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Register a new userYu-Shiba-Rusinov multiplets and clusters of multiorbital adatoms in superconducting substrates: Subgap Greens function approach
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Liliana Arrachea
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We discuss all the characteristics of Yu-Shiba-Rusinov states for clusters of impurities with classical magnetic moments in a superconducting substrate with s-wave symmetry. We consider the effect of the multiorbital structure of the impurities and the effect of the crystal field splitting. We solve the problem exactly and calculate the subgap Greens function, which has poles at the energies of the Shiba states and defines the local density of states associated to their wave functions. For the case of impurities sufficiently separated, we derive an effective Hamiltonian to describe the hybridization mediated by the substrate. We analyze the main features of the spectrum and the spectral density of the subgap excitations for impurities in dimer configurations with different relative orientations of the magnetic moments. We also illustrate how the same formalism applies for the solution of a trimer with frustration in the orientation of the magnetic moments.
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When magnetic atoms are inserted inside a superconductor, the superconducting order is locally depleted as a result of the antagonistic nature of magnetism and superconductivity1. Thereby, distinctive spectral features, known as Yu-Shiba-Rusinov states, appear inside the superconducting gap2-4. The search for Yu-Shiba-Rusinov states in different materials is intense, as they can be used as building blocks to promote Majorana modes5 suitable for topological quantum computing6. Here we report the first realization of Yu-Shiba-Rusinov states in graphene, a non-superconducting 2D material, and without the participation of magnetic atoms. We induce superconductivity in graphene by proximity effect7-9 brought by adsorbing nanometer scale superconducting Pb islands. Using scanning tunneling microscopy and spectroscopy we measure the superconducting proximity gap in graphene and we visualize Yu-Shiba-Rusinov states in graphene grain boundaries. Our results reveal the very special nature of those Yu-Shiba-Rusinov states, which extends more than 20 nm away from the grain boundaries. These observations provide the long sought experimental confirmation that graphene grain boundaries host local magnetic moments10-14 and constitute the first observation of Yu-Shiba-Rusinov states in a chemically pure system.
Magnetic impurities in $s$-wave superconductors lead to spin-polarized Yu-Shiba-Rusinov (YSR) in-gap states. Chains of magnetic impurities offer one of the most viable routes for the realization of Majorana bound states which hold a promise for topological quantum computing. However, this ambitious goal looks distant since no quantum coherent degrees of freedom have yet been identified in these systems. To fill this gap we propose an effective two-level system, a YSR qubit, stemming from two nearby impurities. Using a time-dependent wave-function approach, we derive an effective Hamiltonian describing the YSR qubit evolution as a function of distance between the impurity spins, their relative orientations, and their dynamics. We show that the YSR qubit can be controlled and read out using the state-of-the-art experimental techniques for manipulation of the spins. Finally, we address the effect of the spin noises on the coherence properties of the YSR qubit, and show a robust behaviour for a wide range of experimentally relevant parameters. Looking forward, the YSR qubit could facilitate the implementation of a universal set of quantum gates in hybrid systems where they are coupled to topological Majorana qubits.
Theoretical descriptions of Yu-Shiba-Rusinov (YSR) states induced by magnetic impurities inside the gap of a superconductor typically rely on a classical spin model or are restricted to spin-1/2 quantum spins. These models fail to account for important aspects of YSR states induced by transition-metal impurities, including the effects of higher quantum spins coupled to several conduction-electron channels, crystal or ligand-field effects, and magnetic anisotropy. We introduce and explore a zero-bandwidth model, which incorporates these aspects, is readily solved numerically, and analytically tractable in several limiting cases. The principal simplification of the model is to neglect Kondo renormalizations of the exchange couplings between impurity spin and conduction electrons. Nevertheless, we find excellent correspondence in those cases, in which we can compare our results to existing numerical-renormalization-group calculations. We apply the model to obtain and understand phase diagrams as a function of pairing strength and magnetic anisotropy as well as subgap excitation spectra. The single-channel case is most relevant for transition-metal impurities embedded into metallic coordination complexes on superconducting substrates, while the multi-channel case models transition-metal adatoms.
We study an interacting quantum dot in contact with a small superconducting island described by the interacting pairing model with charging (Coulomb) energy $E_c$. This charge-conserving Hamiltonian admits a compact matrix-product-operator representation and can be accurately solved using the density-matrix renormalization group. We investigate the effects of the $E_c$ term which controls the number of electrons on the superconducting island. Most prominently, the energies of the subgap excited states induced by the impurity are no longer symmetric with respect to the chemical potential and may undergo discontinuous changes as a function of gate voltages. Phase diagrams of spin-singlet and spin-doublet ground states reveal a cross-over from the regime governed by the Yu-Shiba-Rusinov physics to the charge quantization (Coulomb blockade) regime characterized by even-odd electron-number effects. In this regime we find subgap states for both even and odd superconductor occupancy, but with distinctive subgap excitation spectra.
The combination of different exotic properties in materials paves the way for the emergence of their new potential applications. An example is the recently found coexistence of the mutually antagonistic ferromagnetism and superconductivity in hydrogenated boron-doped diamond, which promises to be an attractive system with which to explore unconventional physics. Here, we show the emergence of Yu-Shiba-Rusinov (YSR) bands with a spatial extent of tens of nanometers in ferromagnetic superconducting diamond using scanning tunneling spectroscopy. We demonstrate theoretically how a two-dimensional (2D) spin lattice at the surface of a three-dimensional (3D) superconductor gives rise to the YSR bands, and how their density-of-states profile correlates with the spin lattice structure. The established strategy to realize new forms of the coexistence of ferromagnetism and superconductivity opens a way to engineer the unusual electronic states and also to design better performing superconducting devices.
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