Tuneable topological domain wall states in engineered atomic chains

The research explores the creation and manipulation of topological modes in one-dimensional (1D) systems. These modes, often described using tight-binding (TB) models, possess unique electronic responses and hold potential for various applications. The Su-Schrieffer-Heeger (SSH) model, a prototypical example, features zero-energy, topologically protected end modes at the mid-gap energy. However, other 1D models, such as trimer and coupled dimer chains, exhibit non-zero energy boundary states. The researchers aim to overcome the limitations of existing systems by creating an atomically tunable system allowing explicit control of these edge modes. This is achieved using atomic manipulation with a low-temperature STM, which offers precise placement of atoms to create designer quantum materials. Previous work has successfully demonstrated the creation of quantum-confined 1D and 2D electronic systems and artificial lattices with various symmetries. The current study builds upon this by focusing on topological materials and the construction of systems with interface and edge states. The focus lies on trimer and coupled dimer chains, aiming to demonstrate the formation of tunable interface states between different ground states. The potential applications of these domain walls, such as preparing localized fractional charges and manipulating them, are also highlighted.

The paper reviews existing literature on topological modes in 1D and 2D systems, highlighting their potential applications. It discusses the SSH model and its limitations, introducing alternative models like trimer and coupled dimer chains that exhibit non-zero energy boundary states. The authors discuss previous experimental implementations of topological states in atomic-scale structures and ultra-cold atomic gases, emphasizing the importance of atomic manipulation in creating such systems. Prior work on self-assembled indium atomic wires demonstrating coupled dimer chains and their topological phases is reviewed, along with the limitations imposed by defects in these self-assembled structures. The research builds upon the use of chlorine vacancies in the chlorine c(2 × 2) structure on Cu(100) as building blocks for creating artificial systems with designer electronic structures, referencing related publications.

The researchers utilize chlorine vacancies in a c(2 × 2) chlorine adsorption layer on Cu(100) as building blocks for constructing atomic chains. The sample preparation involves cleaning a Cu(100) single crystal using Ne+ sputtering and annealing, followed by depositing anhydrous CuCl2 from an effusion cell to form the chloride structure. The experimental setup uses a low-temperature STM (Unisoku USM-1300) at 4.2 K. STM images are obtained in constant current mode, while dI/dV spectra are acquired using standard lock-in detection. Atomic manipulation involves precisely positioning the STM tip above a Cl atom adjacent to a vacancy, increasing the current to manipulate the Cl atom and vacancy site positions. Tight-binding (TB) calculations are used to simulate the electronic structure of the chains. Experimental data is analyzed to extract parameters such as on-site energy, energy broadening, and spatial shape of the wavefunction, which are then used to validate the TB model without adjustable parameters. The hopping parameters (t1, t2, t3) are determined from experiments on isolated vacancies and dimers. The researchers construct and characterize trimer and coupled dimer chains with various domain wall structures, employing dI/dV spectroscopy and mapping to investigate the electronic properties of the domain walls. The energy of the domain wall states is systematically tuned by adjusting the nearest-neighbor distances in the trimer chain, thereby modulating the hopping parameter t3. Finally, the experimental results are compared to simulations derived from the validated TB model, showing excellent agreement.

The key findings demonstrate the successful creation and control of topological domain wall states in atomically engineered trimer and coupled dimer chains. In trimer chains, the energy of the domain wall state is shown to be tuneable by adjusting the hopping parameter (t3) to the domain wall site, which is experimentally achieved by manipulating the nearest-neighbor distances. This tuneability is confirmed by comparing experimental dI/dV maps with simulated local density of states (LDOS) maps generated from the TB model, showing excellent agreement. The study also creates various domain walls in coupled dimer chains, demonstrating the existence of domain wall states in these structures, which have a hidden topological origin, as shown previously in self-assembled systems. The energies of the domain wall states depend on the specific domain wall type and the hopping parameters. Analysis of the domain wall electronic states reveals how they couple to the bulk chains, affecting their energy levels. The researchers successfully reproduce the experimental findings through simulations, confirming the accuracy of their TB model and highlighting the potential to design more complex structures.

The findings directly address the research question by demonstrating the successful fabrication of atomically precise structures exhibiting tuneable topological domain wall states. The tuneability of the domain wall energy in trimer chains offers a significant advance over previous systems, opening up new possibilities for controlling and manipulating these states. The successful creation of various domain wall configurations in coupled dimer chains expands the understanding of topological states in more complex systems. The agreement between experimental results and TB simulations validates the chosen model and provides a reliable framework for designing future structures. The study's findings are relevant to both fundamental physics of topological materials and the development of quantum devices, particularly those based on fractional charges and topological charge pumping.

The research successfully demonstrated the atomic-scale fabrication of trimer and coupled dimer chains with controllable topological domain wall states. The tunability of the domain wall energy in trimer chains represents a significant advance. Future work could explore using automated atomic manipulation to investigate fractional charges and topological charge pumping in these systems, potentially leading to the development of novel quantum devices.

The study focuses primarily on 1D chains, limiting the direct generalization to higher-dimensional systems. The energy of the higher-lying states in the trimer chain is difficult to accurately measure due to overlap with the chlorine layer's conduction band. The model used simplifies the complex interactions that occur in the experimental system, although the agreement between theory and experiment suggests that the simplifications do not significantly impact the key findings.