Parity-dependent coupling of molecular spin chains to a superconductor

Abstract

Topological order can fractionalize the quantum numbers of the underlying particles. A paradigmatic example is the spin-1/2 states at the edges of an antiferromagnetic integer-spin chain, protected by a topological Haldane gap in the bulk and mutually coupled in short chains. Owing to their topological protection, they are natural building blocks for hybrid spin-superconductor quantum systems. Whether fractionalization survives the coupling to a superconducting condensate, however, remains an open question. Here we grow molecular Haldane chains of antiferromagnetically coupled spin-1 triangulene units on a proximitized Au(111)/Nb(110) surface and resolve a parity-dependent coupling of their spin-1/2 edge states to the superconducting condensate by scanning tunnelling spectroscopy. Odd-length chains host Yu-Shiba-Rusinov bound states inside the superconducting gap, originating from the net S=1 ground state, whereas even-length chains form an S=0 ground state decoupled from the superconductor. A two-site superconductor model reveals that this alternation arises from the sign and strength of the inter-edge interaction, a mechanism independently validated by extra-gap spin excitations in tunnelling spectra. Collective many-body spin excitation modes are also detected decoupled from the superconductor by the much larger Haldane gap. The length-tunable coupling of the edge spins to the superconductor opens a route toward molecular spin qubits based on $π$-conjugated carbon architectures.