[Paper Review] Designer magnetic topological graphene nanoribbons

Shaotang Song, Pei Wen Ng+16 more|arXiv (Cornell University)|Apr 27, 2022

Graphene research and applications4 citations

TL;DR

This paper presents a rational design strategy for magnetic topological graphene nanoribbons (MT-GNRs) by unifying real-space (Clar's rule) and reciprocal-space (band structure topology) approaches. Using on-surface synthesis of tailored molecular precursors, the authors realize MT-GNRs with robust terminal pi-magnetism and topological edge states, directly observed via single-nickelocene spin sensing, and demonstrate tunable spin coupling from antiferromagnetic to paramagnetic-like behavior by controlling nanoribbon length.

ABSTRACT

The interplay of magnetism and topology lies at the heart of condensed matter physics, which offers great opportunities to design intrinsic magnetic topological materials hosting a variety of exotic topological quantum states including the quantum anomalous Hall effect (QAHE), axion insulator state, and Majorana bound states. Extending this concept to one-dimension (1D) systems offers additional rich quantum spin physics with great promise for molecular-scale spintronics. Despite recent progress in the discovery of symmetry-protected topological quantum phases in 1D graphene nanoribbons (GNRs), the rational design and realization of magnetic topological GNRs (MT-GNRs) represents a grand challenge, as one must tackle multiple dimensions of complexity including time-reversal symmetry (TRS), spatial symmetry (width, edge, end geometry) and many-electron correlations. Here, we devised a new route involving the real- and reciprocal-space descriptions by unifying the chemists and physicists perspectives, for the design of such MT-GNRs with non-trivial electronic topology and robust magnetic terminal. Classic Clar's rule offers a conceptually qualitative real-space picture to predict the transition from closed-shell to open-shell with terminal magnetism, and band gap reopening with possible non-trivial electronic topology in a series of wave-like GNRs, which are further verified by first principle calculations of band-structure topology in a momentum-space. With the advance of on-surface synthesis and careful design of molecular precursors, we have fabricated these MT-GNRs with observation of topological edge bands, whose terminal pi-magnetism can be directly captured using a single-nickelocene spin sensor. Moreover, the transition from strong anti-ferromagnetic to weak coupling (paramagnetism-like) between terminal spins can be controlled by tuning the length of MT-GNRs.

Motivation & Objective

• To overcome the grand challenge of rationally designing magnetic topological graphene nanoribbons (MT-GNRs) with non-trivial topology and robust terminal magnetism.
• To unify chemist's real-space intuition (Clar's rule) with physicists' reciprocal-space band structure analysis for predictive design.
• To realize MT-GNRs with controlled electronic topology and magnetic edge states through precise molecular precursor engineering.
• To experimentally verify topological edge bands and terminal magnetism using advanced spin-sensing techniques.
• To demonstrate tunability of spin coupling (from antiferromagnetic to paramagnetic-like) by varying nanoribbon length.

Proposed method

• Applying Clar's rule to predict open-shell character and terminal magnetism in wave-like graphene nanoribbons based on real-space resonance structures.
• Performing first-principles calculations to analyze band structure topology in momentum space and confirm non-trivial topology.
• Designing and synthesizing custom molecular precursors for on-surface fabrication of graphene nanoribbons with specific width, edge geometry, and end structures.
• Using low-temperature scanning tunneling microscopy (STM) and single-nickelocene spin sensors to directly image and probe terminal pi-magnetism.
• Tuning the nanoribbon length to control the magnetic coupling between terminal spins from strong antiferromagnetic to weakly coupled (paramagnetism-like) states.
• Combining experimental observations with theoretical modeling to validate the emergence of topological edge states and robust magnetic moments.

Experimental results

Research questions

• RQ1 Can Clar's rule in real space reliably predict the emergence of terminal magnetism and open-shell character in wave-like graphene nanoribbons?
• RQ2 What is the relationship between nanoribbon length and the magnetic coupling strength between terminal spins in MT-GNRs?
• RQ3 Can topological edge states be experimentally observed in designed magnetic graphene nanoribbons using spin-sensitive probes?
• RQ4 To what extent can the interplay of time-reversal symmetry, spatial symmetry, and electron correlations be controlled in 1D MT-GNRs?
• RQ5 How does the transition from closed-shell to open-shell electronic structure manifest in the band structure and spin texture of MT-GNRs?

Key findings

• The authors successfully synthesized graphene nanoribbons with non-trivial electronic topology and robust terminal pi-magnetism using on-surface synthesis of designed molecular precursors.
• Topological edge states were experimentally observed in the MT-GNRs, confirming the presence of protected edge modes.
• Terminal magnetism was directly imaged and quantified using a single-nickelocene spin sensor, providing unambiguous evidence of localized magnetic moments.
• The magnetic coupling between terminal spins transitions from strong antiferromagnetic to weakly coupled (paramagnetism-like) as the nanoribbon length increases.
• First-principles calculations confirmed band gap reopening and non-trivial topology in momentum space, consistent with the real-space predictions from Clar's rule.
• The combined real- and reciprocal-space approach enables a predictive framework for designing 1D magnetic topological materials with tailored quantum properties.