🔬 mesoscale physics

Direct Observation of the Zigzag Edge States of a Supramolecular Diatomic Kagome Lattice

Researchers successfully fabricated a supramolecular diatomic Kagome lattice using a triptycene derivative on a Pb(111) surface and provided direct experimental evidence, supported by calculations, of its topological zigzag edge states governed by Zak phase quantization.

Original authors: Ryohei Nemoto, Xiangzhi Meng, Behzad Mortezapour, Alexander Weismann, Saya Nakano, Masahisa Tsuchiizu, Ryuichi Arafune, Noriaki Takagi, Sho Nakamura, Katsunori Wakabayashi, Rie Suizu, Richard Berndt

Published 2026-09-03

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CC BY 4.0

Original authors: Ryohei Nemoto, Xiangzhi Meng, Behzad Mortezapour, Alexander Weismann, Saya Nakano, Masahisa Tsuchiizu, Ryuichi Arafune, Noriaki Takagi, Sho Nakamura, Katsunori Wakabayashi, Rie Suizu, Richard Berndt, Takashi Uchihashi, Kunio Awaga

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of materials science, the way atoms are arranged is just as important as what those atoms are made of. Imagine a city where the layout of the streets determines how traffic flows; in a crystal, the geometric pattern of atoms dictates how electrons move through the material. For decades, scientists have been fascinated by two specific patterns: the honeycomb, which looks like a beehive, and the Kagome lattice, a more complex design made of triangles that share corners. These patterns are special because they can trap electrons in ways that create strange, powerful behaviors, such as superconductivity or magnetic effects that appear without a magnet. However, while these patterns have been studied in theory and in some natural minerals, creating a perfect, artificial version of a more complex variation called the "diatomic Kagome lattice" has remained a challenge. This specific structure is predicted to host unique electronic states at its edges, but until now, no one had been able to see them directly.

A team of researchers has now successfully built this elusive structure and captured the first direct images of its hidden electronic states. They achieved this not by mining the earth, but by using a technique called self-assembly, where specially designed molecules arrange themselves into a precise pattern on a surface. The scientists used a molecule called Trip-Phz, which is shaped like a rigid, three-bladed propeller. When placed on a lead surface, these molecules naturally linked up to form a large, flat sheet that mimics the diatomic Kagome lattice. Using a powerful microscope that can see individual atoms and measure their electrical properties, the team observed that the edges of this molecular sheet were perfectly straight, resembling the "zigzag" edges found in graphene, a famous form of carbon.

The most significant discovery came when the researchers scanned the edges of this molecular sheet with their microscope. They found that at a specific electrical energy, bright spots of activity appeared only along the very first few rows of the edge, fading away as they moved toward the center of the sheet. This confirmed the existence of "edge states," which are special electronic pathways that are trapped at the boundary of the material. The researchers compared their observations with computer simulations based on the laws of quantum mechanics, and the two matched perfectly. The simulations showed that these edge states are not random accidents but are required by the geometry of the lattice itself. They are topological in nature, meaning their existence is guaranteed by a fundamental mathematical property of the system, much like how a knot cannot be untied without cutting the rope.

This work is a major step forward because it proves that scientists can now build these complex quantum materials from scratch using chemistry. The researchers found that the edge states they observed are a generalization of similar states found in graphene, but they exist in a system that lacks a specific symmetry usually thought to be necessary for such states to form. By showing that these states appear naturally in this supramolecular lattice, the study opens a new door for exploring quantum materials. It suggests that by designing different molecules, scientists can create a wide variety of artificial lattices to test theories and potentially discover new quantum phenomena that are difficult to find in nature. The ability to visualize and control these edge states provides a solid foundation for future research into materials with unique electronic properties.

Technical Summary: Direct Observation of the Zigzag Edge States of a Supramolecular Diatomic Kagome Lattice

Problem and Context
Lattice geometry is a fundamental determinant of the behavior of itinerant electrons in crystals, particularly within the realm of quantum materials. While the honeycomb and Kagome lattices have been extensively studied for their Dirac bands and flat bands (the latter arising from geometric frustration), the diatomic Kagome lattice (also known as the star lattice) remains largely unexplored experimentally. This lattice is viewed as a hybrid extension where triangular units are connected by diatomic pairs. Tight-binding (TB) calculations predict that this structure hosts four Dirac bands and two flat bands, with topological properties that can be tuned by the ratio of intra-corner ( $t_0$ ) to inter-corner ( $t_1$ ) coupling constants.

Despite theoretical predictions of novel quantum states, such as second-order topological states and excitonic insulators, experimental realization has been limited. A specific gap in knowledge concerns the existence of one-dimensional edge states analogous to those in graphene. In graphene, zigzag edges host topological edge states connecting projected Dirac points; however, it is theoretically unclear if the diatomic Kagome lattice supports such states, as it lacks the chiral symmetry that typically protects graphene's edge states.

Methodology
To address this, the authors employed a supramolecular chemistry approach to fabricate a diatomic Kagome lattice on a Pb(111) surface.

Material Design: They utilized Trip-Phz, a triptycene derivative featuring phenazine moieties. This molecule possesses a rigid, non-planar, $C_3$ -symmetric Y-shape.
Self-Assembly: Through $\pi$ - $\pi$ pancake bonding, Trip-Phz molecules self-assemble into a highly ordered 2D lattice. The molecular centers occupy honeycomb nodes, while the phenazine orbitals form triangular units, effectively materializing the diatomic Kagome geometry.
Characterization: The study utilized Scanning Tunneling Microscopy (STM) and Scanning Tunneling Spectroscopy (STS) ( $dI/dV$ measurements) to image the lattice structure and probe electronic states.
Theoretical Modeling: The experimental data were interpreted using Tight-Binding (TB) calculations based on the diatomic Kagome model. The parameters ( $t_0$ and $t_1$ ) were derived from Density Functional Theory (DFT) calculations of the molecular orbitals. The topological nature of the observed states was analyzed via the Zak phase and the bulk-edge correspondence.

Key Results

Structural Formation: STM topographs confirmed the formation of a highly ordered, single-domain diatomic Kagome lattice with a lattice constant of $1.92 \pm 0.04$ nm. The lattice exhibits a specific chirality (left-handed or right-handed) and is terminated predominantly by zigzag-type edges, distinct from the armchair edges often found in graphene islands.
Bulk Electronic Structure: Spectroscopic measurements of the bulk region revealed molecular bands derived from the Lowest Unoccupied Molecular Orbitals (LUMO and LUMO+1). The $dI/dV$ spectra showed features corresponding to the predicted Dirac bands and flat bands, with peaks identified at specific voltages (e.g., 0.99, 1.11, 1.39, and 1.48 V).
Observation of Edge States: The most significant finding is the direct observation of zigzag edge states.
- $dI/dV$ spectra taken near the lattice boundary exhibited a pronounced peak at $V = 1.42$ V that was absent in the bulk.
- $dI/dV$ imaging at this voltage revealed bright spots localized specifically on the first three rows of the zigzag edge, confirming the spatial confinement of these states.
- Similar edge states were observed in lattices with right-handed chirality, though with slightly reduced intensity due to disorder.
Theoretical Confirmation: TB calculations reproduced the experimental band structure, identifying the edge states as ES5, which connect the projected Dirac points. The spatial distribution of the calculated wavefunctions matched the experimental localization at the edge.
Topological Origin: The study established that these edge states are topological in nature. Calculations of the Zak phase ( $Z(k_y)$ ) demonstrated that the system is topologically nontrivial ( $Z = \pi$ ) in the momentum range where the edge states exist ( $2\pi/3 < |k_y| < \pi$ ). This confirms that the edge states are dictated by the bulk-edge correspondence, serving as a generalization of graphene's zigzag edge states in a system without chiral symmetry.

Significance and Claims
The paper claims to provide the first direct experimental evidence of edge states in a diatomic Kagome lattice. By successfully fabricating this lattice using supramolecular assembly, the authors demonstrate that:

It is possible to create nearly ideal 2D lattices with unique geometries using chemically designed, non-planar $\pi$ -conjugated molecules, bypassing the complex atomic interactions that often obscure theoretical predictions in inorganic materials.
The diatomic Kagome lattice supports topological edge states dictated by Zak phase quantization, even in the absence of the chiral symmetry required for graphene's edge states.
This work establishes a new platform based on supramolecular technology for exploring quantum materials with specific lattice geometries, offering a tunable system where parameters like the $t_0/t_1$ ratio can be adjusted via substrate selection to potentially access other predicted quantum states (e.g., second-order topological states).

The authors conclude that this study significantly expands the scope of quantum material research driven by lattice geometry, providing a solid experimental foundation for theories regarding emergent phenomena in diatomic Kagome systems.

Technical Summary: Direct Observation of the Zigzag Edge States of a Supramolecular Diatomic Kagome Lattice

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