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Device geometry and a skyrmion crystal. a Planar Josephson junction on top of a skyrmion crystal. The two-dimensional electron gas (2DEG) exhibits both proximity-induced superconductivity from the top superconductor (SC) layers and spatially varying magnetism from the bottom skyrmion crystal that is created in the ferromagnet due to the competition between exchange interactions in the ferromagnet (FM) and the heavy metal or heavy insulator (HM/HI), with a field or anisotropy. The zero-energy Majorana bound states (shown as yellow bubbles) are localized at the two ends of the quasi-one-dimensional metallic channel. b The skyrmion crystal spin texture, spontaneously generated in a Monte Carlo simulation using a 100 × 100 × 6 lattice with ferromagnetic exchange interaction strength J = 1, Dzyaloshinskii-Moriya interaction strength D = 0.3J, magnetic field H z = 0.1J, spin amplitude S = 1, and easy-plane anisotropy A = 0.01J. The colorbar in b denotes the z component of the magnetization m z .
Source publication
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 promi...
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Context 1
... composed of a two-dimensional electron gas and an s-wave superconductor, is placed on top of a Néel-type skyrmion crystal (SkX) in such a way that the two-dimensional electron gas experiences the spatially varying magnetic field from the bottom SkX and it is also proximitized to the electron pairing from the top superconductors, as described in Fig. 1a. The interplay between the SkX spin texture and the proximity-induced superconductivity leads to topological superconductivity near the middle quasi-one-dimensional channel of the Josephson junction with localized MBS at its two ends. The advantages of using the SkX are: (i) the chiral magnetism generates a robust fictitious gauge ...
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... produces a triangular SkX, in the presence of a magnetic field or an anisotropy. Our Monte Carlo simulations reveal that columns of skyrmions, arranged in a triangular array, appear spontaneously within a six-layer ferromagnet, although the DMI exists predominantly at the interface between the ferromagnet and the heavy compound, as shown in Fig. 1b. We perform simulated annealing using the Metropolis energy-minimization algorithm, formulated with the following ...
Citations
... In proximitized one-dimensional (1D) systems, the spatial magnetic modulation can be achieved by interactions [44][45][46], adatoms [47][48][49][50][51][52][53][54][55], or local magnets [56][57][58][59][60]. Planar setups offer more sophisticated magnetic textures in proximity to superconductors [61][62][63][64][65][66][67][68][69][70][71][72][73][74][75]. For example, skyrmion textures on superconductors [76][77][78][79] have been recently measured [80,81] and signatures consistent with MBSs where found in proximitized magnetic monolayers [82][83][84]. Proximitized structures need to be carefully engineered so that the competing magnetic and supercon-ducting orders coexist. ...
Topological superconductors are appealing building blocks for robust and reliable quantum information processing. Most platforms for engineering topological superconductivity rely on a combination of superconductors, materials with intrinsic strong spin-orbit coupling, and external magnetic fields, detrimental for superconductivity. We propose a setup where a conventional Josephson junction is linked via a magnetic-textured barrier. Antiferromagnetic and ferromagnetic insulators with periodically arranged domains are compatible with our proposal which does not require intrinsic spin-orbit or external magnetic fields. We find that the topological phase depends on the magnitude and period of the barrier magnetization. The superconducting phase controls the topological transition, which could be detected as a sharp suppression of the supercurrent across the junction.
... Experimentally, the YSR states and/or the MZMs have been observed by growing magnetic impurities on an s-wave SC substrate [44][45][46][47][48][49][50][51][52][53][54]. Nevertheless, the creation of YSR states goes beyond one-dimensional (1D) systems; in a two-dimensional (2D) arrangement where noncollinear magnetic textures proximitized with an s-wave SC, unique effects like the emergence of 1D Majorana dispersive/flat edge modes emerge [31,[37][38][39][55][56][57][58][59][60][61][62][63], setting them notably different from the typical observation of MZMs. ...
We put forth a theoretical framework for engineering a two-dimensional (2D) second-order topological superconductor (SOTSC) by utilizing a heterostructure: incorporating noncollinear magnetic textures between an s-wave superconductor and a 2D quantum spin Hall insulator. It stabilizes the higher order topological superconducting phase, resulting in Majorana corner modes (MCMs) at four corners of a 2D domain. The calculated nonzero quadrupole moment characterizes the bulk topology. Subsequently, through a unitary transformation, an effective low-energy Hamiltonian reveals the effects of magnetic textures, resulting in an effective in-plane Zeeman field and spin-orbit coupling. This approach provides a qualitative depiction of the topological phase, substantiated by numerical validation within an exact real-space model. Analytically calculated effective pairings in the bulk illuminate the microscopic behavior of the SOTSC. The comprehension of MCM emergence is supported by a low-energy edge theory, which is attributed to the interplay between effective pairings of (px+py)-type and (px+ipy)-type. Our extensive study paves the way for practically attaining the SOTSC phase by integrating noncollinear magnetic textures.
... At the boundaries and vortex cores, a topological superconductor harbors Majorana quasiparticles, with potential value in the longsought area of decoherence-free quantum computing [12][13][14][15][16][17] . Topological superconductivity can be induced, for example, by a Rashba spin-orbit coupling together with a magnetic field [18][19][20][21] , and also by a spatially-modulated spin texture in proximity to a conventional superconductor [22][23][24][25] . A n th -order topological superconductor in d dimensions hosts (d − n)-dimensional Majorana states 26 . ...
Lattice geometry continues providing exotic topological phases in condensed matter physics. Exciting recent examples are the higher-order topological phases, manifesting via localized lower-dimensional boundary states. Moreover, flat electronic bands with a non-trivial topology arise in various lattices and can hold a finite superfluid density, bounded by the Chern number C. Here we consider attractive interaction in the dice lattice that hosts flat bands with C = ± 2 and show that the induced superconducting state exhibits a second-order topological phase with mixed singlet-triplet pairing. The second-order nature of the topological superconducting phase is revealed by the zero-energy Majorana bound states at the lattice corners. Hence, the topology of the normal state dictates the nature of the Majorana localization. These findings suggest that flat bands with a higher Chern number provide feasible platforms for inducing higher-order topological superconductivity.
... Experimentally, the YSR states and/or the MZMs have been observed by growing magnetic impurities on top of an s-wave SC substrate [44][45][46][47][48][49][50][51][52][53][54]. Nevertheless, the creation of YSR states goes beyond 1D systems; in a twodimensional (2D) arrangement where noncollinear magnetic textures proximitized with an s-wave SC, unique effects like the emergence of 1D Majorana dispersive/flat edge modes emerges [37][38][39][55][56][57][58][59][60][61][62][63][64], setting them notably different from the typical observation of MZMs in onedimension. ...
We put forth a theoretical framework for engineering a two-dimensional (2D) second-order topological superconductor (SOTSC) by utilizing a heterostructure: incorporating noncollinear magnetic textures between an s-wave superconductor and a 2D quantum spin Hall insulator. It stabilizes the higher order topological superconducting phase, resulting in Majorana corner modes (MCMs) at four corners of a 2D domain. The calculated non-zero quadrupole moment characterizes the bulk topology. Subsequently, through a unitary transformation, an effective low-energy Hamiltonian reveals the effects of magnetic textures, resulting in an effective in-plane Zeeman field and spin-orbit coupling. This approach provides a qualitative depiction of the topological phase, substantiated by numerical validation within exact real-space model. Analytically calculated effective pairings in the bulk illuminate the microscopic behavior of the SOTSC. The comprehension of MCM emergence is aided by a low-energy edge theory, which is attributed to the interplay between effective pairings of (px + py )-type and (px + ipy )-type. Our extensive study paves the way for practically attaining the SOTSC phase by integrating noncollinear magnetic textures.
... Theoretical studies have explored the potential for creating a coupling between skyrmions and vortices in heterostructures comprising magnetic and superconducting layers. Both single skyrmion (Sk) and skyrmion lattice (SkL) (Mascot et al., 2021;Mohanta et al., 2021;Nakosai et al., 2013) have been found promising hosting MZMs. When the magnetic layer under specific conditions transitions into a skyrmion lattice phase, the boundaries between regions with different skyrmion winding numbers act as one-dimensional channels for the flow of supercurrent. ...
Skyrmionic devices exhibit energy-efficient and high-integration data storage and computing capabilities due to their small size, topological protection, and low drive current requirements. So, to realize these devices, an extensive study, from fundamental physics to practical applications, becomes essential. In this article, we present an exhaustive review of the advancements in understanding the fundamental physics behind magnetic skyrmions and the novel data storage and computing technologies based on them. We begin with an in-depth discussion of fundamental concepts such as topological protection, stability, statics and dynamics essential for understanding skyrmions, henceforth the foundation of skyrmion technologies. For the realization of CMOS-compatible skyrmion functional devices, the writing and reading of the skyrmions are crucial. We discuss the developments in different writing schemes such as STT, SOT, and VCMA. The reading of skyrmions is predominantly achieved via two mechanisms: the Magnetoresistive Tunnel Junction (MTJ) TMR effect and topological resistivity (THE). So, a thorough investigation into the Skyrmion Hall Effect, topological properties, and emergent fields is also provided, concluding the discussion on skyrmion reading developments. Based on the writing and reading schemes, we discuss the applications of the skyrmions in conventional logic, unconventional logic, memory applications, and neuromorphic computing in particular. Subsequently, we present an overview of the potential of skyrmion-hosting Majorana Zero Modes (MZMs) in the emerging Topological Quantum Computation and helicity-dependent skyrmion qubits.
... further the appearance of the charge-neutral MBS in the junction. Charge density profile in the presence of MBS shows a density-wave-like pattern, a feature that generically appears in all geometries including the nanowire and planar Josephson junction ones, and is a manifestation of oscillatory MBS wave functions [42,43]. We use these direct confirmations of MBS to identify topological superconducting phase in our geometries. ...
... These complicated geometries may come with new challenges, one of them clearly being the issue of fixing the direction of the in-plane magnetic field which is required to be along the metallic channel length. This particular problem can be overcome by placing underneath the Josephson junction a chiral magnetic texture such as a skyrmion crystal which can provide a gauge field and create a two-dimensional topological superconductivity in the entire 2DEG [42,66]. Nonetheless, these planar Josephson junctions provide a versatile two-dimensional platform, capable of manipulating MBS with more efficient control knobs [67][68][69][70][71], and it is possible to realize even more exotic states [72,73]. ...
We consider planar Josephson junctions, with dimensions as used in recent experiments, and show using numerical calculations that the junctions undergo topological superconducting transition, revealed by the appearance of zero-energy Majorana bound states at the ends of the non-superconducting channel of the junctions in the presence of an in-plane magnetic field and $\pi$ phase difference between the superconducting leads. Our main finding is that, under realistic parameter settings, the critical supercurrent undergoes a minimum and the ground state phase increases from zero toward $\pi$ at a critical field, without the junctions necessarily transitioning into a topological superconducting phase. Remarkably, the critical supercurrent minimum and a simultaneous sharp jump in the ground state phase appear in junctions that are undoubtedly in trivial superconducting phase. Our results provide updated insights for experimental detection of topological superconductivity in planar Josephson junctions using the supercurrent and phase signatures.
... Our effort invites additional experimental research in this direction, centered on examining topological Hall effects originating from nonskyrmionic chiral magnetic structures. It also invites additional theoretical work addressing the neutron response of the novel phases as in Ref. [65] for a square lattice, using this type of exotic states in geometries searching for Majoranas [66], and unveiling further novel frustrated states in multilayer geometries [67]. ...
Magnetic skyrmions are spin topological textures of potential interest in spintronics-related data storage and processing devices. Here, we show the emergence of unconventional skyrmions in a geometrically frustrated triangular lattice on an inversion-symmetry-breaking two-dimensional electron gas substrate. Starting with a classical double-exchange mechanism, this generic interface induces exotic skyrmionic and unique noncoplanar magnetic states not observed in the equivalent square lattice interface. We study the model by deriving an effective spin Hamiltonian. Large scale classical Monte Carlo simulations provide a quantitative evidence for the emergence of these exotic magnetic states. We found that these chiral magnetic states exhibit a substantial and nonzero topological Hall conductivity. As potential material candidates, we propose Cr/MoS2, Fe/MoS2, and Fe/WSe2 interfaces because they have the requisite underlying triangular lattice structures and large spin-orbit coupling.
... In recent times, the hunt for MZMs has taken an alternative route based on helical spin chain [21][22][23][24][25][26][27][28][29][30][31][32][33] or magnetic adatoms fabricated on the surface of a bulk s-wave superconductor [34][35][36][37][38][39][40][41]. Physically, the scattering between magnetic impurities and the quasiparticles in the superconductor fosters the formation of Yu-Shiba-Rusinov (YSR) states [42][43][44][45][46] inside the superconducting gap. ...
We theoretically explore the Floquet generation of Majorana end modes~(MEMs) (both regular $0$- and anomalous $\pi$-modes) implementing a periodic sinusoidal modulation in chemical potential in an experimentally feasible setup based on one-dimensional chain of magnetic impurity atoms having spin spiral configuration fabricated on the surface of most common bulk $s$-wave superconductor. We obtain a rich phase diagram in the parameter space, highlighting the possibility of generating multiple $0$-/$\pi$-MEMs localized at the end of the chain. We also study the real-time evolution of these emergent MEMs, especially when they start to appear in the time domain. These MEMs are topologically characterized by employing the dynamical winding number. We also discuss the possible experimental parameters in connection to our model. Our work paves the way to realize the Floquet MEMs in a magnet-superconductor heterostructure.
... Applications of quantum dot physics in quantum information science is a vast area of study [43][44][45][46][47][48][49]. More recently, extended topological junctions are receiving a concerted push with promising initial indicators of MBS physics [19,20,[50][51][52][53][54][55]. ...
We describe a scheme to exchange fermion parity between two pairs of Majorana bound states mediated by coupling with a centralized quantum dot. We specifically formulate such a scheme for Majorana bound states nucleated in the Josephson vortices formed in a four-fold crossroads junction of planar topological superconductors in the presence of a perpendicular magnetic field. This platform yields several advantages to the execution of our scheme as compared to similar ideas proposed in wire geometries, including control over the positions of the MBS and hence, a tunable coupling with the quantum dot. We show that moving the MBS along the junctions through voltage pulses can facilitate parity exchange via a two-step process, with intermediate projective measurements of the quantum dot charge. Thus, we formulate a way to achieve single qubit operations for MBS in extended Josephson junctions through projective measurements of quantum dot charge. We also discuss the physical viability of our scheme with a particular focus on changes in quantum dot energy levels as a measurable indicator of the success of the scheme.
... MZMs obey non-abelian exchange statistics. Because they are topologically protected from local perturbations and disorder, they are of value as possible qubits [4][5][6]. Signatures of MZMs are expected to develop in tunneling conductance experiments as zero bias peaks [7][8][9]. The simplest setup to realize Majoranas are quantum wires, where MZMs develop at the two edges [1,14]. ...
We employ a time-dependent real-space local density-of-states method to study the movement and fusion of Majorana zero modes in the one-dimensional interacting Kitaev model, based on the time evolution of many-body states. We analyze the dynamics and both fusion channels of Majoranas using time-dependent potentials, either creating walls or wells. For fast moving Majoranas, we unveil nonequilibrium signatures of the “strong-zero-mode” operator (quasiparity degeneracy in the full spectrum) and its breakdown in the presence of repulsive Coulomb interactions. Focusing on forming a full electron after fusion, we also discuss the upper and lower limits on the Majorana speed needed to reduce nonadiabatic effects and to avoid poisoning due to decoherence.
