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Aceves Rodriguez UA, Guimarães F, Brinker S, Lounis S. Magnetic exchange interactions at the proximity of a superconductor. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:295801. [PMID: 38471158 DOI: 10.1088/1361-648x/ad32de] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2023] [Accepted: 03/12/2024] [Indexed: 03/14/2024]
Abstract
Interfacing magnetism with superconductivity gives rise to a wonderful playground for intertwining key degrees of freedom: Cooper pairs, spin, charge, and spin-orbit interaction, from which emerge a wealth of exciting phenomena, fundamental in the nascent field of superconducting spinorbitronics and topological quantum technologies. Magnetic exchange interactions (MEIs), being isotropic or chiral such as the Dzyaloshinskii-Moriya interactions, are vital in establishing the magnetic behavior at these interfaces as well as in dictating not only complex transport phenomena, but also the manifestation of topologically trivial or non-trivial objects. Here, we propose a methodology enabling the extraction of the tensor of MEI from electronic structure simulations accounting for superconductivity. We apply our scheme to the case of a Mn layer deposited on Nb(110) surface and explore proximity-induced impact on the MEI. The latter are weakly modified by a realistic electron-phonon coupling. However, tuning the superconducting order parameter, we unveil potential change of the magnetic order accompanied with chirality switching, as induced by the interplay of spin-orbit interaction and Cooper pairing. Owing to its simple formulation, our methodology can be readily implemented in state-of-the-art frameworks capable of tackling superconductivity and magnetism. We thus foresee implications in the simulations and prediction of topological superconducting bits as well as of cryogenic superconducting hybrid devices involving magnetic units.
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Affiliation(s)
- Uriel A Aceves Rodriguez
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, 52425 Jülich, Germany
- Faculty of Physics & CENIDE, University of Duisburg-Essen, 47053 Duisburg, Germany
| | - Filipe Guimarães
- Jülich Supercomputing Centre, Forschungszentrum Jülich & JARA, 52425 Jülich, Germany
| | - Sascha Brinker
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, 52425 Jülich, Germany
| | - Samir Lounis
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, 52425 Jülich, Germany
- Faculty of Physics & CENIDE, University of Duisburg-Essen, 47053 Duisburg, Germany
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2
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Aceves Rodriguez UA, Guimarães FSM, Lounis S. Superconductivity in Nb: Impact of Temperature, Dimensionality and Cooper-Pairing. NANOMATERIALS (BASEL, SWITZERLAND) 2024; 14:254. [PMID: 38334524 PMCID: PMC10856455 DOI: 10.3390/nano14030254] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2023] [Revised: 01/17/2024] [Accepted: 01/18/2024] [Indexed: 02/10/2024]
Abstract
The ability to realistically simulate the electronic structure of superconducting materials is important to understand and predict various properties emerging in both the superconducting topological and spintronics realms. We introduce a tight-binding implementation of the Bogoliubov-de Gennes method, parameterized from density functional theory, which we utilize to explore the bulk and thin films of Nb, known to host a significant superconducting gap. The latter is useful for various applications such as the exploration of trivial and topological in-gap states. Here, we focus on the simulation's aspects of superconductivity and study the impact of temperature, Cooper-pair coupling and dimensionality on the value of the superconducting pairing interactions and gaps.
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Affiliation(s)
- Uriel Allan Aceves Rodriguez
- Peter Grünberg Institut & Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, D-52425 Jülich, Germany;
- Faculty of Physics & CENIDE, University of Duisburg-Essen, D-47053 Duisburg, Germany
| | | | - Samir Lounis
- Peter Grünberg Institut & Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, D-52425 Jülich, Germany;
- Faculty of Physics & CENIDE, University of Duisburg-Essen, D-47053 Duisburg, Germany
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3
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Schneider L, Beck P, Rózsa L, Posske T, Wiebe J, Wiesendanger R. Probing the topologically trivial nature of end states in antiferromagnetic atomic chains on superconductors. Nat Commun 2023; 14:2742. [PMID: 37173332 PMCID: PMC10182033 DOI: 10.1038/s41467-023-38369-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2022] [Accepted: 04/25/2023] [Indexed: 05/15/2023] Open
Abstract
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.
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Affiliation(s)
- Lucas Schneider
- Department of Physics, University of Hamburg, D-20355, Hamburg, Germany
| | - Philip Beck
- Department of Physics, University of Hamburg, D-20355, Hamburg, Germany
| | - Levente Rózsa
- Department of Physics, University of Konstanz, D-78457, Konstanz, Germany
- Department of Theoretical Solid State Physics, Institute of Solid State Physics and Optics, Wigner Research Centre for Physics, H-1525, Budapest, Hungary
- Department of Theoretical Physics, Budapest University of Technology and Economics, H-1111, Budapest, Hungary
| | - Thore Posske
- I. Institute for Theoretical Physics, University of Hamburg, D-22607, Hamburg, Germany
- Centre for Ultrafast Imaging, Luruper Chaussee 149, D-22761, Hamburg, Germany
| | - Jens Wiebe
- Department of Physics, University of Hamburg, D-20355, Hamburg, Germany.
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4
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Müller H, Eckstein M, Viola Kusminskiy S. Control of Yu-Shiba-Rusinov States through a Bosonic Mode. PHYSICAL REVIEW LETTERS 2023; 130:106905. [PMID: 36962057 DOI: 10.1103/physrevlett.130.106905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2022] [Revised: 12/18/2022] [Accepted: 02/03/2023] [Indexed: 06/18/2023]
Abstract
We investigate the impact of a bosonic degree of freedom on Yu-Shiba-Rusinov states emerging from a magnetic impurity in a conventional superconductor. Starting from the Anderson impurity model, we predict that an additional p-wave conduction band channel opens up if a bosonic mode is coupled to the tunneling between impurity and host, which implies an additional pair of odd-parity Yu-Shiba-Rusinov states. The bosonic mode can be a vibrational mode or the electromagnetic field in a cavity. The exchange couplings in the two channels depend sensitively on the state of the bosonic mode (ground state, few quanta, or classically driven Floquet state), which opens possibilities for phononics or photonics control of such systems, with a rich variety of ground and excited states.
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Affiliation(s)
- Helene Müller
- Department of Physics, University of Erlangen-Nuremberg, 91058 Erlangen, Germany
- Max Planck Institute for the Science of Light, Staudtstrasse 2, 91058 Erlangen, Germany
| | - Martin Eckstein
- Department of Physics, University of Erlangen-Nuremberg, 91058 Erlangen, Germany
| | - Silvia Viola Kusminskiy
- Max Planck Institute for the Science of Light, Staudtstrasse 2, 91058 Erlangen, Germany
- Institute for Theoretical Solid State Physics, RWTH Aachen University, 52074 Aachen, Germany
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5
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Schulte S, Néel N, Rózsa L, Palotás K, Kröger J. Changing the Interaction of a Single-Molecule Magnetic Moment with a Superconductor. NANO LETTERS 2023; 23:1622-1628. [PMID: 36603183 DOI: 10.1021/acs.nanolett.2c03952] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
The exchange interaction of a brominated Co-porphyrin molecule with the Cooper pair condensate of Pb(111) is modified by reducing the Co-surface separation. The stepwise dehalogenation and dephenylation change the Co adsorption height by a few picometers. Only the residual Co-porphine core exhibits a Yu-Shiba-Rusinov bound state with low binding energy in the Bardeen-Cooper-Schrieffer energy gap. Accompanying density functional calculations reveal that the Co dz2 orbital carries the molecular magnetic moment and is responsible for the intragap state. The calculated spatial evolution of the Yu-Shiba-Rusinov wave function is compatible with the experimentally observed oscillatory attenuation of the electron-hole asymmetry with increasing lateral distance from the magnetic porphine center.
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Affiliation(s)
- Stefan Schulte
- Institut für Physik, Technische Universität Ilmenau, D-98693Ilmenau, Germany
- Peter Grünberg Institut, Forschungszentrum Jülich, D-52425Jülich, Germany
- II. Physikalisches Institut, Universität zu Köln, D-50923Cologne, Germany
| | - Nicolas Néel
- Institut für Physik, Technische Universität Ilmenau, D-98693Ilmenau, Germany
| | - Levente Rózsa
- Fachbereich Physik, Universität Konstanz, D-78457Konstanz, Germany
| | - Krisztián Palotás
- Department of Theoretical Solid State Physics, Institute for Solid State Physics and Optics, Wigner Research Center for Physics, H-1121Budapest, Hungary
- ELKH-SZTE Reaction Kinetics and Surface Chemistry Research Group, University of Szeged, H-6720Szeged, Hungary
- Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H-1111Budapest, Hungary
| | - Jörg Kröger
- Institut für Physik, Technische Universität Ilmenau, D-98693Ilmenau, Germany
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6
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Spin-orbital Yu-Shiba-Rusinov states in single Kondo molecular magnet. Nat Commun 2022; 13:6388. [PMID: 36302772 PMCID: PMC9613647 DOI: 10.1038/s41467-022-34187-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2021] [Accepted: 10/13/2022] [Indexed: 11/18/2022] Open
Abstract
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.
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7
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Goedecke JJ, Schneider L, Ma Y, That KT, Wang D, Wiebe J, Wiesendanger R. Correlation of Magnetism and Disordered Shiba Bands in Fe Monolayer Islands on Nb(110). ACS NANO 2022; 16:14066-14074. [PMID: 36001503 PMCID: PMC9527798 DOI: 10.1021/acsnano.2c03965] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/22/2022] [Accepted: 08/02/2022] [Indexed: 06/15/2023]
Abstract
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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8
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Nagyfalusi B, Udvardi L, Szunyogh L. Magnetic ground state of supported monatomic Fe chains from first principles. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:395803. [PMID: 35853446 DOI: 10.1088/1361-648x/ac8260] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2022] [Accepted: 07/19/2022] [Indexed: 06/15/2023]
Abstract
A new computational scheme is presented based on a combination of the conjugate gradient and the Newton-Raphson method to self-consistently minimize the energy within local spin-density functional theory, thus to identify the ground state magnetic order of a finite cluster of atoms. The applicability of the newab initiooptimization method is demonstrated for Fe chains deposited on different metallic substrates. The optimized magnetic ground states of the Fe chains on Rh(111) are analyzed in details and a good comparison is found with those obtained from an extended Heisenberg model containing first principles based interaction parameters. Moreover, the effect of the different bilinear spin-spin interactions in the formation of the magnetic ground states is monitored. In case of Fe chains on Nb(110) spin-spiral configurations with opposite rotational sense are found as compared to previous spin-model results which hints on the importance of higher order chiral interactions. The wavelength of the spin-spiral states of Fe chains on Re(0001) was obtained in good agreement with scanning tunneling microscopy experiments.
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Affiliation(s)
- B Nagyfalusi
- Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, H-1525 Budapest, Hungary
- Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, Műegyetem rkp. 3, H-1111 Budapest, Hungary
| | - L Udvardi
- Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, Műegyetem rkp. 3, H-1111 Budapest, Hungary
- ELKH-BME Condensed Matter Research Group, Budapest University of Technology and Economics, Műegyetem rkp. 3, Budapest, H-1111, Hungary
| | - L Szunyogh
- Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, Műegyetem rkp. 3, H-1111 Budapest, Hungary
- ELKH-BME Condensed Matter Research Group, Budapest University of Technology and Economics, Műegyetem rkp. 3, Budapest, H-1111, Hungary
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9
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Chiu CK, Wang Z. Yu-Shiba-Rusinov States in a Superconductor with Topological Z_{2} Bands. PHYSICAL REVIEW LETTERS 2022; 128:237001. [PMID: 35749202 DOI: 10.1103/physrevlett.128.237001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2021] [Revised: 04/19/2022] [Accepted: 04/26/2022] [Indexed: 06/15/2023]
Abstract
A Yu-Shiba-Rusinov (YSR) state is a localized in-gap state induced by a magnetic impurity in a superconductor. Recent experiments used an STM tip to manipulate the exchange coupling between an Fe adatom and the FeTe_{0.55}Se_{0.45} superconductor possessing a Z_{2} nontrivial band structure with topological surface states. As the tip moves close to the single Fe adatom, the energy of the in-gap state modulates and exhibits a zero-energy crossing followed by an unusual return to zero energy, which cannot be understood by coupling the magnetic impurity to the superconducting topological surface Dirac cone. Here, we numerically and analytically study the YSR states in superconductors with nontrivial Z_{2} bands and show the emergence of the two zero-energy crossings as a function of the exchange coupling between the magnetic impurity and the bulk states. We analyze the role of the topological surface states and compare in-gap states to systems with trivial Z_{2} bands. The spin polarization of the YSR states is further studied for future experimental measurement.
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Affiliation(s)
- Ching-Kai Chiu
- RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), Wako, Saitama 351-0198, Japan
- Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Ziqiang Wang
- Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA
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10
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Quantum spins and hybridization in artificially-constructed chains of magnetic adatoms on a superconductor. Nat Commun 2022; 13:2160. [PMID: 35443753 PMCID: PMC9021194 DOI: 10.1038/s41467-022-29879-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2021] [Accepted: 04/01/2022] [Indexed: 11/09/2022] Open
Abstract
Magnetic adatom chains on surfaces constitute fascinating quantum spin systems. Superconducting substrates suppress interactions with bulk electronic excitations but couple the adatom spins to a chain of subgap Yu-Shiba-Rusinov (YSR) quasiparticles. Using a scanning tunneling microscope, we investigate such correlated spin-fermion systems by constructing Fe chains adatom by adatom on superconducting NbSe2. The adatoms couple entirely via the substrate, retaining their quantum spin nature. In dimers, we observe that the deepest YSR state undergoes a quantum phase transition due to Ruderman-Kittel-Kasuya-Yosida interactions, a distinct signature of quantum spins. Chains exhibit coherent hybridization and band formation of the YSR excitations, indicating ferromagnetic coupling. Longer chains develop separate domains due to coexisting charge-density-wave order of NbSe2. Despite the spin-orbit-coupled substrate, we find no signatures of Majoranas, possibly because quantum spins reduce the parameter range for topological superconductivity. We suggest that adatom chains are versatile systems for investigating correlated-electron physics and its interplay with topological superconductivity. Previous studies of magnetic adatom chains on superconducting substrates have mostly focused on the regime of dense chains and classical spins. Here, using scanning tunnelling microscopy, the authors study the excitation spectra of Fe chains on a NbSe2 surface, adatom by adatom, in the regime of quantum spins.
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11
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Schneider L, Beck P, Neuhaus-Steinmetz J, Rózsa L, Posske T, Wiebe J, Wiesendanger R. Precursors of Majorana modes and their length-dependent energy oscillations probed at both ends of atomic Shiba chains. NATURE NANOTECHNOLOGY 2022; 17:384-389. [PMID: 35256768 PMCID: PMC9018407 DOI: 10.1038/s41565-022-01078-4] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 01/12/2022] [Indexed: 05/27/2023]
Abstract
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.
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Affiliation(s)
- Lucas Schneider
- Department of Physics, Universität Hamburg, Hamburg, Germany
| | - Philip Beck
- Department of Physics, Universität Hamburg, Hamburg, Germany
| | | | - Levente Rózsa
- Department of Physics, University of Konstanz, Konstanz, Germany
| | - Thore Posske
- I. Institute for Theoretical Physics, Universität Hamburg, Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee, Hamburg, Germany
| | - Jens Wiebe
- Department of Physics, Universität Hamburg, Hamburg, Germany.
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12
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Küster F, Brinker S, Lounis S, Parkin SSP, Sessi P. Long range and highly tunable interaction between local spins coupled to a superconducting condensate. Nat Commun 2021; 12:6722. [PMID: 34795233 PMCID: PMC8602442 DOI: 10.1038/s41467-021-26802-x] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Accepted: 10/19/2021] [Indexed: 11/26/2022] Open
Abstract
Interfacing magnetism with superconducting condensates is rapidly emerging as a viable route for the development of innovative quantum technologies. In this context, the development of rational design strategies to controllably tune the interaction between magnetic moments is crucial. Here we address this problem demonstrating the possibility of tuning the interaction between local spins coupled through a superconducting condensate with atomic scale precision. By using Cr atoms coupled to superconducting Nb, we use atomic manipulation techniques to precisely control the relative distance between local spins along distinct crystallographic directions while simultaneously sensing their coupling by scanning tunneling spectroscopy. Our results reveal the existence of highly anisotropic interactions, lasting up to very long distances, demonstrating the possibility of crossing a quantum phase transition by acting on the direction and interatomic distance between spins. The high tunability provides novel opportunities for the realization of topological superconductivity and the rational design of magneto-superconducting interfaces.
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Affiliation(s)
- Felix Küster
- Max Planck Institute of Microstructure Physics, Halle, 06120, Germany
| | - Sascha Brinker
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, Jülich, D-52425, Germany
| | - Samir Lounis
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, Jülich, D-52425, Germany.
- Faculty of Physics, University of Duisburg-Essen and CENIDE, Duisburg, 47053, Germany.
| | - Stuart S P Parkin
- Max Planck Institute of Microstructure Physics, Halle, 06120, Germany.
| | - Paolo Sessi
- Max Planck Institute of Microstructure Physics, Halle, 06120, Germany.
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13
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Kürtössy O, Scherübl Z, Fülöp G, Lukács IE, Kanne T, Nygård J, Makk P, Csonka S. Andreev Molecule in Parallel InAs Nanowires. NANO LETTERS 2021; 21:7929-7937. [PMID: 34538054 PMCID: PMC8517978 DOI: 10.1021/acs.nanolett.1c01956] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Indexed: 06/13/2023]
Abstract
Coupling individual atoms fundamentally changes the state of matter: electrons bound to atomic cores become delocalized turning an insulating state to a metallic one. A chain of atoms could lead to more exotic states if the tunneling takes place via the superconducting vacuum and can induce topologically protected excitations like Majorana or parafermions. Although coupling a single atom to a superconductor is well studied, the hybridization of two sites with individual tunability was not reported yet. The peculiar vacuum of the Bardeen-Cooper-Schrieffer (BCS) condensate opens the way to annihilate or generate two electrons from the bulk resulting in a so-called Andreev molecular state. By employing parallel nanowires with an Al shell, two artificial atoms were created at a minimal distance with an epitaxial superconducting link between. Hybridization via the BCS vacuum was observed and the spectrum of an Andreev molecule as a function of level positions was explored for the first time.
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Affiliation(s)
- Olivér Kürtössy
- Department
of Physics and Nanoelectronics “Momentum” Research Group
of the Hungarian Academy of Sciences, Budapest
University of Technology and Economics, Budafoki út 8, 1111 Budapest, Hungary
| | - Zoltán Scherübl
- Department
of Physics and Nanoelectronics “Momentum” Research Group
of the Hungarian Academy of Sciences, Budapest
University of Technology and Economics, Budafoki út 8, 1111 Budapest, Hungary
- University
of Grenoble Alpes, CEA, Grenoble INP, IRIG, PHELIQS, 38000 Grenoble, France
| | - Gergö Fülöp
- Department
of Physics and Nanoelectronics “Momentum” Research Group
of the Hungarian Academy of Sciences, Budapest
University of Technology and Economics, Budafoki út 8, 1111 Budapest, Hungary
| | - István Endre Lukács
- Center
for Energy Research, Institute of Technical
Physics and Material Science, Konkoly-Thege Miklós út 29-33, H-1121, Budapest, Hungary
| | - Thomas Kanne
- Center
for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Jesper Nygård
- Center
for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Péter Makk
- Department
of Physics and Nanoelectronics “Momentum” Research Group
of the Hungarian Academy of Sciences, Budapest
University of Technology and Economics, Budafoki út 8, 1111 Budapest, Hungary
| | - Szabolcs Csonka
- Department
of Physics and Nanoelectronics “Momentum” Research Group
of the Hungarian Academy of Sciences, Budapest
University of Technology and Economics, Budafoki út 8, 1111 Budapest, Hungary
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14
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Wang H, Guo Y, Zang J, Hao H, Wang L, Liu T, Bian H, Jiang R, Wen R, Li H, Tong Y, Wang H. Nanoantennas Involved Optical Plasmonic Cavity for Improved Luminescence of Quantum Dots Light-Emitting Diodes. ACS APPLIED MATERIALS & INTERFACES 2021; 13:44760-44767. [PMID: 34505502 DOI: 10.1021/acsami.1c11995] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
The optical plasmonic cavity (OPC) including the metallic optical nanoantennas and a metal film exhibits extreme field enhancement for the increased spontaneous emission rate of emitters. The resonance wavelength of the OPC can be easily controlled by the volume of the OPC and the localized surface plasmonic resonances (LSPRs) of the nanoantennas, facilitating the effective coupling of OPC and the emitters. However, involving the OPC into the light emission-enhanced solution-processed devices is still a difficult challenge. The trade-off between the metallic structure of OPC and the solution procedures limits the performance enhancement of the electrical-driven devices. In this work, we construct a device-compatible OPC that allows the characterization of the carrier dynamics of quantum dot (QD) films in the real devices in-suit. The radiative recombination rate and relaxation rate of carriers in QDs are increased by the LSPR effect of the silver nanocubes for luminescence enhancement. The OPC further increases the spontaneous emission rate of QD films, achieving a Purcell factor of 166 and improving the electroluminescence of the OPC-based QD light-emitting diodes (QLEDs). The design of the OPC-involved QLEDs offers a solution for addressing the limitation of fabrication of OPC-combined solution-processed optoelectronic light sources.
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Affiliation(s)
- Hongyue Wang
- State Key Laboratory of Solidification Processing, Center for Nano Energy Materials, School of Materials Science and Engineering, Shaanxi Joint Laboratory of Graphene (NPU), Northwestern Polytechnical University, Xi'an 710072, P. R. China
| | - Yangyang Guo
- State Key Laboratory of Solidification Processing, Center for Nano Energy Materials, School of Materials Science and Engineering, Shaanxi Joint Laboratory of Graphene (NPU), Northwestern Polytechnical University, Xi'an 710072, P. R. China
| | - Jianyang Zang
- Key Laboratory of Applied Surface and Colloid Chemistry, Ministry of Education, School of Chemistry and Chemical Engineering, Shaanxi Normal University, Xi'an 710119, P. R. China
| | - Hongxing Hao
- Key Laboratory of Applied Surface and Colloid Chemistry, Ministry of Education, School of Chemistry and Chemical Engineering, Shaanxi Normal University, Xi'an 710119, P. R. China
| | - Le Wang
- Shaanxi Key Laboratory for Advanced Energy Devices, Shaanxi Engineering Laboratory for Advanced Energy Technology, School of Materials Science and Engineering, Shaanxi Normal University, Xi'an 710119, P. R. China
| | - Taihong Liu
- Key Laboratory of Applied Surface and Colloid Chemistry, Ministry of Education, School of Chemistry and Chemical Engineering, Shaanxi Normal University, Xi'an 710119, P. R. China
| | - Hongtao Bian
- Key Laboratory of Applied Surface and Colloid Chemistry, Ministry of Education, School of Chemistry and Chemical Engineering, Shaanxi Normal University, Xi'an 710119, P. R. China
| | - Ruibin Jiang
- Shaanxi Key Laboratory for Advanced Energy Devices, Shaanxi Engineering Laboratory for Advanced Energy Technology, School of Materials Science and Engineering, Shaanxi Normal University, Xi'an 710119, P. R. China
| | - Ruijuan Wen
- Key Laboratory of Applied Surface and Colloid Chemistry, Ministry of Education, School of Chemistry and Chemical Engineering, Shaanxi Normal University, Xi'an 710119, P. R. China
| | - Huixin Li
- State Key Laboratory of Solidification Processing, Center for Nano Energy Materials, School of Materials Science and Engineering, Shaanxi Joint Laboratory of Graphene (NPU), Northwestern Polytechnical University, Xi'an 710072, P. R. China
| | - Yu Tong
- State Key Laboratory of Solidification Processing, Center for Nano Energy Materials, School of Materials Science and Engineering, Shaanxi Joint Laboratory of Graphene (NPU), Northwestern Polytechnical University, Xi'an 710072, P. R. China
| | - Hongqiang Wang
- State Key Laboratory of Solidification Processing, Center for Nano Energy Materials, School of Materials Science and Engineering, Shaanxi Joint Laboratory of Graphene (NPU), Northwestern Polytechnical University, Xi'an 710072, P. R. China
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15
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Lászlóffy A, Palotás K, Rózsa L, Szunyogh L. Electronic and Magnetic Properties of Building Blocks of Mn and Fe Atomic Chains on Nb(110). NANOMATERIALS 2021; 11:nano11081933. [PMID: 34443761 PMCID: PMC8401957 DOI: 10.3390/nano11081933] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Revised: 07/15/2021] [Accepted: 07/16/2021] [Indexed: 11/16/2022]
Abstract
We present results for the electronic and magnetic structure of Mn and Fe clusters on Nb(110) surface, focusing on building blocks of atomic chains as possible realizations of topological superconductivity. The magnetic ground states of the atomic dimers and most of the monatomic chains are determined by the nearest-neighbor isotropic interaction. To gain physical insight, the dependence on the crystallographic direction as well as on the atomic coordination number is analyzed via an orbital decomposition of this isotropic interaction based on the spin-cluster expansion and the difference in the local density of states between ferromagnetic and antiferromagnetic configurations. A spin-spiral ground state is obtained for Fe chains along the [11¯0] direction as a consequence of the frustration of the isotropic interactions. Here, a flat spin-spiral dispersion relation is identified, which can stabilize spin spirals with various wave vectors together with the magnetic anisotropy. This may lead to the observation of spin spirals of different wave vectors and chiralities in longer chains instead of a unique ground state.
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Affiliation(s)
- András Lászlóffy
- Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, H-1525 Budapest, Hungary;
- Department of Theoretical Physics, Budapest University of Technology and Economics, H-1111 Budapest, Hungary;
| | - Krisztián Palotás
- Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, H-1525 Budapest, Hungary;
- Department of Theoretical Physics, Budapest University of Technology and Economics, H-1111 Budapest, Hungary;
- MTA-SZTE Reaction Kinetics and Surface Chemistry Research Group, University of Szeged, H-6720 Szeged, Hungary
- Correspondence:
| | - Levente Rózsa
- Department of Physics, University of Konstanz, D-78457 Konstanz, Germany;
| | - László Szunyogh
- Department of Theoretical Physics, Budapest University of Technology and Economics, H-1111 Budapest, Hungary;
- MTA-BME Condensed Matter Research Group, Budapest University of Technology and Economics, H-1111 Budapest, Hungary
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