# Project B9

## 2023

### Proximity superconductivity in atom-by-atom crafted quantum dots

*Lucas Schneider, Khai That Ton, Ioannis Ioannidis, Jannis Neuhaus-Steinmetz, Thore Posske, Roland Wiesendanger, and Jens Wiebe*

Gapless materials in electronic contact with superconductors acquire proximity-induced superconductivity in a region near the interface. Numerous proposals build on this addition of electron pairing to originally non-superconducting systems and predict intriguing phases of matter, including topological, odd-frequency, nodal-point or Fulde–Ferrell–Larkin–Ovchinnikov superconductivity. Here we investigate the most miniature example of the proximity effect on only a single spin-degenerate quantum level of a surface state confined in a quantum corral on a superconducting substrate, built atom by atom by a scanning tunnelling microscope. Whenever an eigenmode of the corral is pitched close to the Fermi energy by adjusting the size of the corral, a pair of particle–hole symmetric states enters the gap of the superconductor. We identify these as spin-degenerate Andreev bound states theoretically predicted 50 years ago by Machida and Shibata, which had—so far—eluded detection by tunnel spectroscopy but were recently shown to be relevant for transmon qubit devices. We further find that the observed anticrossings of the in-gap states are a measure of proximity-induced pairing in the eigenmodes of the quantum corral. Our results have direct consequences on the interpretation of impurity-induced in-gap states in superconductors, corroborate concepts to induce superconductivity into surface states and further pave the way towards superconducting artificial lattices.

### Probing the topologically trivial nature of end states in antiferromagnetic atomic chains on superconductors

*L. Schneider, Ph. Beck, L. Rozsa, Th. Posske, J. Wiebe and R. Wiesendanger*

Spin chains proximitized by s-wave superconductors are predicted to enter a mini-gapped phase with topologically protected Majorana modes (MMs) localized at their ends. However, the presence of non-topological end states mimicking MM properties can hinder their unambiguous observation. Here, we report on a direct method to exclude the non-local nature of end states via scanning tunneling spectroscopy by introducing a locally perturbing defect on one of the chain’s ends. We apply this method to particular end states observed in antiferromagnetic spin chains within a large minigap, thereby proving their topologically trivial character. A minimal model shows that, while wide trivial minigaps hosting end states are easily achieved in antiferromagnetic spin chains, unrealistically large spin-orbit coupling is required to drive the system into a topologically gapped phase with MMs. The methodology of perturbing candidate topological edge modes in future experiments is a powerful tool to probe their stability against local disorder.

### Search for large topological gaps in atomic spin chains on proximitized superconducting heavy-metal layers

*Ph. Beck, B. Nyári, L. Schneider, L. Rózsa, A. Lászlóffy, K. Palotás, L. Szunyogh, B. Ujfalussy, J. Wiebe, and R. Wiesendanger*

One-dimensional systems comprising s-wave superconductivity with meticulously tuned magnetism realize topological superconductors hosting Majorana modes whose stability is determined by the gap size. However, for atomic spin chains on superconductors, the effect of the substrate’s spin-orbit coupling on the topological gap is largely unexplored. Here, we introduce an atomic layer of the heavy metal gold on a niobium surface combining strong spin-orbit coupling and a large superconducting gap with a high crystallographic quality, enabling the assembly of defect-free iron chains using a scanning tunneling microscope tip. Scanning tunneling spectroscopy experiments and density functional theory calculations reveal ungapped Yu–Shiba–Rusinov bands in the ferromagnetic chain despite the heavy substrate. By artificially imposing a spin spiral state, the calculations indicate minigap opening and zero-energy edge state formation. The methodology enables a material screening of heavy-metal layers on elemental superconductors for ideal systems hosting Majorana edge modes protected by large topological gaps.

### Increased localization of Majorana modes in antiferromagnetic chains on superconductors

*Daniel Crawford, Eric Mascot, Makoto Shimizu, Roland Wiesendanger, Dirk K. Morr, Harald O. Jeschke, and Stephan Rachel*

Magnet-superconductor hybrid (MSH) systems are a key platform for custom-designed topological superconductors. Ideally, the ends of a one-dimensional MSH structure will host Majorana zero-modes (MZMs), the fundamental unit of topological quantum computing. However, some experiments with ferromagnetic (FM) chains show a more complicated picture. Due to tiny gap sizes and hence long coherence lengths, MZMs might hybridize and lose their topological protection. Recent experiments on a niobium surface have shown that both FM and antiferromagnetic (AFM) chains may be engineered, with the magnetic order depending on the crystallographic direction of the chain. While FM chains are well understood, AFM chains are less so. Here, we study two models inspired by the niobium surface: A minimal model to elucidate the general topological properties of AFM chains and an extended model to more closely simulate a real system by mimicking the proximity effect. We find that, in general, for AFM chains, the topological gap is larger than for FM ones, and thus, coherence lengths are shorter for AFM chains, yielding more pronounced localization of MZMs in these chains. While for some parameters AFM chains may be topologically trivial, we find in these cases that adding an adjacent chain can result in a nontrivial system, with a single MZM at each chain end.

### Systematic study of Mn atoms, artificial dimers and chains on superconducting Ta(110)

*Ph. Beck, L. Schneider, R. Wiesendanger, and J. Wiebe*

Magnetic adatoms coupled to an s-wave superconductor give rise to local bound states, so-called Yu-Shiba-Rusinov states. Focusing on the ultimate goal of tailoring chains of such adatoms into a topologically superconducting phase, we investigate basic building blocks—single Fe and Mn adatoms and Mn dimers on clean superconducting Ta(110)—using scanning tunneling microscopy and spectroscopy. We perform a systematic study of the hybridizations and splittings in dimers, and their dependence on the crystallographic directions and interatomic spacings, in order to identify potentially interesting chain geometries for this sample type. Subsequently, we study the spin structure as well as the length dependent Shiba band structure in Mn chains of those geometries using spin-resolved scanning tunneling spectroscopy. All results are compared to the according properties of structurally identical dimers and chains on the previously studied Nb(110), which has almost identical surface structure and electronic properties, but an about three times smaller spin-orbit interaction.

## 2022

### Majorana modes with side features in magnet-superconductor hybrid systems

*D. Crawford, E. Mascot, M. Shimizu, L. Schneider, Ph. Beck, J. Wiebe, R. Wiesendanger, H. O. Jeschke, D. K. Morr, and S. Rachel*

Magnet-superconductor hybrid (MSH) systems represent promising platforms to host Majorana zero modes (MZMs), the elemental building blocks for fault-tolerant quantum computers. Theoretical description of such MSH structures is mostly based on simplified models, not accounting for the complexity of real materials. Here, based on density functional theory, we derive a superconducting 80-band model to study an MSH system consisting of a magnetic manganese chain on the s wave superconductor niobium. For a wide range of values of the superconducting order parameter, the system is a topological superconductor, with MZMs exhibiting non-universal spatial patterns and a drastic accumulation of spectral weight on both sides along the magnetic chain. These side feature states can be explained by an effective model which is guided by the ab initio results. Performing scanning tunneling spectroscopy experiments on the same system, we observe a spatial structure in the low-energy local density of states that is consistent with the theoretical findings. Our results open a first-principle approach to the discovery of topological superconductors.

### Correlation of magnetism and disordered Shiba bands in Fe monolayer islands on Nb(110)

* Julia J. Goedecke, Lucas Schneider, Yingqiao Ma, Khai Ton That, Dongfei Wang, Jens Wiebe, and Roland Wiesendanger*

Two-dimensional (2D) magnet–superconductor hybrid systems are intensively studied due to their potential for the realization of 2D topological superconductors with Majorana edge modes. It is theoretically predicted that this quantum state is ubiquitous in spin–orbit-coupled ferromagnetic or skyrmionic 2D spin–lattices in proximity to an s-wave superconductor. However, recent examples suggest that the requirements for topological superconductivity are complicated by the multiorbital nature of the magnetic components and disorder effects. Here, we investigate Fe monolayer islands grown on a surface of the s-wave superconductor with the largest gap of all elemental superconductors, Nb, with respect to magnetism and superconductivity using spin-resolved scanning tunneling spectroscopy. We find three types of islands which differ by their reconstruction inducing disorder, the magnetism and the subgap electronic states. All three types are ferromagnetic with different coercive fields, indicating diverse exchange and anisotropy energies. On all three islands, there is finite spectral weight throughout the substrate’s energy gap at the expense of the coherence peak intensity, indicating the formation of Shiba bands overlapping with the Fermi energy. A strong lateral variation of the spectral weight of the Shiba bands signifies substantial disorder on the order of the substrate’s pairing energy with a length scale of the period of the three different reconstructions. There are neither signs of topological gaps within these bands nor of any kind of edge modes. Our work illustrates that a reconstructed growth mode of magnetic layers on superconducting surfaces is detrimental for the formation of 2D topological superconductivity.

### Precursors of Majorana modes and their length-dependent energy oscillations probed at both ends of atomic Shiba chains

* Lucas Schneider, Philip Beck, Jannis Neuhaus-Steinmetz, Levente Rózsa, Thore Posske, Jens Wiebe & Roland Wiesendanger *

Isolated Majorana modes (MMs) are highly non-local quantum states with non-Abelian exchange statistics, which localize at the two ends of finite-size 1D topological superconductors of sufficient length. Experimental evidence for MMs is so far based on the detection of several key signatures: for example, a conductance peak pinned to the Fermi energy or an oscillatory peak splitting in short 1D systems when the MMs overlap. However, most of these key signatures were probed only on one of the ends of the 1D system, and firm evidence for an MM requires the simultaneous detection of all the key signatures on both ends. Here we construct short atomic spin chains on a superconductor—also known as Shiba chains—up to a chain length of 45 atoms using tip-assisted atom manipulation in scanning tunnelling microscopy experiments. We observe zero-energy conductance peaks localized at both ends of the chain that simultaneously split off from the Fermi energy in an oscillatory fashion after altering the chain length. By fitting the parameters of a low-energy model to the data, we find that the peaks are consistent with precursors of MMs that evolve into isolated MMs protected by an estimated topological gap of 50 μeV in chains of at least 35 nm length, corresponding to 70 atoms.

### Structural and superconducting properties of ultrathin Ir films on Nb(110)

*Philip Beck, Lucas Schneider, Lydia Bachmann, Jens Wiebe, and Roland Wiesendanger*

The ongoing quest for unambiguous signatures of topological superconductivity and Majorana modes in magnet-superconductor hybrid systems creates a high demand for suitable superconducting substrates. Materials that incorporate *s*-wave superconductivity with a wide energy gap, large spin-orbit coupling, and high surface quality, which enable the atom-by-atom construction of magnetic nanostructures using the tip of a scanning tunneling microscope, are particularly desired. Since single materials rarely fulfill all these requirements, we propose and demonstrate the growth of thin films of a high-Z metal, Ir, on a surface of the elemental superconductor with the largest energy gap, Nb. We find a strained Ir(110)/Nb(110)-oriented superlattice for thin films of one to two atomic layers, which transitions to a compressed Ir(111) surface for thick films of ten atomic layers. Using tunneling spectroscopy, we observe proximity-induced superconductivity in the latter Ir(111) film with a hard gap Δ that is 85.3% of that of bare Nb(110).

## 2021

### Correlation of Yu–Shiba–Rusinov States and Kondo Resonances in Artificial Spin Arrays on an s-Wave Superconductor

*A. Kamlapure, L. Cornils, R. Zitko, M. Valentyuk, R. Mozara, S. Pradhan, J. Fransson, A.I. Lichtenstein, J. Wiebe, and R. Wiesendanger*

Mutually interacting magnetic atoms coupled to a superconductor have gained enormous interest due to their potential for the realization of topological superconductivity. Individual magnetic impurities produce states within the superconducting energy gap known as Yu–Shiba–Rusinov (YSR) states. Here, using the tip of a scanning tunneling microscope, we artificially craft spin arrays consisting of an Fe adatom interacting with an assembly of interstitial Fe atoms (IFA) on a superconducting oxygen-reconstructed Ta(100) surface and show that the magnetic interaction between the adatom and the IFA assembly can be tuned by adjusting the number of IFAs in the assembly. The YSR state experiences a characteristic crossover in its energetic position and particle–hole spectral weight asymmetry when the Kondo resonance shows spectral depletion around the Fermi energy. By the help of slave-boson mean-field theory (SBMFT) and numerical renormalization group (NRG) calculations we associate the crossover with the transition from decoupled Kondo singlets to an antiferromagnetic ground state of the Fe adatom spin and the IFA assembly effective spin.

### Topological Shiba bands in artificial spin chains on superconductors

*Lucas Schneider, Philip Beck, Thore Posske, Daniel Crawford, Eric Mascot, Stephan Rachel, Roland Wiesendanger & Jens Wiebe*

A major challenge in developing topological superconductors for implementing topological quantum computing is their characterization and control. It has been proposed that a *p*-wave-gapped topological superconductor can be fabricated with single-atom precision by assembling chains of magnetic atoms on *s*-wave superconductors with spin–orbit coupling. Here we analyse Bogoliubov quasiparticle interference in Mn chains, constructed atom by atom on Nb(110), and reveal the formation of multi-orbital Shiba bands using momentum-resolved measurements. We find evidence that one band features a topologically non-trivial *p*-wave gap, as inferred from its shape and particle–hole asymmetric intensity. Our work is an important step towards a distinct experimental determination of topological phases in multi-orbital systems by bulk electron band structure properties only.

### Spin-orbit coupling induced splitting of Yu-Shiba-Rusinov states in antiferromagnetic dimers

*Beck, P., Schneider, L., Rózsa, L. et al.*

Magnetic atoms coupled to the Cooper pairs of a superconductor induce Yu-Shiba-Rusinov states (in short Shiba states). In the presence of sufficiently strong spin-orbit coupling, the bands formed by hybridization of the Shiba states in ensembles of such atoms can support low-dimensional topological superconductivity with Majorana bound states localized on the ensembles’ edges. Yet, the role of spin-orbit coupling for the hybridization of Shiba states in dimers of magnetic atoms, the building blocks for such systems, is largely unexplored. Here, we reveal the evolution of hybridized multi-orbital Shiba states from a single Mn adatom to artificially constructed ferromagnetically and antiferromagnetically coupled Mn dimers placed on a Nb(110) surface. Upon dimer formation, the atomic Shiba orbitals split for both types of magnetic alignment. Our theoretical calculations attribute the unexpected splitting in antiferromagnetic dimers to spin-orbit coupling and broken inversion symmetry at the surface. Our observations point out the relevance of previously unconsidered factors on the formation of Shiba bands and their topological classification.

### Atomic-scale spin-polarization maps using functionalized superconducting probes

*Schneider, L., Beck, P., Wiebe, J. & Wiesendanger, R.*

A scanning tunneling microscope (STM) with a magnetic tip that has a sufficiently strong spin polarization can be used to map the sample’s spin structure down to the atomic scale but usually lacks the possibility to absolutely determine the value of the sample’s spin polarization. Magnetic impurities in superconducting materials give rise to pairs of perfectly, i.e., 100%, spin-polarized subgap resonances. In this work, we functionalize the apex of a superconducting Nb STM tip with such impurity states by attaching Fe atoms to probe the spin polarization of atom-manipulated Mn nanomagnets on a Nb(110) surface. By comparison with spin-polarized STM measurements of the same nanomagnets using Cr bulk tips, we demonstrate an extraordinary spin sensitivity and the possibility to measure the sample’s spin-polarization values close to the Fermi level quantitatively with our new functionalized probes.

## 2020

### Temperature and magnetic field dependent behavior of atomic-scale skyrmions in Pd/Fe/Ir(111) nanoislands

*P. Lindner, L. Bargsten, S. Kovarik, J. Friedlein, J. Harm, S. Krause, and R. Wiesendanger*

The thermal stability of atomic-scale skyrmions is of high relevance for potential spintronics applications and validation of theoretical models. We investigated Pd/Fe nanoislands on an Ir(111) substrate as a function of temperature and magnetic field. Utilizing noncollinear magnetoresistance contrast in scanning tunneling microscopy, the thermomagnetic phase space is explored up to 3 T within a temperature range between 1 K to 100 K. Evidence is found for the spin spiral, field-polarized, and fluctuating disordered magnetic phases. Evidence for the presence of atomic-scale skyrmions at up to approximately 80 K is found, irrespective of considerable magnetization dynamics arising from thermal agitation.

### Controlling in-gap end states by linking nonmagnetic atoms and artificially-constructed spin chains on superconductors

*Schneider, L., Brinker, S., Steinbrecher, M. et al.*

Chains of magnetic atoms with either strong spin-orbit coupling or spiral magnetic order which are proximity-coupled to superconducting substrates can host topologically non-trivial Majorana bound states. The experimental signature of these states consists of spectral weight at the Fermi energy which is spatially localized near the ends of the chain. However, topologically trivial Yu-Shiba-Rusinov in-gap states localized near the ends of the chain can lead to similar spectra. Here, we explore a protocol to disentangle these contributions by artificially augmenting a candidate Majorana spin chain with orbitally-compatible nonmagnetic atoms. Combining scanning tunneling spectroscopy with ab-initio and tight-binding calculations, we realize a sharp spatial transition between the proximity-coupled spiral magnetic order and the non-magnetic superconducting wire termination, with persistent zero-energy spectral weight localized at either end of the magnetic spiral. Our findings open a new path towards the control of the spatial position of in-gap end states, trivial or Majorana, via different chain terminations, and the realization of designer Majorana chain networks for demonstrating topological quantum computation.

## 2019

### A radio-frequency spin-polarized scanning tunneling microscope

*J. Friedlein, J. Harm, P. Lindner, L. Bargsten, M. Bazarnik, S. Krause and R. Wiesendanger*

A scanning tunneling microscope for spin-resolved studies of dynamic systems is presented. The cryogenic setup allows the scanning tunneling microscope to achieve a cutoff frequency beyond 26 GHz at the tunnel junction and to be operable at temperatures of 1.1 K–100 K in a magnetic field of up to 3 T. For this purpose, the microscope and its wiring as well as the associated cryostat system were specially designed and manufactured. For sample preparation, an ultrahigh vacuum system was developed, which is equipped with modular preparation platforms. Measurements showing the characteristics of the scanning tunneling microscope in the time and frequency domain are presented. As a proof of concept, experimental data of the Pd/Fe/Ir(111) sample system at 95 K in a magnetic field of 3 T are presented.Rev. Sci. Instrum. 90, 123705 (2019)