Quantum phase transition in magnetic nanographenes on a lead superconductor

Technical Summary: Quantum Phase Transition in Magnetic Nanographenes on a Lead Superconductor

Problem Statement
The interaction between quantum spins and superconductivity is a fundamental topic in condensed matter physics, theoretically predicted to host exotic phases such as magnetic bound states (Yu-Shiba-Rusinov states) and Majorana zero modes. While classical spin models predict symmetric bound states, a rigorous description of quantum spins on superconductors is complex. Previous experimental studies have largely relied on magnetic impurities derived from transition metals with localized $d/f$ orbitals. However, these systems suffer from significant magnetic anisotropy induced by spin-orbit coupling and crystal field splitting, which breaks the full SU(2) symmetry and hinders the study of intrinsic quantum spins. Conversely, magnetic nanographenes offer a promising alternative due to their negligible spin-orbit coupling and crystal field splitting, theoretically hosting intrinsic quantum magnetism with delocalized $\pi$-electron spin density. The challenge lies in experimentally realizing these ideal quantum spins on a superconductor and systematically tuning their exchange interaction to observe the predicted quantum phase transition between different ground states.

Methodology
The authors employed low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS) to investigate atomically precise magnetic nanographenes on a superconducting Pb(111) film.

• Sample Fabrication: Three distinct nanographenes (denoted NG1, NG2, and NG3) were synthesized in solution and sublimated onto Au(111). Using STM tip-induced atom manipulation, a single hydrogen atom was controllably dissociated from an $sp^3$ carbon site, introducing an unpaired electron and establishing a magnetic ground state of spin $S=1/2$ via sublattice imbalance.
• Characterization: Non-contact atomic force microscopy (nc-AFM) with a CO-functionalized tip was used to resolve the chemical structures and confirm the presence of out-of-plane distortions.
• Spectroscopic Measurements: High-resolution $dI/dV$ spectra were acquired using a superconducting tip (fabricated by indenting the tip into the Pb film) to minimize thermal broadening and resolve sub-meV energy scales. Measurements were conducted at temperatures of 1 K and 4.3 K.
• Data Analysis: To isolate the intrinsic electronic properties of the sample, the authors numerically deconvoluted the raw $dI/dV$ spectra to remove the convolution effects of the superconducting density of states from the tip.
• Theoretical Modeling: Mean-Field Hubbard (MFH) calculations were performed to simulate spin density distributions and local density of states (LDOS), comparing them with experimental orbital maps.
• Coupling Strength Quantification: The magnetic exchange strength was quantified by applying an out-of-plane magnetic field to quench the superconductivity of both the tip and the substrate, allowing the observation of Kondo resonances and the extraction of Kondo temperatures ($T_K$).

Key Contributions and Results

1. Realization of Intrinsic Quantum Spins: The study successfully fabricated three different nanographenes with an $S=1/2$ ground state on Pb(111). MFH calculations and STS confirmed that the spin density is delocalized within the molecule, and the system exhibits negligible magnetic anisotropy, effectively acting as an ideal quantum spin.
2. Observation of Magnetic Bound States: STS revealed a pair of in-gap magnetic bound states for all three nanographenes. The binding energies varied slightly depending on the specific adsorption configuration (NG1: $\pm 1.3$ meV; NG2: $\pm 1.65$ meV; NG3: $\pm 1.54$ meV).
3. Particle-Hole Asymmetry and Ground State Identification: A critical finding was the observation of particle-hole asymmetry in the spectral weights of the bound states.
   • In the weak coupling regime, the ground state is an underscreened doublet, and the bound states correspond to excitations to a singlet state, manifesting as dominant hole-like spectral weight.
   • In the strong coupling regime, the ground state is a Kondo singlet, and the bound states correspond to excitations to a doublet state, manifesting as dominant particle-like spectral weight.
4. Quantum Phase Transition: By varying the adsorption configuration, the authors tuned the magnetic exchange strength between the nanographene spin and Cooper pairs. They observed a crossing of the magnetic bound state energies accompanied by an inversion of particle-hole asymmetry. This transition occurs at a critical coupling strength of $k_B T_K \approx 1.6 \Delta$ (where $\Delta$ is the superconducting gap), marking a quantum phase transition from a doublet ground state to a singlet ground state.
5. Coexistence of Kondo Screening and Bound States: In the strong coupling regime, the authors observed the coexistence of in-gap bound states and a Kondo resonance (characterized by a Frota-line shape) outside the gap, confirming the quantum spin behavior consistent with numerical renormalization group (NRG) predictions.

Significance and Claims
The paper claims to provide direct experimental evidence of a quantum phase transition in a hybrid system of a quantum spin and a superconductor, driven by the tuning of magnetic exchange strength. The work demonstrates that delocalized graphene magnetism can host highly tunable magnetic bound states that interact with Cooper pairs without the complications of strong magnetic anisotropy found in transition metal impurities.

The authors state that this nanographene-superconductor platform offers a highly tunable system for further exploring quantum physics, specifically:

• The realization of many-body quasiparticle excitations in intrinsic Heisenberg spin chains on superconductors.
• The exploration of multi-channel quasiparticle excitations in high-spin nanographenes.
• Potential applications in fabricating qubits based on spin-singlet bound states or topological qubits based on Majorana zero modes in pure carbon-based systems.

The study validates theoretical models of quantum spins on superconductors and establishes a new material platform for investigating strongly correlated physics and potential quantum technological applications.