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Mode-resolved multiband ballistic transport and conductance thresholds in bilayer graphene junctions
Phys. Rev. Applied 26, 014064 – Published 21 July, 2026
DOI: https://doi.org/10.1103/zw2l-bkwp
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. Notably, 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.
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References (68)
- E. McCann and V. I. Fal’ko, Landau-level degeneracy and quantum hall effect in a graphite bilayer, Phys. Rev. Lett. 96, 086805 (2006).
- E. V. Castro, K. S. Novoselov, S. V. Morozov, N. M. R. Peres, J. M. B. L. dos Santos, J. Nilsson, F. Guinea, A. K. Geim, and A. H. C. Neto, Biased bilayer graphene: Semiconductor with a gap tunable by the electric field effect, Phys. Rev. Lett. 99, 216802 (2007).
- A. Varlet, M-Hao Liu, D. Bischoff, P. Simonet, T. Taniguchi, K. Watanabe, K. Richter, T. Ihn, and K. Ensslin, Band gap and broken chirality in single-layer and bilayer graphene, Phys. Status Solidi 10, 46 (2015).
- N. Gu, M. Rudner, and L. Levitov, Chirality-assisted electronic cloaking of confined states in bilayer graphene, Phys. Rev. Lett. 107, 156603 (2011).
- H. Yamamoto, Y. Kanie, and K. Taniguchi, Transmission coefficient and resonance condition in rectangular -fold barrier structures, Phys. Status Solidi (b) 154, 195 (1989).
- H. Wu, D. W. L. Sprung, J. Martorell, and S. Klarsfeld, Quantum wire with periodic serial structure, Phys. Rev. B 44, 6351 (1991).
- S. E. Ulloa, E. Castao, and G. Kirczenow, Ballistic transport in a novel one-dimensional superlattice, Phys. Rev. B 41, 12350 (1990).
- 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. Tutuc, Gate-tunable resonant tunneling in double bilayer graphene heterostructures, Nano Lett. 15, 428 (2014).
- G. W. Burg, N. Prasad, K. Kim, T. Taniguchi, K. Watanabe, A. H. MacDonald, L. F. Register, and E. Tutuc, Strongly enhanced tunneling at total charge neutrality in double-bilayer graphene- heterostructures, Phys. Rev. Lett. 120, 177702 (2018).
- 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. Bandurin, Tunnel field-effect transistors for sensitive terahertz detection, Nat. Commun. 12, 543 (2021).
- A. Varlet, M.-H. Liu, V. Krueckl, D. Bischoff, P. Simonet, K. Watanabe, T. Taniguchi, K. Richter, K. Ensslin, and T. Ihn, Fabry-pérot interference in gapped bilayer graphene with broken anti-klein tunneling, Phys. Rev. Lett. 113, 116601 (2014).
- M. M. Elahi, H. Vakili, Y. Zeng, C. R. Dean, and A. W. Ghosh, Direct evidence of Klein and anti-Klein tunneling of graphitic electrons in a corbino geometry, Phys. Rev. Lett. 132, 146302 (2024).
- C. W. J. Beenakker, Colloquium: Andreev reflection and Klein tunneling in graphene, Rev. Mod. Phys. 80, 1337 (2008).
- J. Nilsson, A. H. Castro Neto, F. Guinea, and N. M. R. Peres, Transmission through a biased graphene bilayer barrier, Phys. Rev. B 76, 165416 (2007).
- B. Van Duppen and F. M. Peeters, Four-band tunneling in bilayer graphene, Phys. Rev. B 87, 205427 (2013).
- Y. Huang and W. Zeng, Evanescent-mode-assisted Klein tunneling in dual-gated bilayer graphene, arXiv:2509.23096.
- D.-N. Liu, J. Zheng, and P. A. Pantaleón, Mode-selective cloaking and phase-matching cavity resonances in bilayer graphene transport, Phys. Rev. B 113, 165412 (2026).
- M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, Chiral tunnelling and the klein paradox in graphene, Nat. Phys. 2, 620 (2006).
- N. Agrawal (Garg), S. Grover, S. Ghosh, and M. Sharma, Reversal of Klein reflection by magnetic barriers in bilayer graphene, J. Phys. Condens. Matter 24, 175003 (2012).
- X. Chen and J.-W. Tao, Design of electron wave filters in monolayer graphene by tunable transmission gap, Appl. Phys. Lett. 94, 262102 (2009).
- Y. Betancur-Ocampo, G. Monsivais, and V. Jakubský, Topical review: The rise of klein tunneling in low-dimensional materials and superlattices, J. Phys. Condens. Matter, 38, 163002 (2025).
- I. Snyman and C. W. J. Beenakker, Ballistic transmission through a graphene bilayer, Phys. Rev. B 75, 045322 (2007).
- M. B. Barbier, P. Vasilopoulos, F. M. Peeters, and J. M. Pereira, Bilayer graphene with single and multiple electrostatic barriers: Band structure and transmission, Phys. Rev. B 79, 155402 (2009).
- K. Lee, S. Lee, Y. S. Eo, C. Kurdak, and Z. Zhong, Evidence of electronic cloaking from chiral electron transport in bilayer graphene nanostructures, Phys. Rev. B 94, 205418 (2016).
- S. Park and H.-S. Sim, berry phase and veselago lens in a bilayer graphene junction, Phys. Rev. B 84, 235432 (2011).
- L. Wang, S. Zihlmann, A. Baumgartner, J. Overbeck, K. Watanabe, T. Taniguchi, P. Makk, and C. Schonenberger, In situ strain tuning in -encapsulated graphene electronic devices, Nano Lett. 19, 4097 (2019).
- Z. Peng, X. Chen, Y. Fan, D. J. Srolovitz, and D. Lei, Strain engineering of 2D semiconductors and graphene: from strain fields to band-structure tuning and photonic applications, Light Sci. Appl. 9, 190 (2020).
- M. A. H. Vozmediano, M. I. Katsnelson, and F. Guinea, Gauge fields in graphene, Phys. Rep. 496, 109 (2010).
- 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, Imaging quantum oscillations and millitesla pseudomagnetic fields in graphene, Nature (London) 624, 275 (2023).
- X. He, N. Tang, X. Sun, L. Gan, F. Ke, T. Wang, F. Xu, X. Wang, X. Yang, W. Ge, and B. Shen, Tuning the graphene work function by uniaxial strain, Appl. Phys. Lett. 106, 043106 (2015).
- C.-C. Hsu, M. L. Teague, J.-Q. Wang, and N.-C. Yeh, Nanoscale strain engineering of giant pseudo-magnetic fields, valley polarization, and topological channels in graphene, Sci. Adv. 6, eaat9488 (2020).
- H. Shioya, M. F. Craciun, S. Russo, M. Yamamoto, and S. Tarucha, Straining graphene using thin film shrinkage methods, Nano Lett. 14, 1158 (2014).
- 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, Electromechanical properties of graphene drumheads, Science 336, 1557 (2012).
- J. S. Bunch, S. S. Verbridge, J. S. Alden, A. M. van der Zande, J. M. Parpia, H. G. Craighead, and P. L. McEuen, Impermeable atomic membranes from graphene sheets, Nano Lett. 8, 2458 (2008).
- N. C. Georgoulea, S. R. Power, and N. M. Caffrey, Strain-induced stacking transition in bilayer graphene, J. Phys. Condens. Matter 34, 475302 (2022).
- F. M. D. Pellegrino, G. G. N. Angilella, and R. Pucci, Resonant modes in strain-induced graphene superlattices, Phys. Rev. B 85, 195409 (2012).
- S. Wang, H. Tian, and M. Sun, Valley-polarized and enhanced transmission in graphene with a smooth strain profile, J. Phys. Condens. Matter 35, 304002 (2023).
- W. T. Lu, Valley-dependent band structure and valley polarization in periodically modulated graphene, Phys. Rev. B 94, 085403 (2016).
- E. Muñoz and R. Soto-Garrido, Analytic approach to magneto-strain tuning of electronic transport through a graphene nanobubble: Perspectives for a strain sensor, J. Phys. Condens. Matter 29, 445302 (2017).
- F. Sattari, Spin transport in graphene superlattice under strain, J. Magn. Magn. Mater. 414, 19 (2016).
- F. Sattari and S. Mirershadi, Tunneling time and transmission properties in strained graphene with a time-oscillating potential, Phys. Scr. 95, 075702 (2020).
- Y. Wang, Y. Liu, and B. Wang, Graphene spin diode: Strain-modulated spin rectification, Appl. Phys. Lett. 105, 052409 (2014).
- F. M. D. Pellegrino, G. G. N. Angilella, and R. Pucci, Transport properties of graphene across strain-induced nonuniform velocity profiles, Phys. Rev. B 84, 195404 (2011).
- J. M. Pereira Jr, F. M. Peeters, A. Chaves, and G. A. Farias, Klein tunneling in single and multiple barriers in graphene, Semicond. Sci. Technol. 25, 033002 (2010).
- R. Nandkishore and L. Levitov, Common-path interference and oscillatory zener tunneling in bilayer graphene p-n junctions, Proc. Natl. Acad. Sci. U.S.A. 108, 14021 (2011).
- J. B. Oostinga, H. B. Heersche, X. Liu, A. F. Morpurgo, and L. M. K. Vandersypen, Gate-induced insulating state in bilayer graphene devices, Nat. Mater. 7, 151 (2007).
- 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, Interaction-driven spectrum reconstruction in bilayer graphene, Science 333, 860 (2011).
- V. Kleptsyn, A. Okunev, I. Schurov, D. Zubov, and M. I. Katsnelson, Chiral tunneling through generic one-dimensional potential barriers in bilayer graphene, Phys. Rev. B 92, 165407 (2015).
- T. Ando, Quantum point contacts in magnetic fields, Phys. Rev. B 44, 8017 (1991).
- M. Barbier, P. Vasilopoulos, and F. M. Peeters, Kronig-penney model on bilayer graphene: Spectrum and transmission periodic in the strength of the barriers, Phys. Rev. B 82, 235408 (2010).
- M. Farokhnezhad, M. Esmaeilzadeh, and K. Shakouri, Strain-modulated anisotropy of quantum transport properties in single-layer silicene: Spin and valley filtering, Phys. Rev. B 96, 205416 (2017).
- M. Oliva-Leyva and G. G. Naumis, Understanding electron behavior in strained graphene as a reciprocal space distortion, Phys. Rev. B 88, 085430 (2013).
- M. Oliva-Leyva and G. G. Naumis, Generalizing the fermi velocity of strained graphene from uniform to nonuniform strain, Phys. Lett. A 379, 2645 (2015).
- G. G. Naumis, S. Barraza-Lopez, M. Oliva-Leyva, and H. Terrones, Electronic and optical properties of strained graphene and other strained 2d materials: A review, Rep. Prog. Phys. 80, 096501 (2017).
- A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009).
- V. M. Pereira, A. H. Castro Neto, and N. M. R. Peres, Tight-binding approach to uniaxial strain in graphene, Phys. Rev. B 80, 045401 (2009).
For details of the derivation for the monolayer case please refer to Ref. [43].
- D.-N. Liu and Y. Guo, Pure valley current and negative differential resistance in optoelectronic superlattices based on monolayer transition metal dichalcogenides, Phys. Rev. B 106, 035411 (2022).
- M. Van der Donck, F. M. Peeters, and B. Van Duppen, Transport properties of bilayer graphene in a strong in-plane magnetic field, Phys. Rev. B 93, 115423 (2016).
- F. de Juan, M. Sturla, and M. D. A. H. Vozmediano, Space dependent fermi velocity in strained graphene, Phys. Rev. Lett. 108, 227205 (2012).
Although uniform strain breaks the symmetry of the dispersion relation, the Hamiltonian remains translationally invariant along the direction; therefore, is still conserved and remains a good quantum number.
- Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening, ACS Nano 2, 2301 (2008).
- T. M. G. Mohiuddin, A. Lombardo, R. R. Nair, A. Bonetti, G. Savini, R. Jalil, N. Bonini, D. M. Basko, C. Galiotis, N. Marzari, K. S. Novoselov, A. K. Geim, and A. C. Ferrari, Uniaxial strain in graphene by raman spectroscopy g peak splitting, grüneisen parameters, and sample orientation, Phys. Rev. B 79, 205433 (2009).
- N. Levy, S. A. Burke, K. L. Meaker, M. Panlasigui, A. Zettl, F. Guinea, A. H. C. Neto, and M. F. Crommie, Strain-induced pseudo–magnetic fields greater than 300 tesla in graphene nanobubbles, Science 329, 544 (2010).
- W. Yan, W.-Y. He, Z.-D. Chu, M. Liu, L. Meng, R.-F. Dou, Y. Zhang, Z. Liu, J.-C. Nie, and L. He, Strain and curvature induced evolution of electronic band structures in twisted graphene bilayer, Nat. Commun. 4, 2159 (2013).
- D.-H. Kang, H. Sun, M. Luo, K. Lu, M. Chen, Y. Kim, Y. Jung, X. Gao, S. J. Parluhutan, J. Ge, S. W. Koh, D. Giovanni, T. C. Sum, Q. J. Wang, H. Li, and D. Nam, Pseudo-magnetic field-induced slow carrier dynamics in periodically strained graphene, Nat. Commun. 12, 5087 (2021).
- R. Banerjee, V.-H. Nguyen, T. Granzier-Nakajima, L. Pabbi, A. Lherbier, A. R. Binion, J.-C. Charlier, M. Terrones, and E. W. Hudson, Strain modulated superlattices in graphene, Nano Lett. 20, 3113 (2020).
- D. A. Bahamon and V. M. Pereira, Conductance across strain junctions in graphene nanoribbons, Phys. Rev. B 88, 195416 (2013).