Majorana bound states in magnetic skyrmions

Yang, Guang; Stano, Peter; Klinovaja, Jelena; Loss, Daniel

doi:10.1103/physrevb.93.224505

Cited by 146 publications

(133 citation statements)

References 45 publications

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“…[44][45][46]). In this case, spintronic techniques for manipulating the motion of skyrmions may be used to move the Majorana-carrying SVPs in a controlled way.…”

Section: Pacs Numbersmentioning

confidence: 99%

Composite Topological Excitations in Ferromagnet-Superconductor Heterostructures

2016

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We investigate the formation of a new type of composite topological excitation -the skyrmionvortex pair (SVP) -in hybrid systems consisting of coupled ferromagnetic and superconducting layers. Spin-orbit interaction in the superconductor mediates a magnetoelectric coupling between the vortex and the skyrmion, with a sign (attractive or repulsive) that depends on the topological indices of the constituents. We determine the conditions under which a bound SVP is formed, and characterize the range and depth of the effective binding potential through analytical estimates and numerical simulations. Furthermore, we develop a semiclassical description of the coupled skyrmion-vortex dynamics and discuss how SVPs can be controlled by applied spin currents. PACS numbers:Advances in materials and fabrication capabilities in recent years have opened many possibilities for modifying and harnessing the properties of matter in a variety of interesting and powerful ways. In particular, hybrid systems comprised of layers of two or more materials of very different character provide new opportunities to study important fundamental phenomena -such as magnetism and superconductivity [1][2][3][4], or optical and electronic properties [5] -in new regimes and in new combinations of coexistence.Often, the range of phenomena exhibited by a hybrid system is much richer than that of its parts [6]. For example, it was recently demonstrated that hybrid systems comprised of superconductors and semiconductors yield exquisite new levels of fully-electrical control over Josephson-based quantum devices [7]. It has also been proposed that the exchange field of a magnetic layer proximity-coupled to a 3D topological insulator surface may open the possibility to realize a new quantum phase of matter with an intriguing quantized magnetoelectric response [8]. Moreover, the possibilities afforded by the trifold combination of magnetic, superconducting, and semiconducting systems is at the heart of the intense wave of recent activity aimed at realizing topological superconductivity and associated Majorana bound states [9-16] -a key step in the development of topological quantum information processing [17].In this work, we investigate a novel type of composite topological excitation in hybrid systems. Specifically, we investigate the coupling between magnetic skyrmions and superconducting vortices in a two-dimensional (2D) layered ferromagnet-superconductor heterostructure (see Fig. 1). The combination of spin-orbit coupling (SOC) in the superconductor and the lack of inversion symmetry of the heterostructure leads to a magnetoelectric coupling that mediates an interaction between textures of the magnetic and superconducting order parameters. In isolation, both the superconductor and the 2D ferromagnet may host a variety of robust topological excitationsvortices and anti-vortices for the superconductor [18] and The exchange field of a ferromagnetic thin film is induced into a thin film superconductor by proximity coupling. The spatially varying exchange f...

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“…[44][45][46]). In this case, spintronic techniques for manipulating the motion of skyrmions may be used to move the Majorana-carrying SVPs in a controlled way.…”

Section: Pacs Numbersmentioning

confidence: 99%

Composite Topological Excitations in Ferromagnet-Superconductor Heterostructures

2016

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“…With regard to Majorana physics, effective p-wave phases with chiral edge modes have been predicted [44,45], whereas localized MBS may emerge in elongated skyrmions [46] which resemble nanowires. For more complicated skyrmion textures, Yang et al [47] have derived the criterion that a pair of MBS can form for skyrmions of even winding number, with one state being localized at the skyrmion core and the partner state at the outer rim of the skyrmion. We will return to this criterion in more detail later.…”

Section: Introductionmentioning

confidence: 99%

Majorana bound states in magnetic skyrmions imposed onto a superconductor

2019

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We consider a superconducting film exchange-coupled to a close-by chiral magnetic layer and study how magnetic skyrmions can induce the formation of Majorana bound states (MBS) in the superconductor. Inspired by a proposal by Yang et al. [Phys. Rev. B 93, 224505 (2016)], which suggested MBS in skyrmions of even winding number, we explore whether such skyrmions could result from a merger of ordinary skyrmions. We conclude that the formation of higher-winding skyrmions is not realistic in chiral magnets. Subsequently, we present a possibility to obtain MBS from realistic skyrmions of winding number one, if a skyrmion-vortex pair is formed instead of a bare skyrmion. Specifically, we show that MBS are supported in a pair of a circular skyrmion and a vortex which both have a winding number of one. We back up our analytical prediction with results from numerical diagonalization and obtain the spatial profile of the MBS. In light of recent experimental progress on the manipulation of skyrmions, such systems are promising candidates to achieve direct spatial control of MBS. arXiv:1904.04177v2 [cond-mat.supr-con]

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“…In this section, we check our analytical results by comparing them with a numerical tight-binding model for proximity-induced superconductivity [37][38][39] in the geometry shown in Fig. 1.…”

Section: Tight-binding Modelmentioning

confidence: 99%

Finite-size effects in a nanowire strongly coupled to a thin superconducting shell

2017

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We study the proximity effect in a one-dimensional nanowire strongly coupled to a finite superconductor with a characteristic size which is much shorter than its coherence length. Such geometries have become increasingly relevant in recent years in the experimental search for Majorana fermions with the development of thin epitaxial Al shells which form a very strong contact with either InAs or InSb nanowires. So far, however, no theoretical treatment of the proximity effect in these systems has accounted for the finite size of the superconducting film. We show that the finite-size effects become very detrimental when the level spacing of the superconductor greatly exceeds its energy gap. Without any fine-tuning of the size of the superconductor (on the scale of the Fermi wavelength), the tunneling energy scale must be larger than the level spacing in order to reach the "hard gap" regime which is seen ubiquitously in the experiments. However, in this regime, the large tunneling energy scale induces a large shift in the effective chemical potential of the nanowire and pushes the topological phase transition to magnetic field strengths which exceed the critical field of Al.

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Majorana bound states in magnetic skyrmions

Cited by 146 publications

References 45 publications

Composite Topological Excitations in Ferromagnet-Superconductor Heterostructures

Composite Topological Excitations in Ferromagnet-Superconductor Heterostructures

Majorana bound states in magnetic skyrmions imposed onto a superconductor

Finite-size effects in a nanowire strongly coupled to a thin superconducting shell

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