Majorana bound states in magnetic skyrmions imposed onto a superconductor

Rex, Sybille; Gornyi, I. V.; Mirlin, A. D.

doi:10.1103/physrevb.100.064504

Cited by 67 publications

(53 citation statements)

References 76 publications

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“…The inclusion of intrinsic and Rashba spin-orbit couplings would require another in-depth study due to the loss of rotational symmetry, and due to the non-trivial interplay of different effective spin-triplet pairings introduced by these couplings. In the limit that we consider in this work, in absence of skyrmion the spin-orbit length in the superconductor l so = 1/(mα), with α a spin-orbit amplitude, is much larger than the typical lengthscale of the skyrmion, so that the magnetoelectric coupling and appearance of vortices can also be neglected [41][42][43][44][45] .…”

Section: Resultsmentioning

confidence: 99%

Topological superconductivity with deformable magnetic skyrmions

2019

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Magnetic skyrmions are nanoscale spin configurations that are efficiently created and manipulated. They hold great promises for next-generation spintronics applications. In parallel, the interplay of magnetism, superconductivity and spin-orbit coupling has proved to be a versatile platform for engineering topological superconductivity predicted to host non-abelian excitations, Majorana zero modes. We show that topological superconductivity can be induced by proximitizing skyrmions and conventional superconductors, without need for additional ingredients. Apart from a previously reported Majorana zero mode in the core of the skyrmion, we find a more universal chiral band of Majorana modes on the edge of the skyrmion. We show that the chiral Majorana band is effectively flat in the physically relevant parameter regime, leading to interesting robustness and scaling properties. In particular, the number of Majorana modes in the (nearly-)flat band scales with the perimeter length of the system, while being robust to local disorder. 1 arXiv:1904.03005v3 [cond-mat.supr-con] 23 Oct 2019 8 where all energies are in units of the bandwidth t, all distances are in units of the lattice spacing a (see Supplementary Note 1 and Supplementary Figure 1 for details). For precisely |m J | = |m * J | the wire is at the topological transition and has a gapless spectrum, giving our model a bulk-gap-closing point as shown in Fig. 2c.The MFB found here has a protection by a chiral symmetry, as MFB's were found to have in models with translational symmetries 39,40,51 . Note that the wire Hamiltonian and its MFB become a correct model for our texture Eq. (1) if we choose q = 0 and thereby nullify the H slope m J (r) term. Physically, this is a special case where instead of the skyrmion shape the texture becomes coplanar (in the xz-plane, see Eq. (1)), and the orthogonal direction provides a chiral operator Ξ = τ y σ ythat anticommutes with the Hamiltonian (see Eq. (2)). Since all the MFB states have the same chirality, they cannot hybridize among themselves. It is difficult to remove the MFB states 51 , namely, a perturbation must have energy larger than the effective gap; or, it should hybridize the MFB with low energy bulk states at |m J | ≈ |m * J |, which are few; or, chirality symmetry must be broken (out-of-xz-plane exchange field). We note that the proof of existence of the MFB rests on the rotational symmetry of the q = 0 coplanar texture, since this symmetry provides the m J quantum number. Consider now deformations of the shape of the edge imposed on our q = 0 coplanar texture. These geometric deformations would generally mix the m J sectors, yet the described stability of the MFB implies that the deformations would be inefficient in removing the MFB states.We can now proceed to the relevant model for a skyrmion with arbitrary q = 0:The single term H slope m J (r) breaks the chiral symmetry Ξ, and there are no other chiral operators. The term H slope m J (r) exactly contributes an energy ε edgestate (m J ) ∼ m J to an MFB state ...

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Section: Resultsmentioning

confidence: 99%

Topological superconductivity with deformable magnetic skyrmions

2019

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“…45 for Majorana fermions contained inside superconducting vortices. A similar technique could be used to manipulate skyrmions containing Majorana fermion bound states [76][77][78] ; however, in this case, it is necessary to consider the dynamics carefully due to the strong Magnus component of the skyrmion motion, which is likely to affect how the skyrmions move under the influence of the tip and interact with pinning sites 79 . In this work, we considered moving the vortices with an MFM tip; however, there are also proposals for creating vortex logic devices using applied currents and specially structured pinning geometries 84,85 .…”

Section: Discussionmentioning

confidence: 99%

“…74,75 to demonstrate our method for realizing quantum gates using vortices. We also discuss how our technique could be used in a similar scheme for skyrmion systems, based on proposals for the stabilization of bound Majorana states in skyrmions [76][77][78] , the pinning of skyrmions on periodic substrates 79 , and the manipulation of individual skyrmions 80 . There are also systems in which skyrmions and superconducting vortices are coupled 81 .…”

Section: Introductionmentioning

confidence: 99%

Braiding Majorana fermions and creating quantum logic gates with vortices on a periodic pinning structure

Reichhardt

2020

Phys. Rev. B

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We show how vortices that support Majorana fermions when placed on a periodic pinning array can be used for vortex exchange and independent braiding by performing a series of specific moves with a probe tip. Using these braiding operations, we demonstrate realizations of a Hadamard and a CNOT gate. We specifically consider the first matching field at which there is one vortex per pinning site, and we show that there are two basic dynamic operations, move and exchange, from which basic braiding operations can be constructed in order to create specific logic gates. The periodic pinning array permits both control of the world lines of the vortices and freedom for vortex manipulation using a set of specific moves of the probe during which the probe tip strength and height remain unchanged. We measure the robustness of the different moves against thermal effects and show that the three different operations produce distinct force signatures on the moving tip.Nv j=1 K 1 (r ij /λ)r ij , where K 1 is the modified Bessel function of the second kind, r ij = |r i − r j |,r ij = (r i − r j )/r ij , and r j is the position of vortex j. We measure all forces in units of f 0 = φ 2 0 /(2πµ 0 λ 3 ) where φ 0 = h/2e is the flux

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“…Building on the concept of a rotating magnetic field, an intriguing idea for creating a Majorana-zero-mode hosting platform is to couple a vortex in a conventional superconductor to a magnetic vortex called a skyrmion [7]. In this magnetic structure (Fig.…”

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confidence: 99%

“…However, it is still challenging to separate them spatially and energetically from other states so that they can be directly observed. The next step to doing that will be to create skyrmions of different shapes [7] or with magnetic ordering described by different winding numbers [10]. This step will require fine-tuning of the magnetic interactions and careful selection of the magnetic materials but, when interfaced with conventional superconductors, doing so should lead to increased stability of the Majorana zero modes.…”

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confidence: 99%