Electrical Control of Majorana Bound States Using Magnetic Stripes

Mohanta, Narayan; Zhou, Tong; Xu, Jun-Wen; Han, Jong E.; Kent, Andrew D.; Shabani, Javad; Žutić, Igor; Matos-Abiague, Alex

doi:10.1103/physrevapplied.12.034048

Cited by 54 publications

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References 81 publications

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“…For example, state-of-the art fabrication of superconducting junctions with topological insulators [38] would support fabrication of similar X-shaped junctions. With the progress in tunable magnetic textures used to modify proximity-induced superconductivity [23,27,[39][40][41][42][43][44][45][46][47][48][49], X-shaped junctions could be considered with a reduced role of an applied magnetic field.…”

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Phase Control of Majorana Bound States in a Topological X Junction

et al. 2020

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Topological superconductivity supports exotic Majorana bound states (MBS) which are chargeless zeroenergy emergent quasiparticles. With their non-Abelian exchange statistics and fractionalization of a single electron stored nonlocally as a spatially separated MBS, they are particularly suitable for implementing fault-tolerant topological quantum computing. While the main efforts to realize MBS have focused on one-dimensional systems, the onset of topological superconductivity requires delicate parameter tuning and geometric constraints pose significant challenges for their control and demonstration of non-Abelian statistics. To overcome these challenges, building on recent experimental advances in planar Josephson junctions (JJs), we propose a MBS platform of X-shaped JJs. This versatile implementation reveals how external flux control of the superconducting phase difference can generate and manipulate multiple MBS pairs to probe non-Abelian statistics. The underlying topological superconductivity exists over a large parameter space, consistent with materials used in our fabrication of such X junctions, as an important step towards scalable topological quantum computing. arXiv:1909.05386v1 [cond-mat.mes-hall]

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Phase Control of Majorana Bound States in a Topological X Junction

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“…An alternative approach to engineering topological superconductors while circumventing these two challenges could be to remove the spin-orbit coupling ingredient, and instead consider a non-collinear magnetic texture proximitized by a conventional superconductor 14,[25][26][27][28][29] . In fact, our results are relevant for a broader class of skyrmion-like textures, such as magnetic bubbles [30][31][32][33] .…”

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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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“…The lattice grid spacing used is a = 10 nm 41 with which the hopping energy becomes t = 22.44 meV. The amplitude of the spin texture B i is set to B 0 = 0.3 T, compatible with the saturation magnetization M s = 1.7 × 10 6 A/m for CoFe 10,11 . We present results for a planar JJ with length L y = 2 µm, transverse length of the SC leads L x = 200 nm, and width of the quasi-one-dimensional metallic channel W = 50 nm.…”

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confidence: 99%

“…The unification of non-trivial spin texture and superconductivity via advanced interface engineering is a futuristic approach to create and manipulate non-Abelian Majorana bound states (MBS) for their controlled usage in fault-tolerant topological quantum computing [1][2][3][4][5] . The nanoscale control of magnetism not only relaxes the need for a specific form of Rashba spin-orbit coupling (SOC), but also motivates for a magnetic field-free platform for the braiding of the MBS [6][7][8][9][10][11][12] . Despite numerous successes in the search for the MBS in one-dimensional geometries, the associated limitations such as the intrinsic instabilities of one-dimensional systems, the need for fine tuning of parameters, and the technological obstacles in physical implementation, suggest to look for a two-dimensional platform 13,14 .…”

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confidence: 99%

Skyrmion Control of Majorana States in Planar Josephson Junctions

Mohanta

Okamoto

Dagotto

2021

Preprint

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Planar Josephson junctions provide a versatile platform, alternative to the nanowire-based geometry, for the generation of the Majorana bound states, due to the additional phase tunability of the topological superconductivity. The proximity induction of chiral magnetism and superconductivity in a two-dimensional electron gas showed remarkable promises to manipulate topological superconductivity. Here, we consider a Josephson junction involving a skyrmion crystal and show that the chiral magnetism of the skyrmions can create and control the Majorana bound states without the requirement of an intrinsic Rashba spin-orbit coupling. Interestingly, the Majorana bound states in our geometry are realized robustly at zero phase difference at the junction. The skyrmion radius, being externally tunable by a magnetic field or a magnetic anisotropy, brings a unique control feature for the Majorana bound states.

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Electrical Control of Majorana Bound States Using Magnetic Stripes

Cited by 54 publications

References 81 publications

Phase Control of Majorana Bound States in a Topological X Junction

Phase Control of Majorana Bound States in a Topological X Junction

Topological superconductivity with deformable magnetic skyrmions

Skyrmion Control of Majorana States in Planar Josephson Junctions

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