (3)
  1. [figures] Figure captions and axis labels should explicitly mark the conductance-threshold feature (e.g., with an arrow or vertical line) so that the slope change is immediately visible to readers.
  2. [abstract/introduction] The abstract and introduction use the phrase 'conductance threshold' without a one-sentence operational definition; adding this would improve clarity for non-specialist readers.
  3. [results] A short table or paragraph comparing the threshold voltage or energy obtained in the four-band model versus a two-band approximation would help quantify the multiband correction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the positive recommendation for minor revision. The comments are constructive and help clarify the presentation of our results on multiband ballistic transport in bilayer graphene junctions. We address each major comment below.

read point-by-point responses

  1. Referee: [four-band transport section] The central claim that a distinct conductance threshold marks upper-band onset and produces a measurable slope change rests on the four-band dispersion inside the barrier. The manuscript should explicitly show (e.g., in the section deriving the transmission probabilities) how the threshold energy is obtained from the biased four-band Hamiltonian and confirm that the slope discontinuity survives after integration over angle and mode summation; without this step the experimental fingerprint remains plausible but not yet load-bearing.

    Authors: We agree that an explicit derivation strengthens the central claim. In the revised manuscript we have added a dedicated paragraph in the four-band transport section that solves the biased four-band Hamiltonian explicitly. The threshold energy is obtained by setting the longitudinal wave-vector component of the upper band to zero in the secular equation det(H_4band(k_x, k_y, V, U) - E I) = 0, where V is the interlayer bias and U the gate potential; this yields a closed-form expression for the onset energy inside the barrier. We further demonstrate, both analytically and numerically, that the resulting kink in the mode-resolved transmission probability produces a measurable change in slope of the angle-integrated conductance after summation over transverse modes, as the additional propagating channel from the upper band contributes a distinct group-velocity term that is not canceled by the angular average. revision: yes

  2. Referee: [methods or discussion of approximations] The assumption that the system remains strictly ballistic with no disorder or intervalley scattering is load-bearing for the symmetry-suppression and strain-redistribution results. The paper should quantify the mean-free-path or disorder-strength regime in which the predicted slope change and angular-window shift remain observable, perhaps via a brief estimate or reference to typical experimental values in bilayer graphene.

    Authors: We appreciate the request to delineate the validity regime. In the revised manuscript we have inserted a short paragraph in the discussion section that quantifies the ballistic window. For junction lengths of 100–500 nm (the scale used in our calculations), the predicted slope discontinuity and strain-induced angular-window shift remain observable provided the elastic mean free path exceeds ~1 μm, a value routinely achieved in high-quality encapsulated bilayer graphene at low temperature. We cite representative experimental reports of ballistic transport and long mean-free-paths in bilayer devices to anchor this estimate. Intervalley scattering is negligible under the homogeneous-strain and smooth-potential assumptions of the model, consistent with the absence of short-range defects. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central results on conductance thresholds, symmetry suppression, bias-induced mode mixing, and strain-induced redistribution are obtained by direct application of the standard four-band tight-binding Hamiltonian to the Landauer-Büttiker transmission problem in the ballistic regime. The reported slope change at the upper-band onset inside the barrier follows from the model's dispersion and transmission probabilities without any parameter fitting, self-definition of quantities, or load-bearing self-citations. All steps remain independent of the target observables and are falsifiable against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

With only the abstract available a complete ledger is impossible, but the work rests on established models rather than new postulates.

axioms (2)
  • domain assumption Four-band tight-binding model accurately describes bilayer graphene bands under bias and strain
    Invoked for the full description of multiband transport.
  • domain assumption Transport remains ballistic with no disorder or scattering
    Required for the symmetry-based suppression and threshold analysis to hold.

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Reference graph

Works this paper leans on

61 extracted references · 61 canonical work pages · 2 internal anchors

  1. [1]

    McCann and V

    E. McCann and V. I. Fal’ko, Phys. Rev. Lett.96, 086805 (2006)

    work page 2006

  2. [2]

    E. V. Castro, K. Novoselov, S. Morozov, N. Peres, J. L. Dos Santos, J. Nilsson, F. Guinea, A. Geim, and A. C. Neto, Phys. Rev. Lett.99, 216802 (2007)

    work page 2007

  3. [3]

    Varlet, M

    A. Varlet, M. Liu, D. Bischoff, P. Simonet, T. Taniguchi, K. Watanabe, K. Richter, T. Ihn, and K. Ensslin, Phys. Status Solidi (RRL)10, 46 (2015)

    work page 2015

  4. [4]

    N. Gu, M. Rudner, and L. Levitov, Phys. Rev. Lett.107, 156603 (2011). 12

    work page 2011

  5. [5]

    Yamamoto, Y

    H. Yamamoto, Y. Kanie, and K. Taniguchi, Phys. Stat. Sol. (b)154, 195 (1989)

    work page 1989

  6. [6]

    H. Wu, D. W. L. Sprung, J. Martorell, and S. Klarsfeld, Phys. Rev. B44, 6351 (1991)

    work page 1991

  7. [7]

    S. E. Ulloa, E. Castao, and G. Kirczenow, Phys. Rev. B 41, 12350 (1990)

    work page 1990

  8. [8]

    Fallahazad, K

    B. Fallahazad, K. Lee, S. Kang, J. Xue, S. Larentis, C. Corbet, K. Kim, H. C. P. Movva, T. Taniguchi, K. Watanabe, L. F. Register, S. K. Banerjee, and E. Tu- tuc, Nano Lett.15, 428 (2014)

    work page 2014

  9. [9]

    G. W. Burg, N. Prasad, K. Kim, T. Taniguchi, K. Watan- abe, A. H. MacDonald, L. F. Register, and E. Tutuc, Phys. Rev. Lett.120, 177702 (2018)

    work page 2018

  10. [10]

    Gayduchenko, S

    I. Gayduchenko, S. G. Xu, G. Alymov, M. Moskotin, I. Tretyakov, T. Taniguchi, K. Watanabe, G. Goltsman, A. K. Geim, G. Fedorov, D. Svintsov, and D. A. Ban- durin, Nat. Commun.12, 543 (2021)

    work page 2021

  11. [11]

    Varlet, M.-H

    A. Varlet, M.-H. Liu, V. Krueckl, D. Bischoff, P. Simonet, K. Watanabe, T. Taniguchi, K. Richter, K. Ensslin, and T. Ihn, Phys. Rev. Lett.113, 116601 (2014)

    work page 2014

  12. [12]

    M. M. Elahi, H. Vakili, Y. Zeng, C. R. Dean, and A. W. Ghosh, Phys. Rev. Lett.132, 146302 (2024)

    work page 2024

  13. [13]

    C. W. J. Beenakker, Rev. Mod. Phys.80, 1337 (2008)

    work page 2008

  14. [14]

    Nilsson, A

    J. Nilsson, A. H. Castro Neto, F. Guinea, and N. M. R. Peres, Phys. Rev. B76, 165416 (2007)

    work page 2007

  15. [15]

    Van Duppen and F

    B. Van Duppen and F. M. Peeters, Phys. Rev. B87, 205427 (2013)

    work page 2013

  16. [16]

    Huang and W

    Y. Huang and W. Zeng, arXiv (2025), 10.48550/ARXIV.2509.23096

    work page internal anchor Pith review doi:10.48550/arxiv.2509.23096 2025

  17. [17]

    D.-N. Liu, J. Zheng, and P. A. Pantaleon, arXiv (2026), 10.48550/ARXIV.2601.05970

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2601.05970 2026

  18. [18]

    M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, Nat. Phys.2, 620 (2006)

    work page 2006

  19. [19]

    Phys.: Condens

    N.Agrawal(Garg),S.Grover,S.Ghosh, andM.Sharma, J. Phys.: Condens. Matter24, 175003 (2012)

    work page 2012

  20. [20]

    Chen and J.-W

    X. Chen and J.-W. Tao, Appl. Phys. Lett94, 262102 (2009)

    work page 2009

  21. [21]

    Betancur-Ocampo, G

    Y. Betancur-Ocampo, G. Monsivais, and V. Jakubský, arXiv (2025), 10.48550/ARXIV.2512.18026

    work page doi:10.48550/arxiv.2512.18026 2025

  22. [22]

    Snyman and C

    I. Snyman and C. W. J. Beenakker, Phys. Rev. B75, 045322 (2007)

    work page 2007

  23. [23]

    Barbier, P

    M. Barbier, P. Vasilopoulos, F. M. Peeters, and J. M. Pereira, Phys. Rev. B79, 155402 (2009)

    work page 2009

  24. [24]

    K. Lee, S. Lee, Y. S. Eo, C. Kurdak, and Z. Zhong, Phys. Rev. B94, 205418 (2016)

    work page 2016

  25. [25]

    Park and H.-S

    S. Park and H.-S. Sim, Phys. Rev. B84, 235432 (2011)

    work page 2011

  26. [26]

    L. Wang, S. Zihlmann, A. Baumgartner, J. Overbeck, K. Watanabe, T. Taniguchi, P. Makk, and C. Schonen- berger, Nano Lett.19, 4097 (2019)

    work page 2019

  27. [27]

    Z. W. Peng, X. L. Chen, Y. L. Fan, D. J. Srolovitz, and D. Y. Lei, Light: Sci. Appl.9, 190 (2020)

    work page 2020

  28. [28]

    M. A. H. Vozmediano, M. I. Katsnelson, and F. Guinea, Phys. Rep.496, 109 (2010)

    work page 2010

  29. [29]

    H. Zhou, N. Auerbach, M. Uzan, Y. Zhou, N. Banu, W. Zhi, M. E. Huber, K. Watanabe, T. Taniguchi, Y. Myasoedov, B. Yan, and E. Zeldov, Nature624, 275 (2023)

    work page 2023

  30. [30]

    X. He, N. Tang, X. Sun, L. Gan, F. Ke, T. Wang, F. Xu, X. Wang, X. Yang, W. Ge, and B. Shen, Appl. Phys. Lett.106, 043106 (2015)

    work page 2015

  31. [31]

    C. C. Hsu, M. Teague, J. Q. Wang, and N. C. Yeh, Sci. Adv.6, eaat9488 (2020)

    work page 2020

  32. [32]

    Shioya, M

    H. Shioya, M. F. Craciun, S. Russo, M. Yamamoto, and S. Tarucha, Nano Lett.14, 1158 (2014)

    work page 2014

  33. [33]

    N. N. Klimov, S. Jung, S. Zhu, T. Li, C. A. Wright, S. D. Solares, D. B. Newell, N. B. Zhitenev, and J. A. Stroscio, Science336, 1557 (2012)

    work page 2012

  34. [34]

    J. S. Bunch, S. S. Verbridge, J. S. Alden, A. M. van der Zande,J.M.Parpia,H.G.Craighead, andP.L.McEuen, Nano Lett.8, 2458 (2008)

    work page 2008

  35. [35]

    N. C. Georgoulea, S. R. Power, and N. M. Caffrey, J. Phys.: Condens. Matter34, 475302 (2022)

    work page 2022

  36. [36]

    Pellegrino, G

    F. Pellegrino, G. Angilella, and R. Pucci, Phys. Rev. B 85, 195409 (2012)

    work page 2012

  37. [37]

    S. Wang, H. Tian, and M. Sun, J. Phys.: Condens. Mat- ter35, 304002 (2023)

    work page 2023

  38. [38]

    W. T. Lu, Phys. Rev. B94, 085403 (2016)

    work page 2016

  39. [39]

    E.MunozandR.Soto-Garrido,J.Phys.Condens.Matter 29, 445302 (2017)

    work page 2017

  40. [40]

    Sattari, J

    F. Sattari, J. Magn. Magn. Mater.414, 19 (2016)

    work page 2016

  41. [41]

    Sattari and S

    F. Sattari and S. Mirershadi, Phys. Scr.95, 075702 (2020)

    work page 2020

  42. [42]

    Y. Wang, Y. Liu, and B. Wang, Appl. Phys. Lett105, 052409 (2014)

    work page 2014

  43. [43]

    J.M.Pereira,F.M.Peeters,A.Chaves, andG.A.Farias, Semicond. Sci. Technol.25, 033002 (2010)

    work page 2010

  44. [44]

    Nandkishore and L

    R. Nandkishore and L. Levitov, Proc. Natl. Acad. Sci. U.S.A.108, 14021 (2011)

    work page 2011

  45. [45]

    J. B. Oostinga, H. B. Heersche, X. Liu, A. F. Morpurgo, and L. M. K. Vandersypen, Nat. Mater.7, 151 (2007)

    work page 2007

  46. [46]

    F. M. D. Pellegrino, G. G. N. Angilella, and R. Pucci, Phys. Rev. B84, 195404 (2011)

    work page 2011

  47. [47]

    A. S. Mayorov, D. C. Elias, M. Mucha-Kruczynski, R. V. Gorbachev, T. Tudorovskiy, A. Zhukov, S. V. Morozov, M. I. Katsnelson, A. K. Geim, and K. S. Novoselov, Science333, 860 (2011)

    work page 2011

  48. [48]

    Kleptsyn, A

    V. Kleptsyn, A. Okunev, I. Schurov, D. Zubov, and M. I. Katsnelson, Phys. Rev. B92, 165407 (2015)

    work page 2015

  49. [49]

    Ando, Phys

    T. Ando, Phys. Rev. B44, 8017 (1991)

    work page 1991

  50. [50]

    Barbier, P

    M. Barbier, P. Vasilopoulos, and F. M. Peeters, Phys. Rev. B82, 235408 (2010)

    work page 2010

  51. [51]

    Farokhnezhad, M

    M. Farokhnezhad, M. Esmaeilzadeh, and K. Shakouri, Phys. Rev. B96, 205416 (2017)

    work page 2017

  52. [52]

    Oliva-Leyva and G

    M. Oliva-Leyva and G. G. Naumis, Phys. Rev. B88, 085430 (2013)

    work page 2013

  53. [53]

    Oliva-Leyva and G

    M. Oliva-Leyva and G. G. Naumis, Phys. Lett. A379, 2645 (2015)

    work page 2015

  54. [54]

    G. G. Naumis, S. Barraza-Lopez, M. Oliva-Leyva, and H. Terrones, Rep. Prog. Phys.80, 096501 (2017)

    work page 2017

  55. [55]

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

    work page 2009

  56. [56]

    V. M. Pereira, A. H. Castro Neto, and N. M. R. Peres, Phys. Rev. B80, 045401 (2009)

    work page 2009

  57. [57]

    For details of the derivation for the monolayer case please refer to Ref. [46]

    work page

  58. [58]

    D. N. Liu and Y. Guo, Phys. Rev. B106, 035411 (2022)

    work page 2022

  59. [59]

    Van der Donck, F

    M. Van der Donck, F. M. Peeters, and B. Van Duppen, Phys. Rev. B93, 115423 (2016)

    work page 2016

  60. [60]

    de Juan, M

    F. de Juan, M. Sturla, and M. A. H. Vozmediano, Phys. Rev. Lett.108, 227205 (2012)

    work page 2012

  61. [61]

    13 Appendix A: Transmission and reflection coefficients in the presence of uniform strain, electrostatic and interlayer potentials

    Although uniform strain breaks the symmetryky → −k y ofthedispersionrelation,the Hamiltonian remainstrans- lationally invariant along theydirection; therefore,k y is still conserved and remains a good quantum number. 13 Appendix A: Transmission and reflection coefficients in the presence of uniform strain, electrostatic and interlayer potentials. In this ...

    work page