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  • Letter
  • Open Access

Quantum interference tuning of spin-orbit coupling in twisted van der Waals trilayers

Csaba G. Péterfalvi1,*, Alessandro David2, Péter Rakyta3,4, Guido Burkard1,†, and Andor Kormányos3,‡

  • 1Department of Physics, University of Konstanz, D-78464 Konstanz, Germany
  • 2Peter Grünberg Institute - Quantum Control (PGI-8), Forschungszentrum Jülich GmbH, Jülich, Germany
  • 3Department of Physics of Complex Systems, Eötvös Loránd University, Budapest, Hungary
  • 4Quantum Information National Laboratory, Hungary

  • *csaba.peterfalvi@uni-konstanz.de
  • †guido.burkard@uni-konstanz.de
  • ‡andor.kormanyos@ttk.elte.hu

Phys. Rev. Research 4, L022049 – Published 31 May, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L022049

Abstract

We show that in van der Waals stacks of twisted hexagonal layers the proximity induced Rashba spin-orbit coupling can be affected by quantum interference. We calculate the quantum phase responsible for this effect in graphene–transition metal dichalcogenide bilayers as a function of interlayer twist angle. We show how this quantum phase affects the spin polarization of the graphene bands and discuss its potential effect on spin-to-charge conversion measurements. In twisted trilayers symmetries can be broken as well as restored for certain twist angles. This can be used to deduce the effects of induced spin-orbit coupling on spin-lifetime anisotropy and magnetoconductance measurements.

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References (73)

  1. M. Yankowitz, J. Xue, D. Cormode, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, P. Jacquod, and B. J. LeRoy, Emergence of superlattice Dirac points in graphene on hexagonal boron nitride, Nat. Phys. 8, 382 (2012).
  2. L. A. Ponomarenko, R. V. Gorbachev, G. L. Yu, D. C. Elias, R. Jalil, A. A. Patel, A. Mishchenko, A. S. Mayorov, C. R. Woods, J. R. Wallbank, M. Mucha-Kruczynski, B. A. Piot, M. Potemski, I. V. Grigorieva, K. S. Novoselov, F. Guinea, V. I. Fal'ko, and A. K. Geim, Cloning of Dirac fermions in graphene superlattices, Nature (London) 497, 594 (2013).
  3. B. Hunt, J. D. Sanchez-Yamagishi, A. F. Young, M. Yankowitz, B. J. LeRoy, K. Watanabe, T. Taniguchi, P. Moon, M. Koshino, P. Jarillo-Herrero, and R. C. Ashoori, Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure, Science 340, 1427 (2013).
  4. R. Ribeiro-Palau, C. Zhang, K. Watanabe, T. Taniguchi, J. Hone, and C. R. Dean, Twistable electronics with dynamically rotatable heterostructures, Science 361, 690 (2018).
  5. Z. Wang, D.-K. Ki, H. Chen, H. Berger, A. H. MacDonald, and A. F. Morpurgo, Strong interface-induced spin-orbit interaction in graphene on WS2, Nat. Commun. 6, 8339 (2015).
  6. Z. Wang, D.-K. Ki, J. Y. Khoo, D. Mauro, H. Berger, L. S. Levitov, and A. F. Morpurgo, Origin and Magnitude of ‘Designer’ Spin-Orbit Interaction in Graphene on Semiconducting Transition Metal Dichalcogenides, Phys. Rev. X 6, 041020 (2016).
  7. B. Yang, M.-F. Tu, J. Kim, Y. Wu, H. Wang, J. Alicea, R. Wu, M. Bockrath, and J. Shi, Tunable spin-orbit coupling and symmetry-protected edge states in graphene/WS2, 2D Mater. 3, 031012 (2016).
  8. R. Bistritzer and A. H. MacDonald, Moiré bands in twisted double-layer graphene, Proc. Natl. Acad. Sci. USA 108, 12233 (2011).
  9. Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional superconductivity in magic-angle graphene superlattices, Nature (London) 556, 43 (2018).
  10. H. S. Arora, R. Polski, Y. Zhang, A. Thomson, Y. Choi, H. Kim, Z. Lin, I. Z. Wilson, X. Xu, J.-H. Chu, K. Watanabe, T. Taniguchi, J. Alicea, and S. Nadj-Perge, Superconductivity in metallic twisted bilayer graphene stabilized by WSe2, Nature (London) 583, 379 (2020).
  11. J.-X. Lin, Y.-H. Zhang, E. Morissette, Z. Wang, S. Liu, D. Rhodes, K. Watanabe, T. Taniguchi, J. Hone, and J. I. A. Li, Spin-orbit-driven ferromagnetism at half moiré filling in magic-angle twisted bilayer graphene, Science 375, 437 (2022).
  12. J. O. Island, X. Cui, C. Lewandowski, J. Y. Khoo, E. M. Spanton, H. Zhou, D. Rhodes, J. C. Hone, T. Taniguchi, K. Watanabe, L. S. Levitov, M. P. Zaletel, and A. F. Young, Spin–orbit-driven band inversion in bilayer graphene by the van der Waals proximity effect, Nature (London) 571, 85 (2019).
  13. J. Y. Khoo, A. F. Morpurgo, and L. Levitov, On-demand spin-orbit interaction from which-layer tunability in bilayer graphene, Nano Lett. 17, 7003 (2017).
  14. M. Gmitra and J. Fabian, Proximity Effects in Bilayer Graphene on Monolayer WSe2: Field-Effect Spin Valley Locking, Spin-Orbit Valve, and Spin Transistor, Phys. Rev. Lett. 119, 146401 (2017).
  15. D. Wang, S. Che, G. Cao, R. Lyu, K. Watanabe, T. Taniguchi, C. N. Lau, and M. Bockrath, Quantum Hall effect measurement of spin-orbit coupling strengths in ultraclean bilayer graphene/WSe2 heterostructures, Nano Lett. 19, 7028 (2019).
  16. P. Tiwari, S. K. Srivastav, and A. Bid, Electric-Field-Tunable Valley Zeeman Effect in Bilayer Graphene Heterostructures: Realization of the Spin-Orbit Valve Effect, Phys. Rev. Lett. 126, 096801 (2021).
  17. Z. Wang, Y. B. Wang, J. Yin, E. Tóvári, Y. Yang, L. Lin, M. Holwill, J. Birkbeck, D. J. Perello, S. Xu, J. Zultak, R. V. Gorbachev, A.V. Kretinin, T. Taniguchi, K. Watanabe, S. V. Morozov, M. Andjelković, S.P. Milovanović, L. Covaci, F. M. Peeters et al., Composite super-moiré lattices in double-aligned graphene heterostructures, Sci. Adv. 5, eaay8897 (2019).
  18. Z. Zhu, P. Cazeaux, M. Luskin, and E. Kaxiras, Modeling mechanical relaxation in incommensurate trilayer van der Waals heterostructures, Phys. Rev. B 101, 224107 (2020).
  19. L. Wang, S. Zihlmann, M.-H. Liu, P. Makk, K. Watanabe, T. Taniguchi, A. Baumgartner, and C. Schönenberger, New generation of moiré superlattices in doubly aligned hBN/graphene/hBN heterostructures, Nano Lett. 19, 2371 (2019).
  20. D. M. Kennes, M. Claassen, L. Xian, A. Georges, A. J. Millis, J. Hone, C. R. Dean, D. N. Basov, A. N. Pasupathy, and A. Rubio, Moiré heterostructures as a condensed-matter quantum simulator, Nat. Phys. 17, 155 (2021).
  21. B. Yang, M. Lohmann, D. Barroso, I. Liao, Z. Lin, Y. Liu, L. Bartels, K. Watanabe, T. Taniguchi, and J. Shi, Strong electron-hole symmetric Rashba spin-orbit coupling in graphene/monolayer transition metal dichalcogenide heterostructures, Phys. Rev. B 96, 041409(R) (2017).
  22. T. Völkl, T. Rockinger, M. Drienovsky, K. Watanabe, T. Taniguchi, D. Weiss, and J. Eroms, Magnetotransport in heterostructures of transition metal dichalcogenides and graphene, Phys. Rev. B 96, 125405 (2017).
  23. S. Zihlmann, A. W. Cummings, J. H. Garcia, M. Kedves, K. Watanabe, T. Taniguchi, C. Schönenberger, and P. Makk, Large spin relaxation anisotropy and valley-Zeeman spin-orbit coupling in WSe2/graphene/hBN heterostructures, Phys. Rev. B 97, 075434 (2018).
  24. T. Wakamura, F. Reale, P. Palczynski, S. Guéron, C. Mattevi, and H. Bouchiat, Strong Anisotropic Spin-Orbit Interaction Induced in Graphene by Monolayer WS2, Phys. Rev. Lett. 120, 106802 (2018).
  25. T. Wakamura, F. Reale, P. Palczynski, M. Q. Zhao, A. T. C. Johnson, S. Guéron, C. Mattevi, A. Ouerghi, and H. Bouchiat, Spin-orbit interaction induced in graphene by transition metal dichalcogenides, Phys. Rev. B 99, 245402 (2019).
  26. T. S. Ghiasi, J. Ingla-Aynés, A. A. Kaverzin, and B. J. van Wees, Large proximity-induced spin lifetime anisotropy in transition-metal dichalcogenide/graphene heterostructures, Nano Lett. 17, 7528 (2017).
  27. J. C. Leutenantsmeyer, J. Ingla-Aynés, J. Fabian, and B. J. van Wees, Observation of Spin-Valley-Coupling-Induced Large Spin-Lifetime Anisotropy in Bilayer Graphene, Phys. Rev. Lett. 121, 127702 (2018).
  28. L. A. Benítez, J. F. Sierra, W. S. Torres, A. Arrighi, F. Bonell, M. V. Costache, and S. O. Valenzuela, Strongly anisotropic spin relaxation in graphene-transition metal dichalcogenide heterostructures at room temperature, Nat. Phys. 14, 303 (2018).
  29. J. Xu, T. Zhu, Y. K. Luo, Y.-M. Lu, and R. K. Kawakami, Strong and Tunable Spin-Lifetime Anisotropy in Dual-Gated Bilayer Graphene, Phys. Rev. Lett. 121, 127703 (2018).
  30. C. K. Safeer, J. Ingla-Aynés, F. Herling, J. H. Garcia, M. Vila, N. Ontoso, M. R. Calvo, S. Roche, L. E. Hueso, and F. Casanova, Room-temperature spin Hall effect in graphene/MoS2 van der Waals heterostructures, Nano Lett. 19, 1074 (2019).
  31. F. Herling, C. K. Safeer, J. Ingla-Aynés, N. Ontoso, L. E. Hueso, and F. Casanova, Gate tunability of highly efficient spin-to-charge conversion by spin Hall effect in graphene proximitized with WSe2, APL Mater. 8, 071103 (2020).
  32. L. A. Benítez, W. Savero Torres, J. F. Sierra, M. Timmermans, J. H. Garcia, S. Roche, M. V. Costache, and S. O. Valenzuela, Tunable room-temperature spin galvanic and spin Hall effects in van der Waals heterostructures, Nat. Mater. 19, 170 (2020).
  33. A. Md. Hoque, D. Khokhriakov, B. Karpiak, and S. P. Dash, Charge-spin conversion in layered semimetal TaTe2 and spin injection in van der Waals heterostructures, Phys. Rev. Res. 2, 033204 (2020).
  34. T. S. Ghiasi, A. A. Kaverzin, P. J. Blah, and B. J. van Wees, Charge-to-spin conversion by the Rashba-Edelstein effect in two-dimensional van der Waals heterostructures up to room temperature, Nano Lett. 19, 5959 (2019).
  35. D. Khokhriakov, A. Md. Hoque, B. Karpiak, and S. P. Dash, Gate-tunable spin-galvanic effect in graphene-topological insulator van der Waals heterostructures at room temperature, Nat. Commun. 11, 3657 (2020).
  36. L. Li, J. Zhang, G. Myeong, W. Shin, H. Lim, B. Kim, S. Kim, T. Jin, S. Cavill, B. S. Kim, C. Kim, J. Lischner, A. Ferreira, and S. Cho, Gate-tunable reversible Rashba-Edelstein effect in a few-layer graphene/2H-TaS2 heterostructure at room temperature, ACS Nano 14, 5251 (2020).
  37. M. Gmitra, D. Kochan, P. Högl, and J. Fabian, Trivial and inverted Dirac bands and the emergence of quantum spin Hall states in graphene on transition-metal dichalcogenides, Phys. Rev. B 93, 155104 (2016).
  38. M. Milletari, M. Offidani, A. Ferreira, and R. Raimondi, Covariant Conservation Laws and the Spin Hall Effect in Dirac-Rashba Systems, Phys. Rev. Lett. 119, 246801 (2017).
  39. A. W. Cummings, J. H. Garcia, J. Fabian, and S. Roche, Giant Spin Lifetime Anisotropy in Graphene Induced by Proximity Effects, Phys. Rev. Lett. 119, 206601 (2017).
  40. J. H. Garcia, A. W. Cummings, and S. Roche, Spin Hall effect and weak antilocalization in graphene/transition metal dichalcogenide heterostructures, Nano Lett. 17, 5078 (2017).
  41. M. Offidani, M. Milletari, R. Raimondi, and A. Ferreira, Optimal Charge-to-Spin Conversion in Graphene on Transition-Metal Dichalcogenides, Phys. Rev. Lett. 119, 196801 (2017).
  42. J. H. Garcia, M. Vila, A. W. Cummings, and S. Roche, Spin transport in graphene/transition metal dichalcogenide heterostructures, Chem. Soc. Rev. 47, 3359 (2018).
  43. Y. S. Gani, E. J. Walter, and E. Rossi, Proximity-induced spin-orbit splitting in graphene nanoribbons on transition-metal dichalcogenides, Phys. Rev. B 101, 195416 (2020).
  44. S. A. Cavill, C. Huang, M. Offidani, Y.-H. Lin, M. A. Cazalilla, and A. Ferreira, Proposal for Unambiguous Electrical Detection of Spin-Charge Conversion in Lateral Spin Valves, Phys. Rev. Lett. 124, 236803 (2020).
  45. A. M. Alsharari, M. M. Asmar, and S. E. Ulloa, Topological phases and twisting of graphene on a dichalcogenide monolayer, Phys. Rev. B 98, 195129 (2018).
  46. Y. Li and M. Koshino, Twist-angle dependence of the proximity spin-orbit coupling in graphene on transition-metal dichalcogenides, Phys. Rev. B 99, 075438 (2019).
  47. A. David, P. Rakyta, A. Kormányos, and G. Burkard, Induced spin-orbit coupling in twisted graphene–transition metal dichalcogenide heterobilayers: Twistronics meets spintronics, Phys. Rev. B 100, 085412 (2019).
  48. A. Pezo, Z. Zanolli, N. Wittemeier, P. Ordejón, A. Fazzio, S. Roche, and J. H. Garcia, Manipulation of spin transport in graphene/transition metal dichalcogenide heterobilayers upon twisting, 2D Mater. 9, 015008 (2022).
  49. C. L. Kane and E. J. Mele, Quantum Spin Hall Effect in Graphene, Phys. Rev. Lett. 95, 226801 (2005).
  50. H. Min, J. E. Hill, N. A. Sinitsyn, B. R. Sahu, L. Kleinman, and A. H. MacDonald, Intrinsic and Rashba spin-orbit interactions in graphene sheets, Phys. Rev. B 74, 165310 (2006).
  51. S. Konschuh, M. Gmitra, and J. Fabian, Tight-binding theory of the spin-orbit coupling in graphene, Phys. Rev. B 82, 245412 (2010).
  52. K. Zollner, A. W. Cummings, S. Roche, and J. Fabian, Graphene on two-dimensional hexagonal BN, AlN, and GaN: Electronic, spin-orbit, and spin relaxation properties, Phys. Rev. B 103, 075129 (2021).
  53. X. Yang, B. Sa, P. Lin, C. Xu, Q. Zhu, H. Zhan, and Z. Sun, Tunable contacts in graphene/InSe van der Waals heterostructures, J. Phys. Chem. C 124, 23699 (2020).
  54. K. Zollner, M. D. Petrović, K. Dolui, P. Plecháč, B. K. Nikolić, and J. Fabian, Scattering-induced and highly tunable by gate damping-like spin-orbit torque in graphene doubly proximitized by two-dimensional magnet Cr2Ge2Te6 and monolayer WS2, Phys. Rev. Res. 2, 043057 (2020).
  55. K. Zollner and J. Fabian, Single and bilayer graphene on the topological insulator Bi2Se3: Electronic and spin-orbit properties from first principles, Phys. Rev. B 100, 165141 (2019).
  56. K. Kandrai, P. Vancsó, G. Kukucska, J. Koltai, G. Baranka, Á. Hoffmann, Á. Pekker, K. Kamarás, Z. E. Horváth, A. Vymazalová, L. Tapasztó, and P. Nemes-Incze, Signature of large-gap quantum spin hall state in the layered mineral jacutingaite, Nano Lett. 20, 5207 (2020).
  57. B. Fülöp, A. Márffy, S. Zihlmann, M. Gmitra, E. Tóvári, B. Szentpéteri, M. Kedves, K. Watanabe, T. Taniguchi, J. Fabian, C. Schönenberger, P. Makk, and S. Csonka, Boosting proximity spin–orbit coupling in graphene/WSe2 heterostructures via hydrostatic pressure, npj 2D Mater. Appl. 5, 82 (2021).
  58. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.L022049 for (i) discussion of the symmetry properties of the quantum phase ϑR, (ii) details of the numerical calculations shown in Figs. 1–2, (iii) brief discussion of supermoire effects, (iv) details of the magnetotransport calculations shown in Fig. 3, (v) brief discussion of another setup to investigate twist angle dependent transport in a graphene-TMDC heterostructure.
  59. S. Fang, R. Kuate Defo, S. N. Shirodkar, S. Lieu, G. A. Tritsaris, and E. Kaxiras, Ab initio tight-binding Hamiltonian for transition metal dichalcogenides, Phys. Rev. B 92, 205108 (2015).
  60. D. Pierucci, H. Henck, J. Avila, A. Balan, C. H. Naylor, G. Patriarche, Y. J. Dappe, M. G. Silly, F. Sirotti, A. T. C. Johnson, M. C. Asensio, and A. Ouerghi, Band alignment and minigaps in monolayer MoS2-graphene van der Waals heterostructures, Nano Lett. 16, 4054 (2016).
  61. H. Nakamura, A. Mohammed, Ph. Rosenzweig, K. Matsuda, K. Nowakowski, K. Küster, P. Wochner, S. Ibrahimkutty, U. Wedig, H. Hussain, J. Rawle, C. Nicklin, B. Stuhlhofer, G. Cristiani, G. Logvenov, H. Takagi, and U. Starke, Spin splitting and strain in epitaxial monolayer WSe2 on graphene, Phys. Rev. B 101, 165103 (2020).
  62. T. Naimer, K. Zollner, M. Gmitra, and J. Fabian, Twist-angle dependent proximity induced spin-orbit coupling in graphene/transition metal dichalcogenide heterostructures, Phys. Rev. B 104, 195156 (2021).
  63. We describe the energy of the Dirac point of graphene in the band gap of the TMDC by a number fG∈[0,1]. Its value is a linear function of the position of the Dirac point in the TMDC band gap. When fG=0, the Dirac point is aligned with the TMDC valence band edge, for fG=1 the Dirac point has the same energy as the TMDC conduction band edge. In the calculations involving MoS2, we used DFT parameters Eg=1.807eV, fG=0.974 and experimental parameters [60] Eg=2eV, fG=0.55. In the case of WSe2, DFT parameters were Eg=1.638eV, fG=0.161 and experimental ones [61] Eg=1.95eV, fG=0.426.
  64. M. Andjelković, S. P. Milovanović, L. Covaci, and F. M. Peeters, Double moiré with a twist: Supermoiré in encapsulated graphene, Nano Lett. 20, 979 (2020).
  65. H. Oka and M. Koshino, Fractal energy gaps and topological invariants in hBN/graphene/hBN double moiré systems, Phys. Rev. B 104, 035306 (2021).
  66. M. Offidani and A. Ferreira, Microscopic theory of spin relaxation anisotropy in graphene with proximity-induced spin-orbit coupling, Phys. Rev. B 98, 245408 (2018).
  67. A. F. Young and P. Kim, Quantum interference and Klein tunnelling in graphene heterojunctions, Nat. Phys. 5, 222 (2009).
  68. P. Rickhaus, R. Maurand, M.-H. Liu, M. Weiss, K. Richter, and C. Schönenberger, Ballistic interferences in suspended graphene, Nat. Commun. 4, 2342 (2013).
  69. P. Rickhaus, P. Makk, M.-H. Liu, E. Tóvári, M. Weiss, R. Maurand, K. Richter, and C. Schönenberger, Snake trajectories in ultraclean graphene p–n junctions, Nat. Commun. 6, 6470 (2015).
  70. S. Chen, Z. Han, M. M. Elahi, K. M. Masum Habib, L. Wang, B. Wen, Y. Gao, T. Taniguchi, K. Watanabe, J. Hone, A. W. Ghosh, and C. R. Dean, Electron optics with p-n junctions in ballistic graphene, Science 353, 1522 (2016).
  71. C. Handschin, P. Makk, P. Rickhaus, M.-H. Liu, K. Watanabe, T. Taniguchi, K. Richter, and C. Schönenberger, Fabry-Perot resonances in a graphene/hBN moiré superlattice, Nano Lett. 17, 328 (2017).
  72. A. V. Shytov, M. S. Rudner, and L. S. Levitov, Klein Backscattering and Fabry-Pérot Interference in Graphene Heterojunctions, Phys. Rev. Lett. 101, 156804 (2008).
  73. A. Silva, V. E. P. Claerbout, T. Polcar, D. Kramer, and P. Nicolini, Exploring the stability of twisted van der Waals heterostructures, ACS Appl. Mater. Interfaces 12, 45214 (2020).

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