Engineering phase-frustration-induced flat bands in an aza-triangulene covalent kagome lattice
Source abstract
Abstract
π-Conjugated covalent organic frameworks provide a versatile molecular scaffold for the realization of designer quantum nanomaterials. Strong electron-electron correlation within these artificial lattices can give rise to exotic phases of matter. Their experimental realization, however, requires precise control over orbital symmetry, charge localization and band dispersion, all arising from the effective hybridization between molecular linkers and nodes. Here we present a modular strategy for constructing diatomic kagome lattices from aza-[3]triangulene nodes, in which a D3h-symmetric ground state is stabilized through resonance contributions from a cumulenic linker. First-principles density functional theory and scanning tunnelling spectroscopy reveal that the hybridization of a sixfold-degenerate set of edge-localized Wannier functions in the unit cell gives rise to orbital-phase-frustration-induced non-trivial flat bands. These results establish a general design principle for engineering orbital interactions in organic lattices and open a pathway towards programmable covalent-organic-framework-based quantum materials with correlated electronic ground states.
Source: europepmc · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Topological Materials and Phenomena · Advanced Condensed Matter Physics · Metamaterials and Metasurfaces Applications
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References (76)
Show source-provided references
1. Kang, M. G. et al. Topological flat bands in frustrated kagome lattice CoSn. Nat. Commun. 11, 4004 (2020).10.1038/s41467-020-17465-1 ↗
2. Calugaru, D. et al. General construction and topological classification of crystalline flat bands. Nat. Phys. 18, 185–189 (2022).10.1038/s41567-021-01445-3 ↗
3. Regnault, N. et al. Catalogue of flat-band stoichiometric materials. Nature 603, 824–828 (2022).10.1038/s41586-022-04519-1 ↗
4. Guo, Q. B. et al. Ultrathin quantum light source with van der Waals NbOCl2 crystal. Nature 613, 53–59 (2023).10.1038/s41586-022-05393-7 ↗
5. Ye, L. D. et al. Hopping frustration-induced flat band and strange metallicity in a kagome metal. Nat. Phys. 20, 610–614 (2024).10.1038/s41567-023-02360-5 ↗
6. Checkelsky, J. G., Bernevig, B. A., Coleman, P., Si, Q. M. & Paschen, S. Flat bands, strange metals and the Kondo effect. Nat. Rev. Mater. 9, 509–526 (2024).10.1038/s41578-023-00644-z ↗
7. Bergman, D. L., Wu, C. J. & Balents, L. Band touching from real-space topology in frustrated hopping models. Phys. Rev. B 78, 125104 (2008).10.1103/PhysRevB.78.125104 ↗
8. Morell, E. S., Correa, J. D., Vargas, P., Pacheco, M. & Barticevic, Z. Flat bands in slightly twisted bilayer graphene: tight-binding calculations. Phys. Rev. B 82, 121407 (2010).10.1103/PhysRevB.82.121407 ↗
9. Jovanovic, M. & Schoop, L. M. Simple chemical rules for predicting band structures of kagome materials. J. Am. Chem. Soc. 144, 10978–10991 (2022).10.1021/jacs.2c04183 ↗
10. Neves, P. M. et al. Crystal net catalog of model flat band materials. npj Comput. Mater. 10, 39 (2024).10.1038/s41524-024-01220-x ↗
11. Micnas, R., Ranninger, J. & Robaszkiewicz, S. Superconductivity in narrow-band systems with local nonretarded attractive interactions. Rev. Mod. Phys. 62, 113–171 (1990).10.1103/RevModPhys.62.113 ↗
12. Aoki, H. Theoretical possibilities for flat band superconductivity. J. Supercond. Nov. Magn. 33, 2341–2346 (2020).10.1007/s10948-020-05474-6 ↗
13. Mielke, A. Ferromagnetic ground states for the Hubbard model on line graphs. J. Phys. A Math. Gen. 24, L73–L77 (1991).10.1088/0305-4470/24/2/005 ↗
14. Sethi, G., Zhou, Y. N., Zhu, L. H., Yang, L. & Liu, F. Flat-band-enabled triplet excitonic insulator in a diatomic kagome lattice. Phys. Rev. Lett. 126, 196403 (2021).10.1103/PhysRevLett.126.196403 ↗
15. Shayegan, M. Wigner crystals in flat band 2D electron systems. Nat. Rev. Phys. 4, 212–213 (2022).10.1038/s42254-022-00444-4 ↗
16. Tang, E., Mei, J. W. & Wen, X. G. High-temperature fractional quantum Hall states. Phys. Rev. Lett. 106, 236802 (2011).10.1103/PhysRevLett.106.236802 ↗
17. Bergholtz, E. J. & Liu, Z. Topological flat band models and fractional Chern insulators. Int. J. Mod. Phys. B 27, 1330017 (2013).10.1142/S021797921330017X ↗
18. Galeotti, G. et al. Synthesis of mesoscale ordered two-dimensional π-conjugated polymers with semiconducting properties. Nat. Mater. 19, 874–880 (2020).10.1038/s41563-020-0682-z ↗
19. Dettmann, D. et al. Electronic band engineering of two-dimensional kagome polymers. ACS Nano 18, 849–857 (2023).10.1021/acsnano.3c09476 ↗
20. Pawlak, R. et al. On-surface synthesis and characterization of radical spins in kagome graphene. ACS Nano 19, 4768–4777 (2025).10.1021/acsnano.4c15519 ↗
21. Lawrence, J. et al. Topological design and synthesis of high-spin aza-triangulenes without Jahn–Teller distortions. ACS Nano 17, 20237–20245 (2023).10.1021/acsnano.3c05974 ↗
22. Wang, T. et al. Aza-triangulene: on-surface synthesis and electronic and magnetic properties. J. Am. Chem. Soc. 144, 4522–4529 (2022).10.1021/jacs.1c12618 ↗
23. Bieri, M. et al. Surface-supported 2D heterotriangulene polymers. Chem. Commun. 47, 10239–10241 (2011).10.1039/c1cc12490k ↗
24. Schlütter, F. et al. π-Conjugated heterotriangulene macrocycles by solution and surface-supported synthesis toward honeycomb networks. J. Am. Chem. Soc. 135, 4550–4557 (2013).10.1021/ja400857g ↗
25. Mishra, S. et al. Observation of fractional edge excitations in nanographene spin chains. Nature 598, 287–292 (2021).10.1038/s41586-021-03842-3 ↗
26. Zhou, Y. N., Sethi, G., Zhang, C., Ni, X. J. & Liu, F. Giant intrinsic circular dichroism of enantiomorphic flat Chern bands and flatband devices. Phys. Rev. B 102, 125115 (2020).10.1103/PhysRevB.102.125115 ↗
27. Guo, X., Mu, H. M., Hu, T. Y., Li, Q. X. & Wang, Z. F. Bipolar semiconductor in two-dimensional covalent organic frameworks. Phys. Rev. B 105, 155415 (2022).10.1103/PhysRevB.105.155415 ↗
28. Hu, T. Y., Zhang, T. F., Mu, H. M. & Wang, Z. F. Intrinsic second-order topological insulator in two-dimensional covalent organic frameworks. J. Phys. Chem. Lett. 13, 10905–10911 (2022).10.1021/acs.jpclett.2c02683 ↗
29. Ovchinnikov, A. A. Multiplicity of ground state of large alternant organic molecules with conjugated bonds. Theor. Chim. Acta 47, 297–304 (1978).10.1007/BF00549259 ↗
30. Yazyev, O. V. Emergence of magnetism in graphene materials and nanostructures. Rep. Prog. Phys. 73, 056501 (2010).10.1088/0034-4885/73/5/056501 ↗
31. Lieb, E. H. Two theorems on the Hubbard model. Phys. Rev. Lett. 62, 1201–1204 (1989).10.1103/PhysRevLett.62.1201 ↗
32. Zhao, Y. & Truhlar, D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor. Chem. Acc. 120, 215–241 (2008).10.1007/s00214-007-0310-x ↗
33. Lu, T. & Chen, F. W. Multiwfn: a multifunctional wavefunction analyzer. J. Comput. Chem. 33, 580–592 (2012).10.1002/jcc.22885 ↗
34. Neese, F. The ORCA program system. Wires Comput. Mol. Sci. 2, 73–78 (2012).10.1002/wcms.81 ↗
35. Weigend, F. & Ahlrichs, R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: design and assessment of accuracy. Phys. Chem. Chem. Phys. 7, 3297–3305 (2005).10.1039/b508541a ↗
36. Lu, T. A comprehensive electron wavefunction analysis toolbox for chemists, Multiwfn. J. Chem. Phys. 161, 082503 (2024).10.1063/5.0216272 ↗
37. Jahn, H. A. & Teller, E. Stability of polyatomic molecules in degenerate electronic states. I. Orbital degeneracy. Proc. R. Soc. Lond. A 161, 220–235 (1937).10.1098/rspa.1937.0142 ↗
38. Jahn, H. A. Stability of polyatomic molecules in degenerate electronic states II – spin degeneracy. Proc. R. Soc. Lond. A 164, 0117–0131 (1938).10.1098/rspa.1938.0008 ↗
39. Cirera, B. et al. Tailoring topological order and π-conjugation to engineer quasi-metallic polymers. Nat. Nanotechnol. 15, 437–443 (2020).10.1038/s41565-020-0668-7 ↗
40. González-Herrero, H. et al. Atomic scale control and visualization of topological quantum phase transition in π-conjugated polymers driven by their length. Adv. Mater. 33, 2104495 (2021).10.1002/adma.202104495 ↗
41. Jiménez-Martín, A. et al. Atomically precise control of topological state hybridization in conjugated polymers. ACS Nano 18, 29902–29912 (2024).10.1021/acsnano.4c10357 ↗
42. Ramirez, F., Mckelvie, N. & Desai, N. B. A new synthesis of 1,1-dibromoölefins via phosphine-dibromomethylenes. The reaction of triphenylphosphine with carbon tetrabromide. J. Am. Chem. Soc. 84, 1745–1747 (1962).10.1021/ja00868a057 ↗
43. Giguère, J. B., Verolet, Q. & Morin, J. F. 4,10-Dibromoanthanthrone as a new building block for p-type, n-type, and ambipolar π-conjugated materials. Chem. Eur. J. 19, 372–381 (2013).10.1002/chem.201202878 ↗
44. Sun, Q. et al. On-surface formation of cumulene by dehalogenative homocoupling of alkenyl-dibromides. Angew. Chem. Int. Ed. 56, 12165–12169 (2017).10.1002/anie.201706104 ↗
45. Sánchez-Grande, A. et al. On-surface synthesis of ethynylene-bridged anthracene polymers. Angew. Chem. Int. Ed. 58, 6559–6563 (2019).10.1002/anie.201814154 ↗
46. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).10.1103/PhysRevLett.77.3865 ↗
47. Gross, L. et al. High-resolution molecular orbital imaging using a p-wave STM tip. Phys. Rev. Lett. 107, 086101 (2011).10.1103/PhysRevLett.107.086101 ↗
48. Crommie, M. F., Lutz, C. P. & Eigler, D. M. Imaging standing waves in a two-dimensional electron gas. Nature 363, 524–527 (1993).10.1038/363524a0 ↗
49. Hasegawa, Y. & Avouris, P. Direct observation of standing-wave formation at surface steps using scanning tunneling spectroscopy. Phys. Rev. Lett. 71, 1071–1074 (1993).10.1103/PhysRevLett.71.1071 ↗
50. Tersoff, J. & Hamann, D. R. Theory and application for the scanning tunneling microscope. Phys. Rev. Lett. 50, 1998–2001 (1983).10.1103/PhysRevLett.50.1998 ↗
51. Tersoff, J. & Hamann, D. R. Theory of the scanning tunneling microscope. Phys. Rev. B 31, 805–813 (1985).10.1103/PhysRevB.31.805 ↗
52. Januszewski, J. A., Wendinger, D., Methfessel, C. D., Hampel, F. & Tykwinski, R. R. Synthesis and structure of tetraarylcumulenes: characterization of bond-length alternation versus molecule length. Angew. Chem. Int. Ed. 52, 1817–1821 (2013).10.1002/anie.201208058 ↗
53. Gawel, P. et al. Synthesis of cyano-substituted diaryltetracenes from tetraaryl[3]cumulenes. Angew. Chem. Int. Ed. 53, 4341–4345 (2014).10.1002/anie.201402299 ↗
54. Wang, S. K., Zhu, J. M., Blackwell, R. & Fischer, F. R. Automated tip conditioning for scanning tunneling spectroscopy. J. Phys. Chem. A 125, 1384–1390 (2021).10.1021/acs.jpca.0c10731 ↗
55. Giessibl, F. J. Advances in atomic force microscopy. Rev. Mod. Phys. 75, 949–983 (2003).10.1103/RevModPhys.75.949 ↗
56. Bartels, L., Meyer, G. & Rieder, K. H. Controlled vertical manipulation of single CO molecules with the scanning tunneling microscope: a route to chemical contrast. Appl. Phys. Lett. 71, 213–215 (1997).10.1063/1.119503 ↗
57. Mohn, F., Schuler, B., Gross, L. & Meyer, G. Different tips for high-resolution atomic force microscopy and scanning tunneling microscopy of single molecules. Appl. Phys. Lett. 102, 073109 (2013).10.1063/1.4793200 ↗
58. Necas, D. & Klapetek, P. Gwyddion: an open-source software for SPM data analysis. Cent. Eur. J. Phys. 10, 181–188 (2012).
59. Weigend, F. Accurate Coulomb-fitting basis sets for H to Rn. Phys. Chem. Chem. Phys. 8, 1057–1065 (2006).10.1039/b515623h ↗
60. Weigend, F. Hartree-Fock exchange fitting basis sets for H to Rn. J. Comput. Chem. 29, 167–175 (2008).10.1002/jcc.20702 ↗
61. Kollmar, C., Sivalingam, K., Guo, Y. & Neese, F. An efficient implementation of the NEVPT2 and CASPT2 methods avoiding higher-order density matrices. J. Chem. Phys. 155, 234104 (2021).10.1063/5.0072129 ↗
62. Riplinger, C. & Neese, F. An efficient and near linear scaling pair natural orbital based local coupled cluster method. J. Chem. Phys. 138, 034106 (2013).10.1063/1.4773581 ↗
63. Vydrov, O. A. & Van Voorhis, T. Nonlocal van der Waals density functional: the simpler the better. J. Chem. Phys. 133, 244103 (2010).10.1063/1.3521275 ↗
64. Hujo, W. & Grimme, S. Performance of the van der Waals density functional VV10 and (hybrid)GGA variants for thermochemistry and noncovalent interactions. J. Chem. Theory Comput. 7, 3866–3871 (2011).10.1021/ct200644w ↗
65. Mardirossian, N. & Head-Gordon, M. ωB97M-V: a combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation. J. Chem. Phys. 144, 214110 (2016).10.1063/1.4952647 ↗
66. Ekstrom, U., Visscher, L., Bast, R., Thorvaldsen, A. J. & Ruud, K. Arbitrary-order density functional response theory from automatic differentiation. J. Chem. Theory Comput. 6, 1971–1980 (2010).10.1021/ct100117s ↗
67. Yanai, T., Tew, D. P. & Handy, N. C. A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP). Chem. Phys. Lett. 393, 51–57 (2004).10.1016/j.cplett.2004.06.011 ↗
68. Chai, J. D. & Head-Gordon, M. Systematic optimization of long-range corrected hybrid density functionals. J. Chem. Phys. 128, 084106 (2008).10.1063/1.2834918 ↗
69. Heyd, J., Scuseria, G. E. & Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207–8215 (2003).10.1063/1.1564060 ↗
70. Quantum Espresso v7.4.1 (Quantum Espresso Foundation, 2023).
71. Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Mat. 21, 395502 (2009).10.1088/0953-8984/21/39/395502 ↗
72. Wannier90 v3.1.0 (Wannier Developers Group, 2024).
73. Pizzi, G. et al. Wannier90 as a community code: new features and applications. J. Phys. Condens. Matter 32, 165902 (2020).10.1088/1361-648X/ab51ff ↗
74. Python Tight Binding (PythTB) v2.0.0 (PythTB Team, 2023).
75. Groom, C. R., Bruno, I. J., Lightfoot, M. P. & Ward, S. C. The Cambridge Structural Database. Acta Crystallogr. B 72, 171–179 (2016).10.1107/S2052520616003954 ↗
76. CrysAlisPro v.1.172.43.143a (Oxford Diffraction/Agilent Technologies UK, 2024).