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  • Open Access

Optical spin angular momentum sensitivity of topological nanoflakes

D. Dams*

C. Rockstuhl

  • *Contact author: david.dams@kit.edu

Phys. Rev. B 111, 235147 – Published 27 June, 2025

DOI: https://doi.org/10.1103/sbly-4chz

Abstract

Two-dimensional Chern insulators, characterized by broken time-reversal symmetry and chiral edge states, are a promising platform to engineer exotic light-matter interactions. While most previous studies focused on bulk optical properties in extended media, investigations uncovering the unique photonic features of finite topological structures have been rare. In this work, we consider the optical response in nanoflakes of the prototypical Haldane model, which describes graphene-like systems where time reversal and sublattice symmetry breaking drive a topological phase. A simple argument elucidating the interplay between these fundamental properties and the optical spin angular momentum (SAM) of external light singles out these nanoflakes as prime candidates for SAM-sensitive optics. Building on these insights, we conduct a linear response analysis which reveals highly selective optical behavior, manifesting in strongly enhanced preferential absorption. Our results bridge topological materials and photonics, highlighting a direct link between topological properties and characteristics of electromagnetic radiation.

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References (50)

  1. Z. Dong, F. Yang, and J. S. Ho, Enhanced electromagnetic energy harvesting with subwavelength chiral structures, Phys. Rev. Appl. 8, 044026 (2017).
  2. G. K. E. Scriba, Chiral electromigration techniques in pharmaceutical and biomedical analysis, Bioanal. Rev. 3, 95 (2011).
  3. S. Parkin, G. Knüner, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Measurement of the total optical angular momentum transfer in optical tweezers, Opt. Express 14, 6963 (2006).
  4. A. Qu, L. Xu, C. Xu, and H. Kuang, Chiral nanomaterials for biosensing, bioimaging, and disease therapies, Chem. Commun. 58, 12782 (2022).
  5. A. Schimmoller, S. Walker, and A. S. Landsman, Photonic angular momentum in intense light–matter interactions, Photonics 11, 871 (2024).
  6. A. B. Khanikaev and A. Alú, Topological photonics: Robustness and beyond, Nat. Commun. 15, 931 (2024).
  7. J. D. Cox, M. R. Singh, G. Gumbs, M. A. Anton, and F. Carreno, Dipole-dipole interaction between a quantum dot and a graphene nanodisk, Phys. Rev. B 86, 125452 (2012).
  8. A. Babaze, E. Ogando, P. E. Stamatopoulou, C. Tserkezis, N. A. Mortensen, J. Aizpurua, A. G. Borisov, and R. Esteban, Quantum surface effects in the electromagnetic coupling between a quantum emitter and a plasmonic nanoantenna: Time-dependent density functional theory vs. semiclassical Feibelman approach, Opt. Express 30, 21159 (2022).
  9. O. Dmytruk and M. Schiró, Controlling topological phases of matter with quantum light, Commun. Phys. 5, 271 (2022).
  10. L. Ge, T. Zhan, D. Han, X. Liu, and J. Zi, Unusual electromagnetic scattering by cylinders of topological insulator, Opt. Express 22, 30833 (2014).
  11. M. Shah, M. S. Anwar, R. Asgari, and G. Xianlong, Photonic spin Hall effect in Haldane model materials, Phys. Rev. B 109, 235418 (2024).
  12. S. Mitra, Á. Jiménez-Galán, M. Aulich, M. Neuhaus, R. E. F. Silva, V. Pervak, M. F. Kling, and S. Biswas, Light-wave-controlled Haldane model in monolayer hexagonal boron nitride, Nature (London) 628, 752 (2024).
  13. S. Traverso, M. Sassetti, and N. Traverso Ziani, Emerging topological bound states in Haldane model zigzag nanoribbons, npj Quantum Mater. 9, 9 (2024).
  14. P. Mai, B. E. Feldman, and P. W. Phillips, Topological Mott insulator at quarter filling in the interacting Haldane model, Phys. Rev. Res. 5, 013162 (2023).
  15. G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, Experimental realization of the topological Haldane model with ultracold fermions, Nature (London) 515, 237 (2014).
  16. H. S. Kim and H.-Y. Kee, Realizing Haldane model in Fe-based honeycomb ferromagnetic insulators, npj Quantum Mater. 2, 20 (2017).
  17. W. Zhao, K. Kang, Y. Zhang, P. Knüppel, Z. Tao, L. Li, C. L. Tschirhart, E. Redekop, K. Watanabe, T. Taniguchi et al., Realization of the Haldane Chern insulator in a moiré lattice, Nat. Phys. 20, 275 (2024).
  18. S. K. Kim, H. Ochoa, R. Zarzuela, and Y. Tserkovnyak, Realization of the Haldane-Kane-Mele model in a system of localized spins, Phys. Rev. Lett. 117, 227201 (2016).
  19. C. Ding and M. Zhao, Chiral response in two-dimensional bilayers with time-reversal symmetry: A universal criterion, Phys. Rev. B 108, 125415 (2023).
  20. J. Li, S. Sanz, N. Merino-Díez, M. Vilas-Varela, A. Garcia-Lekue, M. Corso, D. G. de Oteyza, T. Frederiksen, D. Peña, and J. I. Pascual, Topological phase transition in chiral graphene nanoribbons: From edge bands to end states, Nat. Commun. 12, 5538 (2021).
  21. V. Peano, M. Houde, C. Brendel, F. Marquardt, and A. A. Clerk, Topological phase transitions and chiral inelastic transport induced by the squeezing of light, Nat. Commun. 7, 10779 (2016).
  22. K. Ghalamkari, Y. Tatsumi, and R. Saito, Perfect circular dichroism in the Haldane model, J. Phys. Soc. Jpn. 87, 063708 (2018).
  23. M. Vila, N. T. Hung, S. Roche, and R. Saito, Tunable circular dichroism and valley polarization in the modified Haldane model, Phys. Rev. B 99, 161404(R) (2019).
  24. F. D. M. Haldane, Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the “parity anomaly”, Phys. Rev. Lett. 61, 2015 (1988).
  25. M. Gmitra, D. Kochan, P. Högl, and J. Fabian, Trivial and inverted Dirac band gaps and the emergence of quantum spin Hall states in graphene on transition-metal dichalcogenides, Phys. Rev. B 93, 155104 (2016).
  26. G. B. Liu, W. Y. Shan, Y. Yao, W. Yao, and D. Xiao, Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides, Phys. Rev. B 88, 085433 (2013).
  27. N. Hao, P. Zhang, Z. Wang, W. Zhang, and Y. Wang, Topological edge states and quantum Hall effect in the Haldane model, Phys. Rev. B 78, 075438 (2008).
  28. K. Kondo and R. Ito, Quantum spin Hall phase in honeycomb nanoribbons with two different atoms: Edge shape effect to bulk-edge correspondence, J. Phys. Commun. 3, 055007 (2019).
  29. F. Calleja, H. Ochoa, M. Garnica, S. Barja, J. J. Navarro, A. Black, M. M. Otrokov, E. V. Chulkov, Y. H. W. Son, G. Pratzer et al., Spatial variation of a giant spin-orbit effect induces electron confinement in graphene on Pb islands, Nat. Phys. 11, 43 (2015).
  30. S. Mishra, X. Yao, Q. Chen, K. Eimre, O. Gröning, R. Ortiz, M. D. Giovannantonio, J. C. Sancho-García, J. Fernández-Rossier, C. A. Pignedoli et al., Large magnetic exchange coupling in rhombus-shaped nanographenes with zigzag periphery, Nat. Chem. 13, 581 (2021).
  31. S. Lindenthal, D. Fazzi, N. F. Zorn, A. A. E. Yumin, S. Settele, B. Weidinger, E. Blasco, and J. Zaumseil, Understanding the optical properties of doped and undoped 9-armchair graphene nanoribbons in dispersion, ACS Nano 17, 18240 (2023).
  32. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms: Introduction to Quantum Electrodynamics (Wiley-VCH, Berlin, 1997), Chap. 1.
  33. I. Fernandez-Corbaton, X. Zambrana-Puyalto, and G. Molina-Terriza, Helicity and angular momentum: A symmetry-based framework for the study of light-matter interactions, Phys. Rev. A 86, 042103 (2012).
  34. T. G. Pedersen, Graphene fractals: Energy gap and spin polarization, Phys. Rev. B 101, 235427 (2020).
  35. D. Vanderbilt, Berry Phases in Electronic Structure Theory: Electric Polarization, Orbital Magnetization and Topological Insulators (Cambridge University Press, Cambridge, 2018).
  36. H. Jürß and D. Bauer, Topological edge-state contributions to high-order harmonic generation in finite flakes, Phys. Rev. B 106, 054303 (2022).
  37. I. Fernandez-Corbaton, M. Fruhnert, and C. Rockstuhl, Objects of maximum electromagnetic chirality, Phys. Rev. X 6, 031013 (2016).
  38. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).
  39. S. Thongrattanasiri, A. Manjavacas, and F. J. García de Abajo, Quantum finite-size effects in graphene plasmons, ACS Nano 6, 1766 (2012).
  40. M. M. Müller, M. Kosik, M. Pelc, G. W. Bryant, A. Ayuela, C. Rockstuhl, and K. Słowik, Energy-based plasmonicity index to characterize optical resonances in nanostructures, J. Phys. Chem. C 124, 24331 (2020).
  41. M. Schüler, J. A. Marks, Y. Murakami, C. Jia, and T. P. Devereaux, Gauge invariance of light-matter interactions in first-principle tight-binding models, Phys. Rev. B 103, 155409 (2021).
  42. H. Schlömer, Z. Jiang, and S. Haas, Plasmons in two-dimensional topological insulators, Phys. Rev. B 103, 115116 (2021).
  43. T. Stauber, T. Low, and G. Gómez-Santos, Chiral response of twisted bilayer graphene, Phys. Rev. Lett. 120, 046801 (2018).
  44. G. M. Andolina, F. M. D. Pellegrino, V. Giovannetti, A. H. MacDonald, and M. Polini, Cavity quantum electrodynamics of strongly correlated electron systems: A no-go theorem for photon condensation, Phys. Rev. B 100, 121109(R) (2019).
  45. P. Potasz, A. D. Güçlü, and P. Hawrylak, Spin and electronic correlations in gated graphene quantum rings, Phys. Rev. B 82, 075425 (2010).
  46. J. D. Cox and F. Javier García de Abajo, Electrically tunable nonlinear plasmonics in graphene nanoislands, Nat. Commun. 5, 5725 (2014).
  47. T.-C. Yi, S. Hu, E. V. Castro, and R. Mondaini, Interplay of interactions, disorder, and topology in the Haldane-Hubbard model, Phys. Rev. B 104, 195117 (2021).
  48. F. Aguillon, D. C. Marinica, and A. G. Borisov, Plasmons in graphene nanostructures with point defects and impurities, J. Phys. Chem. C 125, 21503 (2021).
  49. D. Dams, M. Kosik, M. Müller, A. Ghosh, A. Babaze, J. Szczuczko, G. W. Bryant, C. Rockstuhl, M. Pelc, and K. Słowik, Granad—Simulating graphene nanoflakes with adatoms (unpublished).
  50. D. Dams, Haldane model code repository, https://github.com/GRANADlauncher/granad-scripts/tree/main/haldane_array (2025).

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