​​Polyacetylene is a one-dimensional polymer. The long chain of carbon atoms shows a spontaneous dimerization with a succession of single and double bonds. The dimerization allows two ground sta​tes of the same energy (Fig.1a). When both coexist in the molecule, a bound state — a domain wall excitation dubbed soliton — emerges at the interface. The soliton has a neutral charge Q=0 and a spin S=1/2. It gains a charge Q=±e but becomes spinless S=0 when ionizing the molecule. These spin-charge relations are remarkable. They cannot be obtained from combinations of the elementary constituents of the system, such as the electrons and holes characterized by Q=±e and S=1/2. In-stead, the unconventional spin-charge relation of the soliton roots down to the fractionalization of the elementary charge e. This phenomenon is all the more intriguing that it can play a key role in the surface currents observed in some insulators and the development of robust quantum computers.

Physicists have recently predicted a generalization of the fractional charges of polyacetylene in two dimensions [1]. Here, fractionalization occurs to the bound state of a Kekulé vortex, a twisting elec-tronic structure localized on the atomic bonds. However, the realization of such a topological defect has long remained elusive. An international collaboration involving a researcher of the LOMA has just reported in Nature Communications the realization and the observation of a Kekulé vortex in graphene [2].

Graphene is a crystal of carbon atoms realizing a honeycomb lattice. The chemical composition ena-bles every third hexagon to form double covalent bonds (see Fig.1b). This periodic arrangement al-lows three electronic configurations of the same energy. Each configuration is known as Kekulé configuration, in reference to the discovery of carbon's tetravalence by German chemist F. A. Kekule. Unlike polyacetylene, however, graphene does not stabilize in just one double-bond configura-tion. It remains instead in a quantum superposition of the three.

Researchers have just uncovered the possibility of stabilizing each of the three Kekulé configura-tions [2] (see Fig.1c). To lift the degeneracy, they broke translational invariance while preserving the threefold symmetry by grafting a hydrogen atom onto the graphene sheet. The hydrogen atom cova-lently binds a carbon atom, forcing the electrons to rearrange. By imaging the real-space distribution of the electronic states with a tunneling electron microscope, the researchers observed the coexist-ence of the three Kekulé structures in different regions of space around the hydrogen atom (see Figs.1d,e). They could show that, to connect from one Kekule domain to another, the electronic states must accommodate their phase continuously, thus realizing a vortex (see Fig.1f). Three com-plementary theoretical methods further support the observation and demonstrate that the electron twist in the Kekule structure is reminiscent of the Berry phase of the massless relativistic electrons.

Akin polyacetylene, the coexistence of different Kekulé configurations in graphene leads to the emergence of a (quasi-)bound state, here at the core of the vortex, with a potential fractional charge [1]. The realization of the Kekule vortex then revives interest in further evidence of fractionalization in graphene, such as unconventional spin-charge relations.