Spatially dispersing Yu-Shiba-Rusinov states in the unconventional superconductor FeTe0.55Se0.45

Observation of Rashba-Surface-Band-Dependent Yu-Shiba-Rusinov States in a Gold-Based Superconductor AuSn4

The interplay between the Rashba effect, superconductivity, and magnetism in gold-based superconductors provides a platform for exploring topological superconductivity, yet the interaction between Rashba bands and superconducting bound states remains unexplored. Here, we report Rashba-surface-band-dependent Yu-Shiba-Rusinov (YSR) states around Fe adatoms on the surfaces of AuSn4, using ultralow temperature (5 mK) scanning tunneling microscope/spectroscopy. On Au-terminated surfaces with Rashba bands, most Fe atoms occupy Au vacancies, while only a few adsorb on the Sn-terminated surfaces with dominant bulk metallic states. Remarkably, YSR states localized on the Fe atom are observed on Sn-terminated surfaces but absent on Au-terminated surfaces. First-principle calculations reveal a significant magnetic moment for Fe adatoms on Sn surfaces compared to a nearly negligible value on Au surfaces, which elucidates the observed surface-dependent YSR states. The termination-dependence local moment arises from the interplay of Rashba surface bands and s-d coupling, as described by the Anderson s-d exchange model.

Signatures of Amorphous Shiba State in FeTe0.55Se0.45

The iron-based superconductor FeTe0.55Se0.45 is a peculiar material: it hosts surface states with a Dirac dispersion, is a putative topological superconductor hosting Majorana modes in vortices, and has an unusually low Fermi energy. The superconducting state is generally characterized by three gaps in different bands, with the homogeneous, spatially extended Bogoliubov excitations─in this work, we uncover evidence that it is instead of a very different nature. Our scanning tunneling spectroscopy data show several peaks in the density of states above a full gap, and by analyzing their spatial and junction-resistance dependence, we conclude the peaks above the first one are not coherence peaks from different bands. Instead, comparisons with our simulations indicate they originate from generalized Shiba states that are spatially overlapping. This can lead to an amorphous state of Bogoliubov quasiparticles, reminiscent of impurity bands in semiconductors. We discuss the origin and implications of this new state.

Individual Assembly of Radical Molecules on Superconductors: Demonstrating Quantum Spin Behavior and Bistable Charge Rearrangement

High-precision molecular manipulation techniques are used to control the distance between radical molecules on superconductors. Our results show that the molecules can host single electrons with a spin 1/2. By changing the distance between tip and sample, a quantum phase transition from the singlet to doublet ground state can be induced. Due to local screening and charge redistribution, we observe either charged or neutral molecules, which couple in a sophisticated way, showing quantum spin behavior that deviates from the classical spins. Dimers at different separations show multiple Yu-Shiba-Rusinov peaks in tunneling spectroscopy of varying intensity, which are in line with the superconducting two-impurity Anderson model, where singlet (S = 0) and doublet (S = 1/2) ground states are found. The assembly of chains of 3, 4, and 5 molecules shows alternating charge patterns, where the edge molecules always host a charge/spin. The tetramer is observed in two configurations, where the neutral site is moved by one position. We show that these two configurations can be switched by the action of the probing tip in a nondestructive manner, demonstrating that the tetramer is an information unit, based on single-electron charge reorganization.

Observation of Yu-Shiba-Rusinov-like states at the edge of CrBr3/NbSe2 heterostructure

The hybrid ferromagnet-superconductor heterostructures have attracted extensive attention as they potentially host topological superconductivity. Relevant experimental signatures have recently been reported in CrBr3/NbSe2 ferromagnet-superconductor heterostructure, but controversies remain. Here, we reinvestigate CrBr3/NbSe2 by an ultralow temperature scanning tunneling microscope with higher spatial and energy resolutions. We find that the single-layer CrBr3 film is insulating and acts likely as a vacuum barrier, the measured superconducting gap and vortex state on it are nearly the same as those of NbSe2 substrate. Meanwhile, in-gap features are observed at the edges of CrBr3 island, which display either a zero-energy conductance peak or a pair of particle-hole symmetric bound states. They are discretely distributed at the edges of CrBr3 film, and their appearance is found closely related to the atomic lattice reconstruction near the edges. By increasing tunneling transmissivity, the zero-energy conductance peak quickly splits, while the pair of nonzero in-gap bound states first approach each other, merge, and then split again. These behaviors are unexpected for Majorana edge modes, but in consistent with the conventional Yu-Shiba-Rusinov states. Our results provide critical information for further understanding the interfacial coupling in CrBr3/NbSe2 heterostructure.

Hund's coupling mediated multi-channel quantum phase transition of a single magnetic impurity in Fe(Se, Te)

Understanding the interplay between individual magnetic impurities and superconductivity is crucial for bottom-up construction of novel phases of matter. Sub-gap bound states that are used in this endeavor are typically considered as independent entities that each result from the exchange scattering between the respective impurity orbitals and electrons of the superconducting condensate. Here we present experimental evidence of individual multi-spin impurities where the sub-gap states are not independent. Specifically, we find that by tuning the energy of the state closest to zero through zero, all other sub-gap states change particle-hole asymmetry as well. We show that this can be understood by including Hund's coupling, which favors high-spin configurations, into a multi-orbital Anderson model. Unlike for the case of independent spins, the transition we observe signals the simultaneous departure of more than one quasiparticle from the impurity, while the parity of the ground state may remain unchanged. Our results show that Hund's coupling is not only crucial in generating high-spin impurities, but also to understand the transition between two distinct ground states, and should therefore be taken into account for e.g. impurity-based band-structure engineering.

Spatially Dependent in-Gap States Induced by Andreev Tunneling through a Single Electronic State

By using low-temperature scanning tunneling microscopy and spectroscopy (STM/STS), we observe in-gap states induced by Andreev tunneling through a single impurity state in a low carrier density superconductor (NaAlSi). The energy-symmetric in-gap states appear when the impurity state is located within the superconducting gap. In-gap states can cross the Fermi level, and they show X-shaped spatial variation. We interpret the in-gap states as a consequence of the Andreev tunneling through the impurity state, which involves the formation or breakup of a Cooper pair. Due to the low carrier density in NaAlSi, the in-gap state is tunable by controlling the STM tip-sample distance. Under strong external magnetic fields, the impurity state shows Zeeman splitting when it is located near the Fermi level. Our findings not only demonstrate the Andreev tunneling involving single electronic state but also provide new insights for understanding the spatially dependent in-gap states in low carrier density superconductors.

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.

Interface-induced superconductivity in magnetic topological insulators

The interface between two different materials can show unexpected quantum phenomena. In this study, we used molecular beam epitaxy to synthesize heterostructures formed by stacking together two magnetic materials, a ferromagnetic topological insulator (TI) and an antiferromagnetic iron chalcogenide (FeTe). We observed emergent interface-induced superconductivity in these heterostructures and demonstrated the co-occurrence of superconductivity, ferromagnetism, and topological band structure in the magnetic TI layer-the three essential ingredients of chiral topological superconductivity (TSC). The unusual coexistence of ferromagnetism and superconductivity is accompanied by a high upper critical magnetic field that exceeds the Pauli paramagnetic limit for conventional superconductors at low temperatures. These magnetic TI/FeTe heterostructures with robust superconductivity and atomically sharp interfaces provide an ideal wafer-scale platform for the exploration of chiral TSC and Majorana physics.

Tracking a spin-polarized superconducting bound state across a quantum phase transition

The magnetic exchange coupling between magnetic impurities and a superconductor induce so-called Yu-Shiba-Rusinov (YSR) states which undergo a quantum phase transition (QPT) upon increasing the exchange interaction beyond a critical value. While the evolution through the QPT is readily observable, in particular if the YSR state features an electron-hole asymmetry, the concomitant change in the ground state is more difficult to identify. We use ultralow temperature scanning tunneling microscopy to demonstrate how the change in the YSR ground state across the QPT can be directly observed for a spin-1/2 impurity in a magnetic field. The excitation spectrum changes from featuring two peaks in the doublet (free spin) state to four peaks in the singlet (screened spin) ground state. We also identify a transition regime, where the YSR excitation energy is smaller than the Zeeman energy. We thus demonstrate a straightforward way for unambiguously identifying the ground state of a spin-1/2 YSR state.

Single-electron charge transfer into putative Majorana and trivial modes in individual vortices

Majorana bound states are putative collective excitations in solids that exhibit the self-conjugate property of Majorana fermions-they are their own antiparticles. In iron-based superconductors, zero-energy states in vortices have been reported as potential Majorana bound states, but the evidence remains controversial. Here, we use scanning tunneling noise spectroscopy to study the tunneling process into vortex bound states in the conventional superconductor NbSe₂, and in the putative Majorana platform FeTe_0.55Se_0.45. We find that tunneling into vortex bound states in both cases exhibits charge transfer of a single electron charge. Our data for the zero-energy bound states in FeTe_0.55Se_0.45 exclude the possibility of Yu-Shiba-Rusinov states and are consistent with both Majorana bound states and trivial vortex bound states. Our results open an avenue for investigating the exotic states in vortex cores and for future Majorana devices, although further theoretical investigations involving charge dynamics and superconducting tips are necessary.

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.

Exactly solving the Kitaev chain and generating Majorana-zero-modes out of noisy qubits

Majorana-zero-modes (MZMs) were predicted to exist as edge states of a physical system called the Kitaev chain. MZMs should host particles that are their own antiparticles and could be used as a basis for a qubit which is robust-to-noise. However, all attempts to prove their existence gave inconclusive results. Here, the Kitaev chain is exactly solved with a quantum computing methodology and properties of MZMs are probed by generating eigenstates of the Kitev Hamiltonian on 3 noisy qubits of a publicly available quantum computer. After an ontological elaboration I show that two eigenstates of the Kitaev Hamiltonian exhibit eight signatures attributed to MZMs. The results presented here are a most comprehensive set of validations of MZMs ever conducted in an actual physical system. Furthermore, the findings of this manuscript are easily reproducible for any user of publicly available quantum computers, solving another important problem of research with MZMs—the result reproducibility crisis.

Observation of robust zero-energy state and enhanced superconducting gap in a trilayer heterostructure of MnTe/Bi2Te3/Fe(Te, Se)

The interface between magnetic material and superconductors has long been predicted to host unconventional superconductivity, such as spin-triplet pairing and topological nontrivial pairing state, particularly when spin-orbital coupling (SOC) is incorporated. To identify these unconventional pairing states, fabricating homogenous heterostructures that contain such various properties are preferred but often challenging. Here, we synthesized a trilayer-type van der Waals heterostructure of MnTe/Bi₂Te₃/Fe(Te, Se), which combined s-wave superconductivity, thickness-dependent magnetism, and strong SOC. Via low-temperature scanning tunneling microscopy, we observed robust zero-energy states with notably nontrivial properties and an enhanced superconducting gap size on single unit cell (UC) MnTe surface. In contrast, no zero-energy state was observed on 2-UC MnTe. First-principle calculations further suggest that the 1-UC MnTe has large interfacial Dzyaloshinskii-Moriya interaction and a frustrated AFM state, which could promote noncolinear spin textures. It thus provides a promising platform for exploring topological nontrivial superconductivity.

Monolayer 1T-NbSe2 as a 2D-correlated magnetic insulator

Monolayer group V transition metal dichalcogenides in their 1T phase have recently emerged as a platform to investigate rich phases of matter, such as spin liquid and ferromagnetism, resulting from strong electron correlations. Newly emerging 1T-NbSe₂ has inspired theoretical investigations predicting collective phenomena such as charge transfer gap and ferromagnetism in two dimensions; however, the experimental evidence is still lacking. Here, by controlling the molecular beam epitaxy growth parameters, we demonstrate the successful growth of high-quality single-phase 1T-NbSe₂. By combining scanning tunneling microscopy/spectroscopy and ab initio calculations, we show that this system is a charge transfer insulator with the upper Hubbard band located above the valence band maximum. To demonstrate the electron correlation resulted magnetic property, we create a vertical 1T/2H NbSe₂ heterostructure, and we find unambiguous evidence of exchange interactions between the localized magnetic moments in 1T phase and the metallic/superconducting phase exemplified by Kondo resonances and Yu-Shiba-Rusinov–like bound states.

Observation of Yu-Shiba-Rusinov States in Superconducting Graphene

When magnetic atoms are inserted inside a superconductor, the superconducting order is locally depleted as a result of the antagonistic nature of magnetism and superconductivity. Thereby, distinctive spectral features, known as Yu-Shiba-Rusinov states, appear inside the superconducting gap. The search for Yu-Shiba-Rusinov states in different materials is intense, as they can be used as building blocks to promote Majorana modes suitable for topological quantum computing. Here, the first observation of Yu-Shiba-Rusinov states in graphene, a non-superconducting 2D material, and without the participation of magnetic atoms, is reported. Superconductivity in graphene is induced by proximity effect brought by adsorbing nanometer-scale superconducting Pb islands. Using scanning tunneling microscopy and spectroscopy the superconducting proximity gap is measured in graphene, and Yu-Shiba-Rusinov states are visualized in graphene grain boundaries. The results reveal the very special nature of those Yu-Shiba-Rusinov states, which extends more than 20 nm away from the grain boundaries. These observations provide the long-sought experimental confirmation that graphene grain boundaries host local magnetic moments and constitute the first observation of Yu-Shiba-Rusinov states in a chemically pure system.