Non-Majorana modes in diluted spin chains proximitized to a superconductor

Küster, Felix; Brinker, Sascha; Hess, Richard; Loss, Daniel; Parkin, S. S. P.; Klinovaja, Jelena; Lounis, Samir; Sessi, Paolo

doi:10.1073/pnas.2210589119

Cited by 21 publications

(22 citation statements)

References 46 publications

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“…Before we continue with the investigation of Fe dimers, we consider some intuitive ideas about the most promising orientations of chains built from individual Fe atoms towards the goal of topologically gapped YSR bands. As found in previous works [23][24][25]45 , enabling a sufficient hybridization of a YSR state which is already close to E F , while, at the same time, minimizing the hybridizations of all the other YSR states far from E F may lead to a single YSR band overlapping with E F . Together with SOC, this can be a sufficient condition for the opening of a topologically non-trivial gap in the lowest-energy band.…”

Section: Ysr States Of Fe Dimerssupporting

confidence: 60%

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

Beck¹,

Nyári²,

Schneider³

et al. 2023

Preprint

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One-dimensional systems comprising s-wave superconductivity with meticulously tuned magnetism and spin-orbit coupling can realize topologically gapped superconductors hosting Majorana edge modes whose stability is determined by the gap's size. The ongoing quest for larger topological gaps evolved into a material science issue. However, for atomic spin chains on superconductor surfaces, the effect of the substrate's spin-orbit coupling on the system's topological gap size is largely unexplored. Here, we introduce an atomic layer of the heavy metal Au on Nb(110) which combines strong spin-orbit coupling and a large superconducting gap with a high crystallographic quality enabling the assembly of defect-free Fe chains using a scanning tunneling microscope tip. Scanning tunneling spectroscopy experiments and density functional theory calculations reveal ferromagnetic coupling and ungapped YSR bands in the chain despite of the heavy substrate. By artificially imposing a spin spiral state our calculations indicate a minigap opening and zero-energy edge state formation. The presented methodology paves the way towards a material screening of heavy metal layers on elemental superconductors for ideal systems hosting Majorana edge modes protected by large topological gaps.

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Section: Ysr States Of Fe Dimerssupporting

confidence: 60%

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

Beck¹,

Nyári²,

Schneider³

et al. 2023

Preprint

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“…Naively thinking, the system might fulfill all requirements for topological superconductivity, i.e., a ferromagnetic spin–lattice which realizes Shiba bands that are overlapping with E F and very likely have a considerable spin–orbit interaction . However, as shown in previous publications on 1D systems, the formation of topological edge modes can be hindered by the interaction of multiple Shiba bands originating from the five 3d orbitals of the Fe lattice. , Additionally, in the reconstructed ML system investigated here, we have experimentally proven a substantial disorder in the Shiba bands which can have both, a potential and a magnetic origin. As outlined in the introduction, excluding very specific and rare values of the chemical potential or specific types of disorder, ,, the strong disorder on the order of the pairing energy present in the investigated lattices would destroy any topological gap as well as topological edge modes. ,, We, therefore, conclude that besides a specific design of the multiorbital Shiba bands in ferromagnetic layers in direct contact with elemental superconductors, a pseudomorphic growth with the least amount of disorder is probably best suited for the design of two-dimensional topological superconductivity and the related Majorana edge modes.…”

Section: Discussionsupporting

confidence: 56%

“…55 However, as shown in previous publications on 1D systems, the formation of topological edge modes can be hindered by the interaction of multiple Shiba bands originating from the five 3d orbitals of the Fe lattice. 56,57 Additionally, in the reconstructed ML system investigated here, we have experimentally proven a substantial disorder in the Shiba bands which can have both, a potential and a magnetic origin. As outlined in the introduction, excluding very specific and rare values of the chemical potential or specific types of disorder, 17,35,38 the strong disorder on the order of the pairing energy present in the investigated lattices would destroy any topological gap as well as topological edge modes.…”

Section: Discussionmentioning

confidence: 67%

Correlation of Magnetism and Disordered Shiba Bands in Fe Monolayer Islands on Nb(110)

Goedecke

Schneider

et al. 2022

ACS Nano

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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.

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“…Being able to calculate the properties of Shiba states and to describe their formation conditions has been shown to be pivotal in understanding of topological end modes [8][9][10][11][12][13][14][15][16][17][18][19] in the presence of spin-orbit coupling (SOC) or spiral magnetic order. Very recently, a scanning tunneling microscopy/spectroscopy experiment [20] showed zero-energy end modes in dilute spin chains in proximity to an s-wave SC substrate. These end modes turned out to be topologically trivial Shiba states.…”

Section: Introductionmentioning

confidence: 99%

Effects of strong spin-orbit coupling on Shiba states from magnetic adatoms using first-principles theory

et al. 2023

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Magnetic impurities at surfaces of superconductors can induce bound states referred to as Yu-Shiba-Rusinov states (i.e., Shiba states) within superconducting (SC) gaps. For superconductors with strong spin-orbit coupling (SOC), Shiba states arising from even single magnetic adatoms are too complex to be fully understood using effective models alone because SOC cannot be treated perturbatively and multiple orbitals are strongly mixed with spin projections. Here we investigate Shiba states of single magnetic adatoms at the surface of strongly spin-orbit coupled SC Pb, by solving the fully relativistic Dirac-Bogoliubov-de Gennes equations using multiple scattering Green's function methods. For Fe and Co adatoms on Pb(110), we show that the Shiba states are better characterized by total angular momentum, $J$, and its projections on the $z$ axis, $m_J$. As a hallmark of the SOC effect, the Shiba states show a strong dependence of the orientation of the adatom moment. As the orientation of the Fe/Co moment changes, the deepest Shiba states merge at zero energy. This zero-energy state disappears with an additional non-magnetic adatom next to the magnetic adatom, although the other Shiba states unchange. For a Mn adatom on Pb, our Shiba states overall agree with experiments. The characteristics of our Shiba states are also observed with the similar energies and characters in the experiments. The deepest Shiba states that we compute, however, do not appear as close to the Fermi level as the experimental data. It would be interesting to compute the Shiba states with continuously varying vertical distances of the Mn adatom from the surface or with varying the charge state of the adatom, and to calculate the spatial dependence of the spectral density. Our findings will be also useful for understanding of Shiba states for dimers and longer spin chains on the Pb surface considering noncollinear magnetic structures in them.

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Non-Majorana modes in diluted spin chains proximitized to a superconductor

Cited by 21 publications

References 46 publications

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

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

Correlation of Magnetism and Disordered Shiba Bands in Fe Monolayer Islands on Nb(110)

Effects of strong spin-orbit coupling on Shiba states from magnetic adatoms using first-principles theory

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