Topological Shiba bands in artificial spin chains on superconductors

Schneider, Lucas; Beck, Philip; Posske, Thore; Crawford, Daniel; Mascot, Eric; Rachel, Stephan; Wiesendanger, R.; Wiebe, Jens

doi:10.1038/s41567-021-01234-y

Cited by 107 publications

(151 citation statements)

References 53 publications

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“…In comparison with pure Shiba bands the subgap band structure is richer and shows marked features and further gap closings at high momenta, near or beyond k F . Such features resemble the recently reported band structure of ferromagnetic Mn chains on a Nb superconductor [31,32], and a comparison with the present theory would likely be useful. We discuss ferromagnetic and spiral orders but not any mechanism causing a specific spiral (such as in Refs.…”

Section: Introductionsupporting

confidence: 83%

“…As shown by Yu, Shiba, and Rusinov (YSR) in the 1960s [10][11][12][13] a bound state develops in the superconducting gap at the location of a magnetic impurity. This work has found a renaissance when it was realized that arranging such impurities in chains, such that the bound electrons can hop between different impurity sites, can lead to subgap bands of different topological classifications upon tuning the impurity strength and the alignment of the magnetic moments [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. These Shiba chains provide a complementary approach for the current vast activities on other one-dimensional (1D) systems with topological physics.…”

Section: Introductionmentioning

confidence: 99%

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Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. I. Continuum description

Carroll

Braunecker

2021

Phys. Rev. B

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We consider subgap bands induced in a two-dimensional superconductor by a densely packed chain of magnetic moments with ferromagnetic or spiral alignments. We show that by contrast with sparsely packed chains a consistent description requires that all wavelengths are taken into account for the scattering at the magnetic moments. The resulting subgap states are a composition of Yu-Shiba-Rusinov-type states and magnetic scattering states, whose mixture becomes especially important to understand the nature and dimensional renormalization of gap closures for spiral magnetic alignments under increasing scattering strength, particularly as the spiral becomes commensurate with the Fermi wavelength. The results are fully analytic in the form of Green's functions and provide the tools for further analysis of the properties of the subgap states.

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Section: Introductionsupporting

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. I. Continuum description

Carroll

Braunecker

2021

Phys. Rev. B

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“…The presence of magnetic impurities on a superconducting surface leads to the emergence of so-called Yu-Shiba-Rusinov (YSR) states [4][5][6][7][8][9], due to the coupling of the localized magnetic moment to the Cooper pairs. In atomic chains, hybridized YSR states develop into bands [10,11], that can give rise to topological superconductivity and consequently to the appearance of Majorana bound states [12][13][14][15][16]. In a recent study by Beck et al [7], an Mn adatom and Mn dimers on Nb(110) were investigated in the superconducting state.…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper, we investigate the magnetic properties of Mn and Fe adatoms, dimers, and monatomic chains on Nb(110) along different crystallographic directions. Mn and Fe adatoms, Mn dimers, and Mn chains have already been studied on Nb(110) [7,8,14,28], the magnetic properties of which are now systematically investigated from the theoretical side. Determining the magnetic properties of atomic chains from first principles is a long-standing challenge [25,[29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Electronic and Magnetic Properties of Building Blocks of Mn and Fe Atomic Chains on Nb(110)

et al. 2021

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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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“…Superconductorferromagnet heterostructures do not require the application of an external magnetic field and, therefore, are advantageous with respect to other platforms. Following this line of argument, topological superconductivity and MZMs have been demonstrated to emerge in half-metal/superconductor [14] or ferromagnet/unconventional superconductor [15] heterostructures, in ferromagnetic wires proximised to conventional superconductors [16][17][18] and in ferromagnetically aligned chains of magnetic impurities embedded in conventional superconductors [19][20][21][22][23][24][25][26]. Spin-orbit coupling is an essential component in all of these proposals.…”

Section: Majorana Zero Modes In Superconductor/ferromagnet Heterostructuresmentioning

confidence: 99%

Majorana Zero Modes in Ferromagnetic Wires without Spin-Orbit Coupling

2021

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We present a novel controllable platform for engineering Majorana zero modes. The platform consists of a ferromagnetic metallic wire placed among conventional superconductors, which are in proximity to ferromagnetic insulators. We demonstrate that Majorana zero modes emerge localised at the edges of the ferromagnetic wire, due to the interplay of the applied supercurrents and the induced by proximity exchange fields with conventional superconductivity. Our mechanism does not rely on the pairing of helical fermions by combining conventional superconductivity with spin-orbit coupling, but rather exploits the misalignment between the magnetization of the ferromagnetic insulators and that of the ferromagnetic wire.

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Topological Shiba bands in artificial spin chains on superconductors

Cited by 107 publications

References 53 publications

Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. I. Continuum description

Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. I. Continuum description

Electronic and Magnetic Properties of Building Blocks of Mn and Fe Atomic Chains on Nb(110)

Majorana Zero Modes in Ferromagnetic Wires without Spin-Orbit Coupling

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