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Register a new userYu-Shiba-Rusinov bound states versus topological edge states in Pb/Si(111)
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Added by
Gerbold M\\'enard C. B.
Publication date
2018
fields
Physics
and research's language is
English
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There is presently a tremendous activity around the field of topological superconductivity and Majorana fermions. Among the many questions raised, it has become increasingly important to establish the topological or non-topological origin of features associated with Majorana fermions such as zero-bias peaks. Here, we compare in-gap features associated either with isolated magnetic impurities or with magnetic clusters strongly coupled to the atomically thin superconductor Pb/Si(111). We study this system by means of scanning tunneling microscopy and spectroscopy (STM/STS). We take advantage of the fact that the Pb/Si(111) monolayer can exist either in a crystal-ordered phase or in an incommensurate disordered phase to compare the observed spectroscopic features in both phases. This allows us to demonstrate that the strongly resolved in-gap states we found around the magnetic clusters in the disordered phase of Pb have a clear topological origin.
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Chains of magnetic atoms placed on the surface of an s-wave superconductor with large spin-orbit coupling provide a promising platform for the realization of topological superconducting states characterized by the presence of Majorana zero-energy modes. In this work we study the properties of the one-dimensional chain of Yu-Shiba-Rusinov states induced by magnetic impurities using a realistic model for the magnetic atoms that include the presence of multiple scattering channels. These channels are mixed by the spin-orbit coupling and, via the hybridization of the Yu-Shiba-Rusinov states at different sites of the chain, result in a multi-band structure for the chain. We obtain the topological phase diagram for such band structure. We identify the parameter regimes for which the different bands lead to a topological phase and show that the inclusion of higher bands can greatly enlarge the phase space for the realization of topological states.
We study a chain of magnetic moments exchange coupled to a conventional three dimensional superconductor. In the normal state the chain orders into a collinear configuration, while in the superconducting phase we find that ferromagnetism is unstable to the formation of a magnetic spiral state. Beyond weak exchange coupling the spiral wavevector greatly exceeds the inverse superconducting coherence length as a result of the strong spin-spin interaction mediated through the subgap band of Yu-Shiba-Rusinov states. Moreover, the simple spin-spin exchange description breaks down as the subgap band crosses the Fermi energy, wherein the spiral phase becomes stabilized by the spontaneous opening of a $p-$wave superconducting gap within the band. This leads to the possibility of electron-driven topological superconductivity with Majorana boundary modes using magnetic atoms on superconducting surfaces.
Recent studies of mutually interacting magnetic atoms coupled to a superconductor have gained enormous interest due to the potential realization of topological superconductivity. The Kondo exchange coupling J_K of such atoms with the electrons in the superconductor has a pair-breaking effect which produces so-called Yu-Shiba-Rusinov (YSR) states within the superconducting energy gap, whose energetic positions are intimately connected with the requirements for topological superconductivity. Here, using the tip of a scanning tunneling microscope, we artificially craft a multi-impurity Kondo system coupled to a superconducting host consisting of an Fe adatom interacting with an assembly of interstitial Fe atoms on an oxygen-reconstructed Ta(100) surface and we experimentally investigate the signatures of Kondo screening and the YSR states. With the help of numerical renormalization group (NRG) calculations, we show that the observed behavior can be qualitatively reproduced by a two-impurity Kondo system whose inter-impurity antiferromagnetic interaction J is adjusted by the number of interstitial Fe atoms in the assembly. When driving the system from the regime of two decoupled Kondo singlets (small J) to that of an antiferromagnetic dimer (large J), the YSR state shows a characteristic cross-over in its energetic position and particle-hole asymmetry.
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.
The coupling of a spin to an underlying substrate is the basis for a plethora of phenomena. In the case of a metallic substrate, Kondo screening of the adatom magnetic moment can occur. As the substrate turns superconducting, an intriguing situation emerges where the pair breaking due to the adatom spins leads to Yu-Shiba-Rusinov bound states, but also intertwines with Kondo phenomena. Through scanning tunneling spectroscopy, we analyze the interdependence of Kondo screening and superconductivity. Our data obtained on single Fe adatoms on Nb(110) show that the coupling and the resulting YSR states are strongly adsorption site-dependent and reveal a quantum phase transition at a Kondo temperature comparable to the superconducting gap. The experimental signatures are rationalized by combined density functional theory and continuous-time quantum Monte-Carlo calculations to rigorously treat magnetic and hybridization effects on equal footing.
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