Katerina Vaxevani and colleagues at CIC nanoGUNE-BRTA have demonstrated parity-dependent coupling between molecular spin chains and a superconductor. The researchers grew molecular Haldane chains of antiferromagnetically coupled spin-1 triangulene units on a surface and used scanning tunnelling spectroscopy to observe how the chains interact with a superconducting condensate. Odd-length chains hosted Yu-Shiba-Rusinov bound states, while even-length chains remained decoupled, revealing a mechanism driven by the interaction between edge states. This length-tunable coupling, the work shows, opens a route toward molecular spin qubits based on carbon architectures.
Molecular Triangulene Chains for Topological Quantum Systems
The creation of these molecular spin chains relies on a proximitized Au(111)/Nb(110) surface, a platform that allows for on-surface synthesis at elevated temperatures while preserving superconducting correlations. Stepwise annealing of molecular precursors induces Ullmann coupling and subsequent cyclodehydrogenation, resulting in triangulene chains of varying lengths across the gold surface. The reconstruction of the gold surface and the superconducting gap remain unaltered throughout this process, indicating the compatibility of the synthesis with the superconducting substrate.
This careful construction enables the observation of topological edge states, which are considered building blocks for quantum spin devices. The research reveals that odd-length chains host Yu-Shiba-Rusinov (YSR) bound states within the superconducting gap, originating from a net spin-1 ground state. Conversely, even-length chains, possessing a spin-0 ground state, remain decoupled from the superconductor. This alternation in coupling is attributed to the sign and strength of the inter-edge interaction, a mechanism validated by the detection of extra-gap spin excitations in tunnelling spectra.
The ability to switch the magnetic ground state based on chain length, read out through the presence or absence of these sub-gap YSR excitations, represents a novel method for encoding and detecting spin correlations at the molecular scale. The observed robustness of these topological edge states within a superconducting environment is significant, as it demonstrates the potential for integrating molecular systems with superconducting circuits.
The researchers note that this work establishes proximitized gold films as a platform for engineering correlated spin-superconductor hybrids based on atomically precise carbon nanostructures. Collective many-body spin excitation modes were also detected, and these excitations remain decoupled from the superconductor due to the much larger Haldane gap. This decoupling further supports the topological protection of the spin states within the chains. The implications of this research extend beyond fundamental materials science, offering a pathway toward molecular spin qubits based on π-conjugated carbon architectures.
The researchers state that extending this approach to other designer spin systems in carbon-based π-conjugated architectures could give access to regimes where entanglement between fractional edge spins and screening by the superconducting condensate coexist and compete, envisioning a future where these systems enable novel hybrid quantum devices. The work builds on the understanding that exotic phases of matter can emerge when collective interactions reshape fundamental particles into fractional entities with new quantum numbers. This fractionalization is a hallmark of strongly correlated systems, and in one-dimensional antiferromagnetic integer spin chains, it manifests as symmetry-protected spin-1/2 edge states.
These edge states, protected by a topological Haldane gap, are considered ideal building blocks for hybrid spin-superconductor quantum systems, but the survival of fractionalization when coupled to a superconducting condensate remained an open question until now. The results presented demonstrate that these fractional states not only survive but can be actively controlled through chain length.
Parity Defines Coupling in Molecular Spin Chains
Analysis of spectral data revealed systematic differences between chains, with the excitation energy of spin states decreasing with chain length in even-numbered chains, and the presence of Yu-Shiba-Rusinov states in odd-numbered chains. “The spectral differences between chains extend systematically to other lengths, alternating with the parity of the chain length,” the researchers report, highlighting the consistent pattern observed. This alternating behavior is a direct consequence of the chains’ ground state spin.
A two-site spin-superconductor model indicates that parallel alignment of edge spins in odd-length chains stabilizes a spin-triplet ground state with a net magnetic moment, while antiparallel alignment in even-length chains favors an open-shell singlet. This model predicts a renormalized Kondo coupling, approaching zero for the singlet state and for the triplet state, aligning with experimental observations.
The researchers determined inter-edge coupling values of |J| by observing transitions in the spin states, finding that removing one edge spin releases a spin at the opposite end, systematically showing YSR states at lower energies with an average of 0. 6 ± 0. 2 meV. The ability to control coupling based on chain length offers a pathway toward manipulating quantum information encoded in these molecular systems.
Averaged spectra from chains ranging from N=3 to N=11 demonstrate this clearly, with collective spin excitation features alternating in number and position, a pattern accurately reproduced by theoretical models. This precise control over the coupling, achieved through a relatively simple manipulation of chain length, suggests a scalable approach to building molecular spin qubits. The researchers note that the Au(111) herringbone reconstruction likely contributes to site-dependent variations in the coupling strength, but the overall parity-dependent trend remains consistent.
The implications of this work extend beyond simply demonstrating a new control mechanism. The Au(111)/Nb(110) platform itself represents an advancement, allowing for the on-surface synthesis of molecular chains without compromising the superconducting properties of the substrate.
This compatibility opens up possibilities for integrating other carbon-based topological phases into superconducting circuits, potentially leading to more complex and robust quantum devices. The model’s ability to reproduce experimental results with high fidelity validates the underlying physics and provides a framework for designing future molecular spin systems with tailored properties.
Yu-Shiba-Rusinov States Reveal Odd-Chain Edge Spins
Researchers observed that odd-length chains hosted Yu-Shiba-Rusinov (YSR) resonances, localized states originating from spin-1/2 edge states, while even-length chains exhibited only extra-gap singlet-triplet excitations, indicating a decoupled state. This parity-dependent coupling arises from alternating magnetic ground states determined by inter-edge exchange interactions, establishing a mechanism for controlling spin interactions at the molecular level.
The team’s two-site spin-superconductor model demonstrates that the exchange coupling between edge spins becomes renormalized by the inter-edge interaction, resulting in an effective coupling that explains the observed spectral alternation. By extracting inter-edge coupling values from the observed transitions, the model accurately reproduces the experimental evolution, predicting YSR states in all odd-length chains and their absence in even-length chains.
This observation aligns with predictions from a valence-bond-solid description of a spin-1 Haldane chain, solidifying the topological origin of the YSR states. The binding energy of these states fluctuates due to site-dependent variations in the exchange coupling, likely caused by the gold surface’s herringbone reconstruction, but the overall pattern of alternating coupling remains consistent. Long-range dI/dV spectra acquired on the terminal and inner triangulene units of an 11-unit chain reveal distinct spectral signatures, confirming the localization of the edge states and their decoupling from the bulk excitations.
This work paves the way toward topologically protected molecular spin qubits and novel hybrid quantum devices, offering a new avenue for manipulating and controlling quantum information at the nanoscale. The findings demonstrate that the topological edge states of molecular Haldane chains remain robust in a superconducting environment, offering a promising pathway for building advanced quantum technologies.
Inter-Edge Interactions Control Superconducting Coupling
The model describes edge states as two spin-1/2 impurities interacting with a strength J, each coupled to a single-site superconductor with Kondo-like coupling JK. The ability to predict and observe this behavior confirms the critical role of inter-edge interactions in mediating the coupling between the molecular spins and the superconducting condensate. The research team’s analysis of chains ranging from three to fourteen triangulene units revealed a clear trend in sub-gap dI/dV spectra.
Odd-length chains consistently displayed YSR resonances at their termini, distinct from the differential density of states features, while even-length chains showed no such states. This observation establishes a finite Kondo exchange coupling JK between the edge states and the superconducting substrate, confirming their magnetic origin and highlighting the importance of the chain’s parity in determining its superconducting response. The extracted inter-edge coupling values, determined by analyzing singlet-triplet (ST) and triplet-singlet (TS) transitions, fall within a range of |J| and provide further validation of the theoretical model.
Further investigation revealed a direct link between inter-edge coupling and the presence of YSR states. The researchers note, emphasizing the sensitivity of the system to changes in the chain’s topology.
The successful integration of triangulene Haldane chains onto a superconducting platform addresses a significant challenge in the field. Previous attempts at on-surface synthesis often relied on catalytic gold surfaces incompatible with superconductivity. The Au(111)/Nb(110) platform, however, maintains the catalytic properties necessary for chain growth while simultaneously hosting superconducting correlations, effectively extending the scope of carbon-based topological phases into the superconducting regime. Spatially resolved maps of the YSR spectral weight confirm that these states are confined to the terminal triangulene units, exhibiting a characteristic shape resembling radical states at zigzag edges.
See today’s quantum computing news on Quantum Zeitgeist for the latest breakthroughs in qubits, hardware, algorithms, and industry deals.
