Tuning interactions between spins in a superconductor

Abstract

Novel many-body and topological electronic phases can be created in assemblies of interacting spins coupled to a superconductor, such as one-dimensional topological superconductors with Majorana zero modes (MZMs) at their ends. Understanding and controlling interactions between spins and the emergent band structure of the in-gap Yu-Shiba-Rusinov (YSR) states they induce in a superconductor are fundamental for engineering such phases. Here, by precisely positioning magnetic adatoms with a scanning tunneling microscope (STM), we demonstrate both the tunability of exchange interaction between spins and precise control of the hybridization of YSR states they induce on the surface of a bismuth (Bi) thin film that is made superconducting with the proximity effect. In this platform, depending on the separation of spins, the interplay between Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, spin-orbit coupling, and surface magnetic anisotropy stabilizes different types of spin alignments. Using high-resolution STM spectroscopy at millikelvin temperatures, we probe these spin alignments through monitoring the spin-induced YSR states and their energy splitting. Such measurements also reveal a quantum phase transition between the ground states with different electron number parity for a pair of spins in a superconductor tuned by their separation. Experiments on larger assemblies show that spin-spin interactions can be mediated in a superconductor over long distances. Our results show that controlling hybridization of the YSR states in this platform provides the possibility of engineering the band structure of such states for creating topological phases.

26 pages, 4 figures, and Supplementary Information (42 pages, 27 figures, 2 tables)

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Cited by in corpus (35)

• Quantum spins and hybridization in artificially-constructed chains of magnetic adatoms on a superconductor
• Two-dimensional Shiba lattices as possible platform for crystalline topological superconductivity
• Non-Majorana modes in diluted spin chains proximitized to a superconductor
• Yu-Shiba-Rusinov qubit
• Atomic Manipulation of In-gap States on the $\beta$-Bi${}_2$Pd Superconductor
• Dynamical quantum phase transitions in a mesoscopic superconducting system
• Generalized atomic limit of a double quantum dot coupled to superconducting leads
• Quantum Yu-Shiba-Rusinov dimers
• Prevalence of trivial zero-energy sub-gap states in non-uniform helical spin chains on the surface of superconductors
• Yu-Shiba-Rusinov states in 2D superconductors with arbitrary Fermi contours
• Wave-function engineering on superconducting substrates: Chiral Yu-Shiba-Rusinov molecules
• Impurity states in altermagnetic superconductors
• Universal scaling of tunable Yu-Shiba-Rusinov states across the quantum phase transition
• Calculations of in-gap states of ferromagnetic spin chains on \textit{s}-wave wide-band superconductors
• Boosting the STM's spatial and energy resolution with double-functionalized probe tips
• Systematic study of Mn atoms, artificial dimers and chains on superconducting Ta(110)
• Search for large topological gaps in atomic spin chains on proximitized superconducting heavy metal layers
• Electron-boson-interaction induced particle-hole symmetry breaking of conductance into subgap states in superconductors
• Shiba states in systems with density of states singularities
• Gate-tunable topological superconductivity in a supramolecular electron spin lattice
• Fractional Spin Quantum Hall Effect in Weakly Coupled Spin Chain Arrays
• RKKY interaction at helical edges of topological superconductors
• Topological Quantum Phase Transitions in Metallic Shiba Lattices
• Diluted Yu-Shiba-Rusinov arrays on the $\beta$-Bi${}_2$Pd anisotropic superconductor
• RKKY interaction in triplet superconductors: Dzyaloshinskii-Moriya-type interaction mediated by spin-polarized Cooper pairs
• Subgap modes in two-dimensional magnetic Josephson junctions
• Fractional spin excitations and conductance in the spiral staircase Heisenberg ladder
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• Spin-dependent transport in a driven noncolinear antiferromagnetic fractal network
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• Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots
• Yu-Shiba-Rusinov multiplets and clusters of multiorbital adatoms in superconducting substrates: Subgap Green's function approach
• Andreev molecule in parallel InAs nanowires
• Detecting and Distinguishing Majorana Zero Modes with the Scanning Tunneling Microscope
• Spin-polarized zero-bias peak from a single magnetic impurity at an s-wave superconductor: first-principles study