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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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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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Karan S, Huang H, Ivanovic A, Padurariu C, Kubala B, Kern K, Ankerhold J, Ast CR. Tracking a spin-polarized superconducting bound state across a quantum phase transition. Nat Commun 2024; 15:459. [PMID: 38212303 PMCID: PMC10784290 DOI: 10.1038/s41467-024-44708-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2023] [Accepted: 01/02/2024] [Indexed: 01/13/2024] Open
Abstract
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.
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Affiliation(s)
- Sujoy Karan
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569, Stuttgart, Germany.
| | - Haonan Huang
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569, Stuttgart, Germany
| | - Alexander Ivanovic
- Institute for Complex Quantum Systems and IQST, Universität Ulm, Albert-Einstein-Allee 11, 89069, Ulm, Germany
| | - Ciprian Padurariu
- Institute for Complex Quantum Systems and IQST, Universität Ulm, Albert-Einstein-Allee 11, 89069, Ulm, Germany
| | - Björn Kubala
- Institute for Complex Quantum Systems and IQST, Universität Ulm, Albert-Einstein-Allee 11, 89069, Ulm, Germany
- Institute for Quantum Technologies, German Aerospace Center (DLR), Wilhelm-Runge-Straße 10, 89081, Ulm, Germany
| | - Klaus Kern
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569, Stuttgart, Germany
- Institut de Physique, Ecole Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland
| | - Joachim Ankerhold
- Institute for Complex Quantum Systems and IQST, Universität Ulm, Albert-Einstein-Allee 11, 89069, Ulm, Germany
| | - Christian R Ast
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569, Stuttgart, Germany.
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Non-Majorana modes in diluted spin chains proximitized to a superconductor. Proc Natl Acad Sci U S A 2022; 119:e2210589119. [PMID: 36215505 PMCID: PMC9586262 DOI: 10.1073/pnas.2210589119] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Spin chains proximitized with superconducting condensates have emerged as one of the most promising platforms for the realization of Majorana modes. Here, we craft diluted spin chains atom by atom following a seminal theoretical proposal suggesting indirect coupling mechanisms as a viable route to trigger topological superconductivity. Starting from single adatoms hosting deep Shiba states, we use the highly anisotropic Fermi surface of the substrate to create spin chains characterized by different magnetic configurations along distinct crystallographic directions. By scrutinizing a large set of parameters we reveal the ubiquitous emergence of boundary modes. Although mimicking signatures of Majorana modes, the end modes are identified as topologically trivial Shiba states. Our work demonstrates that zero-energy modes in spin chains proximitized to superconductors are not necessarily a link to Majorana modes while simultaneously identifying other experimental platforms, driving mechanisms, and test protocols for the determination of topologically nontrivial superconducting phases.
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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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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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Brinker S, Küster F, Parkin SSP, Sessi P, Lounis S. Anomalous excitations of atomically crafted quantum magnets. SCIENCE ADVANCES 2022; 8:eabi7291. [PMID: 35080983 PMCID: PMC8791613 DOI: 10.1126/sciadv.abi7291] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/26/2021] [Accepted: 12/06/2021] [Indexed: 06/14/2023]
Abstract
High-energy resolution spectroscopic studies of quantum magnets proved extremely valuable in accessing magnetodynamics quantities, such as energy barriers, magnetic interactions, and lifetime of excited states. Here, we investigate a previously unexplored flavor of low-energy spin excitations for quantum spins coupled to an electron bath. In sharp contrast to the usual tunneling signature of two steps symmetrically centered around the Fermi level, we find a single step in the conductance. Combining time-dependent and many-body perturbation theories, magnetic field-dependent tunneling spectra are explained as the result of an interplay between weak magnetic anisotropy energy, magnetic interactions, and Stoner-like electron-hole excitations that are strongly dependent on the magnetic states of the nanostructures. The results are rationalized in terms of a noncollinear magnetic ground state and the dominance of ferro- and antiferromagnetic interactions. The atomically crafted nanomagnets offer an appealing model for the exploration of electrically pumped spin systems.
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Affiliation(s)
- Sascha Brinker
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, Jülich D-52425, Germany
| | - Felix Küster
- Max Planck Institute of Microstructure Physics, Halle 06120, Germany
| | | | - Paolo Sessi
- Max Planck Institute of Microstructure Physics, Halle 06120, Germany
| | - Samir Lounis
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, Jülich D-52425, Germany
- Faculty of Physics, University of Duisburg-Essen and CENIDE, 47053 Duisburg, Germany
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