Electronic Solitons and Bound States in Higher-Order Topological Graphitic Structures

Electronic soliton states can be generated at the heterojunction between inequivalent topological phases. Our recent work [1] demonstrates the existence of such states in a class of graphene nanoribbons (GNRs) called square-root GNRs, where domain walls are induced by a transverse electric field. These 1D graphitic structures are shown to be nontrivial topological insulators, providing a versatile platform to study and observe soliton states. In addition to symmetry-protected soliton states, here we explore additional 0D localized states arising from the interface in similar systems, associated with massive surface states, known as Volkov-Pankratov states (VPS) [2]. We outline the conditions necessary to induce VPS and differentiate them from conventional topological boundary states. Finally, we propose strategies to identify soliton states in 2D graphitic structures, where the combination of quadrupole and dipole moments give rise to quantized charge accumulation with co-dimension 2.



[1] Huang, H., Sarker, M., Zahl, P., Hellberg, C.S., Levy, J., Petrides, I., Sinitskii, A. and Narang, P., 2024. Topological Solitons in Square-root Graphene Nanoribbons Controlled by Electric Fields. arXiv preprint arXiv:2406.13978.

[2] Lu, X. and Goerbig, M.O., 2020. Dirac quantum well engineering on the surface of a topological insulator. Physical Review B, 102(15), p.155311.