Coupled Yu-Shiba-Rusinov States Induced by a Many-Body Molecular Spin on a Superconductor

Quantum spin driven Yu-Shiba-Rusinov multiplets and fermion-parity-preserving phase transition in K3C60

Magnetic impurities in superconductors are of increasing interest due to emergent Yu-Shiba-Rusinov (YSR) states and Majorana zero modes for fault-tolerant quantum computation. However, a direct relationship between the YSR multiple states and magnetic anisotropy splitting of quantum impurity spins remains poorly characterized. By using scanning tunneling microscopy, we systematically resolve individual transition-metal (Fe, Cr, and Ni) impurities induced YSR multiplets as well as their Zeeman effects in the K3C60 superconductor. The YSR multiplets show identical d orbital-like wave functions that are symmetry-mismatched to the threefold K3C60(1 1 1) host surface, breaking point-group symmetries of the spatial distribution of YSR bound states in real space. Remarkably, we identify an unprecedented fermion-parity-preserving quantum phase transition between ground states with opposite signs of the uniaxial magnetic anisotropy that can be manipulated by an external magnetic field. These findings can be readily understood in terms of anisotropy splitting of quantum impurity spins, and thus elucidate the intricate interplay between the magnetic anisotropy and YSR multiplets.

Quantum Phase Transition in Magnetic Nanographenes on a Lead Superconductor

Quantum spins, also known as spin operators that preserve SU(2) symmetry, lack a specific orientation in space and are hypothesized to display unique interactions with superconductivity. However, spin-orbit coupling and crystal field typically cause a significant magnetic anisotropy in d/f shell spins on surfaces. Here, we fabricate atomically precise S = 1/2 magnetic nanographenes on Pb(111) through engineering sublattice imbalance in the graphene honeycomb lattice. Through tuning the magnetic exchange strength between the unpaired spin and Cooper pairs, a quantum phase transition from the singlet to the doublet state has been observed, consistent with the quantum spin models. From our calculations, the particle-hole asymmetry is induced by the Coulomb scattering potential and gives a transition point about kBTk ≈ 1.6Δ. Our work demonstrates that delocalized π electron magnetism hosts highly tunable magnetic bound states, which can be further developed to study the Majorana bound states and other rich quantum phases of low-dimensional quantum spins on superconductors.

Cooper Pair Excitation Mediated by a Molecular Quantum Spin on a Superconducting Proximitized Gold Film

Breaking a correlated pair in a superconductor requires an even number of fermions providing at least twice the pairing energy Δ. Here, we show that a single tunneling electron can also excite a pair breaking excitation in a proximitized gold film in the presence of magnetic impurities. Combining scanning tunneling spectroscopy with theoretical modeling, we map the excitation spectrum of an Fe-porphyrin molecule on the Au/V(100) proximitized surface into a manifold of entangled Yu-Shiba-Rusinov and spin excitations. Pair excitations emerge in the tunneling spectra as peaks outside the spectral gap only in the strong coupling regime, where the presence of a bound quasiparticle in the ground state ensures the even fermion parity of the excitation. Our results unravel the quantum nature of magnetic impurities on superconductors and demonstrate that pair excitations unequivocally reveal the parity of the ground state.

Quantum nanomagnets in on-surface metal-free porphyrin chains

Unlike classic spins, quantum magnets are spin systems that interact via the exchange interaction and exhibit collective quantum behaviours, such as fractional excitations. Molecular magnetism often stems from d/f-transition metals, but their spin-orbit coupling and crystal field induce a significant magnetic anisotropy, breaking the rotation symmetry of quantum spins. Thus, it is of great importance to build quantum nanomagnets in metal-free systems. Here we have synthesized individual quantum nanomagnets based on metal-free multi-porphyrin systems. Covalent chains of two to five porphyrins were first prepared on Au(111) under ultrahigh vacuum, and hydrogen atoms were then removed from selected carbons using the tip of a scanning tunnelling microscope. The conversion of specific porphyrin units to their radical or biradical state enabled the tuning of intra- and inter-porphyrin magnetic coupling. Characterization of the collective magnetic properties of the resulting chains showed that the constructed S = 1/2 antiferromagnets display a gapped excitation, whereas the S = 1 antiferromagnets exhibit distinct end states between even- and odd-numbered spin chains, consistent with Heisenberg model calculations.

Controlling the Spin States of FeTBrPP on Au(111)

Spin-flip excitations of iron porphyrin molecules on Au(111) are investigated with a low-temperature scanning tunneling microscope. The molecules adopt two distinct adsorption configurations on the surface that exhibit different magnetic anisotropy energies. Density functional theory calculations show that the different structures and excitation energies reflect unlike occupations of the Fe 3d levels. We demonstrate that the magnetic anisotropy energy can be controlled by changing the adsorption site, the orientation, or the tip-molecule distance.

Spin-orbital Yu-Shiba-Rusinov states in single Kondo molecular magnet

Studies of single-spin objects are essential for designing emergent quantum states. We investigate a molecular magnet Tb₂Pc₃ interacting with a superconducting Pb(111) substrate, which hosts unprecedented Yu-Shiba-Rusinov (YSR) subgap states, dubbed spin-orbital YSR states. Upon adsorption of the molecule on Pb, the degeneracy of its lowest unoccupied molecular orbitals (LUMO) is lifted, and the lower LUMO forms a radical spin via charge transfer. This leads to Kondo screening and subgap states. Intriguingly, the YSR states display two pairs of resonances with clearly distinct behavior. The energy of the inner pair exhibits prominent inter and intra molecular variation, and it strongly depends on the tip height. The outer pair, however, shifts only slightly. As is unveiled through theoretical calculations, the two pairs of YSR states originate from the ligand spin and charge-fluctuating higher LUMO, coexisting in a single molecule, but only weakly coupled presumably due to different spatial distribution. Our work paves the way for understanding complex many-body excitations and constructing molecule-based topological superconductivity.

Yu-Shiba-Rusinov (YSR) states result from the exchange coupling between a localized magnetic moment and a superconductor. Traditionally, the YSR states have been studied for magnetic atoms. For molecular magnets with extended ligand spin, the entanglement of spin and ligand orbital gives rise to new forms of YSR excitations. Here, Xia et al uncovered spin-orbital YSR states in an unpaired ligand spin in the molecular magnet Tb2Pc3 on Pb.

On-Surface Synthesis and Spectroscopy of Aluminum Phthalocyanine on Superconducting Lead

Large ordered islands of aluminum phthalocyanine (AlPc) molecules, which are unstable in air, are synthesized from ClAlPc on Pb(100) via dechlorination. Low-temperature scanning tunneling microscopy reveals that isolated AlPc molecules lose their spin moment on superconducting Pb(100). Molecular magnetism, which is detected via Yu-Shiba-Rusinov (YSR) resonances, may be restored by surrounding a molecule with an array of neighbor molecules in artificial arrays or in a self-assembled monolayer. Unlike phthalocyanine (H₂Pc) or lead phthalocyanine (PbPc) monolayers, where the YSR energy was found to depend strongly on the detailed configuration of the neighboring molecules, we find a similar magnetic moment on every second molecule for AlPc. In addition, YSR resonances lead to unusually high conductance peaks that are due to vibrational excitations. Twelve vibrational modes are resolved and discussed with respect to similar results from PbPc. The enhancement of the inelastic transitions is tentatively attributed to the large amplitude of the YSR resonances and the long lifetime of electrons in the molecular bound state. By assembling neighboring molecules into configurations that differ from those of the monolayer, the YSR energy may be fine-tuned, and a simple spin-state switching device is constructed.

Resonance-Enhanced Vibrational Spectroscopy of Molecules on a Superconductor

Molecular vibrational spectroscopy with the scanning tunneling microscope is feasible but usually detects few vibrational modes. We harness sharp Yu-Shiba-Rusinov states observed from molecules on a superconductor to significantly enhance the vibrational signal. From a lead phthalocyanine molecule 46 vibrational peaks are resolved enabling a comparison with calculated modes. The energy resolution is improved beyond the thermal broadening limit and shifts induced by neighbor molecules or the position of the microscope tip are determined. Vice versa, spectra of vibrational modes are used to measure the effect of an electrical field on the energy of Yu-Shiba-Rusinov states. The method may help to further probe the interaction of molecules with their environment and to better understand selection rules for vibrational excitations.

Extending the Spin Excitation Lifetime of a Magnetic Molecule on a Proximitized Superconductor

Molecular spins on surfaces potentially used in quantum information processing and data storage require long spin excitation lifetimes. Normally, coupling of the molecular spin with the conduction electrons of metallic surfaces causes fast relaxation of spin excitations. However, the presence of superconducting pairing effects in the substrate can protect the excited spin from decaying. In this work, we show that a proximity-induced superconducting gold film can sustain spin excitations of a FeTPP-Cl molecule for more than 80 ns. This long value was determined by studying inelastic spin excitations of the S = 5/2 multiplet of FeTPP-Cl on Au films over V(100) using scanning tunneling spectroscopy. The spin lifetime decreases with increasing film thickness, along with the decrease of the effective superconducting gap. Our results elucidate the use of proximitized gold electrodes for addressing quantum spins on surfaces, envisioning new routes for tuning the value of their spin lifetime.

Magnetic Moment Preservation and Emergent Kondo Resonance of Co-Phthalocyanine on Semimetallic Sb(111)

Magnetic molecules on surfaces have been widely investigated to reveal delicate interfacial couplings and for potential technological applications. In these endeavors, one prevailing challenge is how to preserve or recover the molecular spins, especially on highly metallic substrates that can readily quench the magnetic moments of the admolecules. Here, we use scanning tunneling microscopy and spectroscopy to exploit the semimetallic nature of antimony and observe, surprisingly yet pleasantly, that the spin of Co-phthalocyanine is well preserved on Sb(111), as unambiguously evidenced by the emergent strong Kondo resonance across the molecule. Our first-principles calculations further confirm that the optimal density of states near the Fermi level of the semimetal is a decisive factor, weakening the overall interfacial coupling, while still ensuring sufficiently effective electron-spin scattering in the many-body system. Beyond isolated admolecules, we discover that each of the magnetic moments in a molecular dimer or a densely packed island is distinctly preserved as well, rendering such molecular magnets immense potentials for ultrahigh density memory devices.

Observation of Yu-Shiba-Rusinov States and Inelastic Tunneling Spectroscopy for Intramolecule Magnetic Exchange Interaction Energy of Terbium Phthalocyanine (TbPc) Species Adsorbed on Superconductor NbSe2

We investigated the spin properties of the terbium phthalocyanine (TbPc) species adsorbed on the superconductor NbSe2 surface using scanning tunneling microscopy and spectroscopy. TbPc2 is a molecule in a class of single-molecule magnets (SMMs), and the use of superconductor electrodes attracts attention for the application to the devices using the spin degree of freedom. TbPc is a building block of TbPc2 and can reveal the spin component's behavior. In the experiment, TbPc species were placed on the surface of the superconductor NbSe2. We measured Yu-Shiba-Rusinov (YSR) states caused by the interaction between the superconducting state and magnetic impurity and inelastic tunneling spectroscopy (IETS) for the spin excitation, below 1 K. We also measured the Kondo state formed by the magnetic singlet formation. We detected the radical spin at the ligand position of the TbPc by the presence of the Kondo peak and demonstrated that the radical spin forms the YSR feature. In addition, the exchange interaction energy (Eex) between the spins of the radical ligand (Pc) and the center 4f metal atom (Tb3+) is determined by using the IETS technique. Eex is a critical parameter that determines the blocking temperature, below which the sample behaves as an SMM. IETS results show that the statistical distribution of Eex has peaked at 1.3, 1.6, and 1.9 meV. The energy range is comparable to the recent theoretical calculation result. In addition, we show that the energy variation is correlated with the bonding configuration of TbPc.

Sub-gap Fano resonances in a topological superconducting wire with on-site Coulomb interactions

We consider theoretically a 1D-semiconducting wire with strong Rashba interaction in proximity withs-wave superconductor, driven into topological phase by external magnetic field. Additionally, we take into account on-site Coulomb interactions inside the wire. The system is modelled by a tight binding Hamiltonian with Rashba hopping term and induceds-wave superconductivity. Calculations are performed utilizing recursive Green's function method, and Coulomb interactions are treated selfconsistently within Hubbard I approximation. For the Hubbard levels residing withinp-wave superconducting gap, particle-hole symmetric four-resonance structure develops in the density of states, apart from Majorana resonance. One pair of particle-hole symmetric resonances is created by the discrete II-Hubbard levels of the particular site, and the second pair of Hubbard sub-bands originates from recursive summation over the sites of the wire. Quantum interference between both types of pairs of states creates in-gap charge-conjugated Fano resonances with opposite asymmetry factors. We demonstrate that when quantum interference is dominated by two-particle tunneling, the Majorana resonance is strongly diminished, while it is not altered when single-particle tunneling dominates in interference process. We also discuss some consequences for experimental distinction of true Majorana states, and show that on-site Coulomb interactions support the appearance of topological phase.