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  • Letter
  • Open Access

Aharonov-Bohm interferometer in inverted-band pn junctions

Yuhao Zhao1,*, Oded Zilberberg2, and Antonio Štrkalj3,†

  • *Contact author: yzhao.phy@gmail.com
  • †Contact author: astrkalj@phy.hr
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Phys. Rev. Research 7, L022030 – Published 7 May, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022030

Abstract

Inverted-band pn junctions in two-dimensional materials offer a promising platform for electron optics in condensed matter, as they allow to manipulate and guide electron beams without the need for spatial confinement. In this work, we propose the realization of an Aharonov-Bohm (AB) interferometer using such pn junctions. We observe AB oscillations in numerically obtained conductance and analytically identify the conditions for their appearance by analyzing the scattering processes at the pn interface. To support experimental implementation, we also consider junctions with a graded interface, where the potential varies smoothly between the p− and n-doped regions. Our results reveal an abrupt change in the AB-oscillation frequency, which we attribute to a distinct transition in the hybridization across the interface. We verify that our reported AB oscillations are robust to realistic disorder and temperature decoherence channels. Our study paves the way for realizing the Aharonov-Bohm effect in bulk mesoscopic systems without the need for external spatial confinement, offering new possibilities in electron optics.

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References (36)

  1. W. Ehrenberg and R. E. Siday, The refractive index in electron optics and the principles of dynamics, Proc. Phys. Soc. B 62, 8 (1949).
  2. Y. Aharonov and D. Bohm, Significance of electromagnetic potentials in the quantum theory, Phys. Rev. 115, 485 (1959).
  3. Y. Aharonov and D. Bohm, Further considerations on electromagnetic potentials in the quantum theory, Phys. Rev. 123, 1511 (1961).
  4. T. Ihn, Semiconductor Nanostructures: Quantum States and Electronic Transport (Oxford University Press, Oxford, UK, 2009).
  5. E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University Press, Cambridge, UK, 2007).
  6. W. Chen, H.-Z. Lu, and O. Zilberberg, Weak localization and antilocalization in nodal-line semimetals: Dimensionality and topological effects, Phys. Rev. Lett. 122, 196603 (2019).
  7. A. van Oudenaarden, M. H. Devoret, Y. V. Nazarov, and J. E. Mooij, Magneto-electric Aharonov–Bohm effect in metal rings, Nature (London) 391, 768 (1998).
  8. A. Bachtold, C. Strunk, J.-P. Salvetat, J.-M. Bonard, L. Forró, T. Nussbaumer, and C. Schönenberger, Aharonov–Bohm oscillations in carbon nanotubes, Nature (London) 397, 673 (1999).
  9. S. Russo, J. B. Oostinga, D. Wehenkel, H. B. Heersche, S. S. Sobhani, L. M. K. Vandersypen, and A. F. Morpurgo, Observation of Aharonov-Bohm conductance oscillations in a graphene ring, Phys. Rev. B 77, 085413 (2008).
  10. M. Kremer, I. Petrides, E. Meyer, M. Heinrich, O. Zilberberg, and A. Szameit, A square-root topological insulator with non-quantized indices realized with photonic Aharonov-Bohm cages, Nat. Commun. 11, 907 (2020).
  11. S. Iwakiri, A. Mestre-Torà, E. Portolés, M. Visscher, M. Perego, G. Zheng, T. Taniguchi, K. Watanabe, M. Sigrist, T. Ihn, and K. Ensslin, Tunable quantum interferometer for correlated moiré electrons, Nat. Commun. 15, 390 (2024).
  12. Y. Kawaguchi, D. Smirnova, F. Komissarenko, S. Kiriushechkina, A. Vakulenko, M. Li, A. Alù, and A. B. Khanikaev, Pseudo-spin switches and Aharonov-Bohm effect for topological boundary modes, Sci. Adv. 10, eadn6095 (2024).
  13. J. Kim, H. Dev, R. Kumar, A. Ilin, A. Haug, V. Bhardwaj, C. Hong, K. Watanabe, T. Taniguchi, A. Stern, and Y. Ronen, Aharonov–Bohm interference and statistical phase-jump evolution in fractional quantum Hall states in bilayer graphene, Nat. Nanotechnol. 19, 1619 (2024).
  14. S. Biswas, H. K. Kundu, R. Bhattacharyya, V. Umansky, and M. Heiblum, Anomalous Aharonov-Bohm interference in the presence of edge reconstruction, Phys. Rev. Lett. 132, 076301 (2024).
  15. O. Zilberberg, A. Romito, and Y. Gefen, Charge sensing amplification via weak values measurement, Phys. Rev. Lett. 106, 080405 (2011).
  16. S. Iwakiri, F. K. De Vries, E. Portolés, G. Zheng, T. Taniguchi, K. Watanabe, T. Ihn, and K. Ensslin, Gate-defined electron interferometer in bilayer graphene, Nano Lett. 22, 6292 (2022).
  17. K. v. Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45, 494 (1980).
  18. B. Özyilmaz, P. Jarillo-Herrero, D. Efetov, D. A. Abanin, L. S. Levitov, and P. Kim, Electronic transport and quantum Hall effect in bipolar graphene p-n-p junctions, Phys. Rev. Lett. 99, 166804 (2007).
  19. F. Amet, J. R. Williams, K. Watanabe, T. Taniguchi, and D. Goldhaber-Gordon, Selective equilibration of spin-polarized quantum Hall edge states in graphene, Phys. Rev. Lett. 112, 196601 (2014).
  20. F. Nichele, H. J. Suominen, M. Kjaergaard, C. M. Marcus, E. Sajadi, J. A. Folk, F. Qu, A. J. A. Beukman, F. K. d. Vries, J. v. Veen, S. Nadj-Perge, L. P. Kouwenhoven, B.-M. Nguyen, A. A. Kiselev, W. Yi, M. Sokolich, M. J. Manfra, E. M. Spanton, and K. A. Moler, Edge transport in the trivial phase of InAs/GaSb, New J. Phys. 18, 083005 (2016).
  21. B.-M. Nguyen, A. A. Kiselev, R. Noah, W. Yi, F. Qu, A. J. A. Beukman, F. K. de Vries, J. van Veen, S. Nadj-Perge, L. P. Kouwenhoven, M. Kjaergaard, H. J. Suominen, F. Nichele, C. M. Marcus, M. J. Manfra, and M. Sokolich, Decoupling edge versus bulk conductance in the trivial regime of an InAs/GaSb double quantum well using Corbino ring geometry, Phys. Rev. Lett. 117, 077701 (2016).
  22. Y. Zhao, A. Leuch, O. Zilberberg, and A. Štrkalj, Electron optics using negative refraction in two-dimensional inverted-band pn junctions, Phys. Rev. B 108, 195301 (2023).
  23. V. V. Cheianov and V. I. Fal'ko, Selective transmission of Dirac electrons and ballistic magnetoresistance of n-p junctions in graphene, Phys. Rev. B 74, 041403(R) (2006).
  24. M. Karalic, A. Štrkalj, M. Masseroni, W. Chen, C. Mittag, T. Tschirky, W. Wegscheider, T. Ihn, K. Ensslin, and O. Zilberberg, Electron-hole interference in an inverted-band semiconductor bilayer, Phys. Rev. X 10, 031007 (2020).
  25. C. W. Groth, M. Wimmer, A. R. Akhmerov, and X. Waintal, Kwant: a software package for quantum transport, New J. Phys. 16, 063065 (2014).
  26. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L022030 for the details on (1) setup of the numeric simulations, (2) results for finite temperatures and the disorder, (3) analytic calculation using the scattering matrix formalism, (4) determining the effective path, the focal point and the carried phases, (5) results at the higher magnetic field, (6) comparison to an AB interferometer with the spatial confinement, (7) the fate of the injected particle-like spinor, (8) determining the angle of the maximal transmission, (9) scattering at the graded interface.
  27. R. Peierls, Zur theorie des diamagnetismus von leitungselektronen, Zeitschrift für Physik 80, 763 (1933).
  28. M. Büttiker, Absence of backscattering in the quantum Hall effect in multiprobe conductors, Phys. Rev. B 38, 9375 (1988).
  29. J. Yao, B. Zhou, X. Zhou, X. Xiao, and G. Zhou, Anomalous quantum scattering and transport of electrons with Mexican-hat dispersion induced by electrical potential, arXiv:2403.09319.
  30. A. Štrkalj, X.-R. Chen, W. Chen, D. Y. Xing, and O. Zilberberg, Tomasch oscillations as above-gap signature of topological superconductivity, Phys. Rev. Lett. 132, 066301 (2024).
  31. G. M. Minkov, A. V. Germanenko, O. E. Rut, A. A. Sherstobitov, S. A. Dvoretski, and N. N. Mikhailov, Two-dimensional semimetal in a wide HgTe quantum well: Magnetotransport and energy spectrum, Phys. Rev. B 88, 155306 (2013).
  32. X. Li, M.-W. Lin, A. A. Puretzky, J. C. Idrobo, C. Ma, M. Chi, M. Yoon, C. M. Rouleau, I. I. Kravchenko, D. B. Geohegan, and K. Xiao, Controlled vapor phase growth of single crystalline, two-dimensional gase crystals with high photoresponse, Sci. Rep. 4, 5497 (2014).
  33. X. Qian, J. Liu, L. Fu, and J. Li, Quantum spin Hall effect in two-dimensional transition metal dichalcogenides, Science 346, 1344 (2014).
  34. H. Min, B. Sahu, S. K. Banerjee, and A. H. MacDonald, Ab initio theory of gate induced gaps in graphene bilayers, Phys. Rev. B 75, 155115 (2007).
  35. E. V. Castro, K. S. Novoselov, S. V. Morozov, N. M. R. Peres, J. M. B. Lopes Dos Santos, J. Nilsson, F. Guinea, A. K. Geim, and A. H. Castro Neto, Biased bilayer graphene: semiconductor with a gap tunable by the electric field effect, Phys. Rev. Lett. 99, 216802 (2007).
  36. E. McCann, D. S. Abergel, and V. I. Fal'ko, The low energy electronic band structure of bilayer graphene, Eur. Phys. J.: Spec. Top. 148, 91 (2007).

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Phys. Rev. Research 7, L022030– Published 7 May, 2025
  • Received 29 October 2024
  • Accepted 7 March 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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