Observation of fractional edge excitations in nanographene spin chains

摘要

Using scanning tunnelling microscopy and spectroscopy, fractional edge excitations are observed in nanographene spin chains, enabling the potential to study strongly correlated phases in purely organic materials.Fractionalization is a phenomenon in which strong interactions in a quantum system drive the emergence of excitations with quantum numbers that are absent in the building blocks. Outstanding examples are excitations with charge e/3 in the fractional quantum Hall effect(1,2), solitons in one-dimensional conducting polymers(3,4) and Majorana states in topological superconductors(5). Fractionalization is also predicted to manifest itself in low-dimensional quantum magnets, such as one-dimensional antiferromagnetic S = 1 chains. The fundamental features of this system are gapped excitations in the bulk(6) and, remarkably, S = 1/2 edge states at the chain termini(7-9), leading to a four-fold degenerate ground state that reflects the underlying symmetry-protected topological order(10,11). Here, we use on-surface synthesis(12) to fabricate one-dimensional spin chains that contain the S = 1 polycyclic aromatic hydrocarbon triangulene as the building block. Using scanning tunnelling microscopy and spectroscopy at 4.5 K, we probe length-dependent magnetic excitations at the atomic scale in both open-ended and cyclic spin chains, and directly observe gapped spin excitations and fractional edge states therein. Exact diagonalization calculations provide conclusive evidence that the spin chains are described by the S = 1 bilinear-biquadratic Hamiltonian in the Haldane symmetry-protected topological phase. Our results open a bottom-up approach to study strongly correlated phases in purely organic materials, with the potential for the realization of measurement-based quantum computation(13).