Atomic-Scale Imaging of Fractional Spinon Quasiparticles in Open-Shell Triangulene Spin-$\frac{1}{2}$ Chains

TL;DR

This study demonstrates real-space imaging of fractional spinon quasiparticles in atomic-scale open-shell triangulene spin-$rac{1}{2}$ chains, revealing their dispersion and gap behavior with chain length.

Contribution

It constructs and probes individual spin-$rac{1}{2}$ chains using triangulene molecules, providing direct visualization of spinon quasiparticles at atomic resolution.

Findings

Excitation gap decreases with chain length, approaching zero for long chains.

Inelastic tunneling spectroscopy shows an m-shaped energy dispersion of spinons.

Chains exhibit properties consistent with gapless Haldane's prediction.

Abstract

The emergence of spinon quasiparticles, which carry spin but lack charge, is a hallmark of collective quantum phenomena in low-dimensional quantum spin systems. While the existence of spinons has been demonstrated through scattering spectroscopy in ensemble samples, real-space imaging of these quasiparticles within individual spin chains has remained elusive. In this study, we construct individual Heisenberg antiferromagnetic spin-$\frac{1}{2}$ chains using open-shell [2]triangulene molecules as building blocks. Each [2]triangulene unit, owing to its sublattice imbalance, hosts a net spin-$\frac{1}{2}$ in accordance with Lieb's theorem, and these spins are antiferromagnetically coupled within covalent chains with a coupling strength of $J = 45$ meV. Through scanning tunneling microscopy and spectroscopy, we probe the spin states, excitation gaps, and their spatial excitation weights within covalent spin chains of varying lengths with atomic precision. Our investigation reveals that the excitation gap decreases as the chain length increases, extrapolating to zero for long chains, consistent with Haldane's gapless prediction. Moreover, inelastic tunneling spectroscopy reveals an m-shaped energy dispersion characteristic of confined spinon quasiparticles in a one-dimensional quantum box. These findings establish a promising strategy for exploring the unique properties of excitation quasiparticles and their broad implications for quantum information.