In 2005, Kane and Mele revolutionized solid-state physics by introducing the time-reversal symmetric quantum spin Hall insulator (QSHI), a novel insulating phase whose band order cannot be adiabatically deformed to match the atomic limit of trivial insulators without closing its band gap 1, 2. As a result, QSHIs are inherently surrounded by metallic, spin-momentum locked edge modes, which are connected in Kramers pairs due to time-reversal symmetry (TRS), rendering them immune to certain types of backscattering 3, 4. These holographic properties make QSHIs highly attractive for next-generation spintronic or quantum technologies and thus sparked an intensive search for novel QSHI materials 5–9. However, many proposed models, including the Kane-Mele model itself, are inefficient in leveraging the QSHI driving spin-orbit coupling (SOC) term, highlighting the need for new materials and proposals with larger topological band gaps that ensure stability at technologically relevant temperatures. The most successful approach to date was realized in the form of bismuthene on SiC(0001), where strong atomic SOC is activated via in-plane p-orbitals 10, 11. Yet, the large honeycomb motif on the smaller substrate unit cell leads to domain formation with typical sizes around 100 nm, insufficient for practical applications. Only recently, a novel QSHI model was developed following the serendipitous discovery of indenene, a triangular lattice of an indium monolayer grown on SiC(0001) 12–14. This model for a p-orbital manifold on a triangular lattice retains the atomic SOC term of bismuthene, while perfectly matching the surface periodicity of common substrates, thereby offering a QSHI model for a more scalable triangular lattice geometry. The scope of this thesis is the comprehensive topological classification of indenene – from its bulk to boundary states – aimed at establishing a strong case for the QSHI phase within this triangular lattice model. This involves the design of experimental strategies for topological classification, which can be readily applied to related materials, as well as taking first steps toward ex-situ applications by developing an environmentally stable capping technique 15. Regarding the synthesis of indenene, a detailed growth protocol for high-quality films is presented, which reproducibly achieves micron-sized single domains of indenene, as demonstrated by scanning tunneling microscopy (STM) 16. The lattice and electronic structure of indenene are further scrutinized by STM, scanning tunneling spectroscopy (STS) and angle-resolved photoelectron spectroscopy (ARPES), revealing T1 indium adsorption in the aspired triangular lattice geometry, an insulating band gap of ∼ 120 meV, and the presence of symmetry-reducing terms induced by the SiC substrate. A key feature of the triangular QSHI model is the unambiguous link between the topological character and an orbital angular momentum (OAM) staggering in its electronic bulk band structure. This OAM staggering is promoted by the symmetry-reducing terms induced by the substrate and encodes whether the band gap is inverted or topologically trivial. Experimentally, the OAM staggering associated with the QSHI phase is independently confirmed by circular dichroism (CD) in ARPES and by STS, the latter revealing a distinct charge localization pattern associated with the OAM pattern due to real-space interference of the Bloch wavefunction 12, 17–22. The QSHI phase of indenene is further evidenced by the detection of chiral in-plane OAM texture in CD-ARPES, along with corresponding scattering selection rules investigated by quasiparticle interference (QPI) in STS, both reflecting the underlying chirality of the OAM and spin textures. These findings are closely tied to the sizable splitting of the indenene valence bands, establishing it as a paradigmatic model system for the orbital-driven Rashba effect 18. In line with the bulk-boundary correspondence, the QSHI nature of indenene is further corroborated by the observation of metallic edge states via STS. Intriguingly, and contrary to the idealized notion of linearly dispersing edge bands, the edge states in indenene exhibit a non-monotonic dispersion relation, giving rise to multiple Kramers pairs, a situation relevant to many QSHI materials 23–33. This edge band dispersion enables an unprecedented experimental demonstration of TRS-allowed inter-Kramers pair backscattering processes, leading to the pairwise localization of edge states at defects and the formation of quantum-well-like states, as observed by QPI in STS. Although such pairwise localization occurs, one edge mode always remains perfectly transmitted across defects, preserving consistency with the underlying topological protection by TRS 34. Despite this inherent topological protection, the edge states of indenene are inevitably destroyed under non-ultra-high vacuum (UHV) conditions due to rapid oxidation, underscoring the need for a non-invasive capping strategy. In this regard, intercalation of indenene to the graphene/SiC interface proves highly effective in preserving its electronic, structural, and topological properties, as demonstrated by ARPES, STM, STS, and the reproduction of OAM-related topological signatures. This graphene-capped indenene film exhibits high stability at ambient conditions, as demonstrated by X-ray photoelectron spectroscopy (XPS), thereby enabling exsitu investigation of indenene and providing a benchmark system for future capping approaches using insulating capping materials instead of graphene 15. Beyond the QSHI phase of indenene, the rich topological phase diagram of the triangular lattice model motivated further exploration of indenene growth on the C-face of SiC and the Ga/SiC(0001) system, leading to the identification of a second QSHI candidate and a potentially superconducting Ga bilayer, respectively 35. Building on the findings of this thesis, it is further proposed that the already existing Tl/Si(111) monolayer realizes the intriguing higher order topological insulator (HOTI) phase described by the triangular lattice model 36, 37, an avenue that may reveal exotic corner states whose topological protection is currently under active debate. To this end, the classification of indenene presented in this work provides a definitive benchmark, outlining both the key challenges and opportunities for future research on triangular lattice systems.
Jonas Andreas Erhardt (Thu,) studied this question.