Chiral Skyrmions Interacting with Chiral Flowers.

The chiral nature of active matter plays an important role in the dynamics of active matter interacting with chiral structures. Skyrmions are chiral objects, and their interactions with chiral nanostructures can lead to intriguing phenomena. Here, we explore the random-walk dynamics of a thermally activated chiral skyrmion interacting with a chiral flower-like obstacle in a ferromagnetic layer, which could create topology-dependent outcomes. It is a spontaneous mesoscopic order-from-disorder phenomenon driven by the thermal fluctuations and topological nature of skyrmions that exists only in ferromagnetic and ferrimagnetic systems. The interactions between the skyrmions and chiral flowers at finite temperatures can be utilized to control the skyrmion position and distribution without applying any external driving force or temperature gradient. The phenomenon that thermally activated skyrmions are dynamically coupled to chiral flowers may provide a new way to design topological sorting devices.

Universal Quantum Computation Based on Nanoscale Skyrmion Helicity Qubits in Frustrated Magnets.

We propose a skyrmion-based universal quantum computer. Skyrmions have the helicity degree of freedom in frustrated magnets, where twofold degenerated Bloch-type skyrmions are energetically favored by the magnetic dipole-dipole interaction. We construct a qubit based on them. A skyrmion must become a quantum-mechanical object when its size is of the order of nanometers. It is shown that the universal quantum computation is possible based on nanoscale skyrmions in a magnetic bilayer system. The one-qubit quantum gates are materialized by controlling the electric field and the spin current. The two-qubit gate is materialized with the use of the Ising-type exchange coupling. The merit of the present mechanism is that external magnetic field is not necessary. Our results may open a possible way toward universal quantum computation based on nanoscale topological spin textures.

Quantum Spin Hall States and Topological Phase Transition in Germanene.

We present the first experimental evidence of a topological phase transition in a monoelemental quantum spin Hall insulator. Particularly, we show that low-buckled epitaxial germanene is a quantum spin Hall insulator with a large bulk gap and robust metallic edges. Applying a critical perpendicular electric field closes the topological gap and makes germanene a Dirac semimetal. Increasing the electric field further results in the opening of a trivial gap and disappearance of the metallic edge states. This electric field-induced switching of the topological state and the sizable gap make germanene suitable for room-temperature topological field-effect transistors, which could revolutionize low-energy electronics.

Reversible Transformation between Isolated Skyrmions and Bimerons.

Skyrmions and bimerons are versatile topological spin textures that can be used as information bits for both classical and quantum computing. The transformation between isolated skyrmions and bimerons is an essential operation for computing architecture based on multiple different topological bits. Here we report the creation of isolated skyrmions and their subsequent transformation to bimerons by harnessing the electric current-induced Oersted field and temperature-induced perpendicular magnetic anisotropy variation. The transformation between skyrmions and bimerons is reversible, which is controlled by the current amplitude and scanning direction. Both skyrmions and bimerons can be created in the same system through the skyrmion-bimeron transformation and magnetization switching. Deformed skyrmion bubbles and chiral labyrinth domains are found as nontrivial intermediate transition states. Our results may provide a unique way for building advanced information-processing devices using different types of topological spin textures in the same system.

Current-Induced Dynamics and Chaos of Antiferromagnetic Bimerons.

A magnetic bimeron is a topologically nontrivial spin texture carrying an integer topological charge, which can be regarded as the counterpart of the skyrmion in easy-plane magnets. The controllable creation and manipulation of bimerons are crucial for practical applications based on topological spin textures. Here, we analytically and numerically study the dynamics of an antiferromagnetic bimeron driven by a spin current. Numerical simulations demonstrate that the spin current can create an isolated bimeron in the antiferromagnetic thin film via the dampinglike spin torque. The spin current can also effectively drive the antiferromagnetic bimeron without a transverse drift. The steady motion of an antiferromagnetic bimeron is analytically derived and is in good agreement with the simulation results. Also, we find that the alternating-current-induced motion of the antiferromagnetic bimeron can be described by the Duffing equation due to the presence of the nonlinear boundary-induced force. The associated chaotic behavior of the bimeron is analyzed in terms of the Lyapunov exponents. Our results demonstrate the inertial dynamics of an antiferromagnetic bimeron, and may provide useful guidelines for building future bimeron-based spintronic devices.

Electric Field-Induced Creation and Directional Motion of Domain Walls and Skyrmion Bubbles.

Magnetization dynamics driven by an electric field could provide long-term benefits to information technologies because of its ultralow power consumption. Meanwhile, the Dzyaloshinskii-Moriya interaction in interfacially asymmetric multilayers consisting of ferromagnetic and heavy-metal layers can stabilize topological spin textures, such as chiral domain walls, skyrmions, and skyrmion bubbles. These topological spin textures can be controlled by an electric field and hold promise for building advanced spintronic devices. Here, we present an experimental and numerical study on the electric field-induced creation and directional motion of topological spin textures in magnetic multilayer films and racetracks with thickness gradient and interfacial Dzyaloshinskii-Moriya interaction at room temperature. We find that the electric field-induced directional motion of chiral domain wall is accompanied by the creation of skyrmion bubbles at certain conditions. We also demonstrate that the electric field variation can induce motion of skyrmion bubbles. Our findings may provide opportunities for developing skyrmion-based devices with ultralow power consumption.

Topological Switch between Second-Order Topological Insulators and Topological Crystalline Insulators.

We investigate a topological switch between second-order topological insulators (SOTIs) and topological crystalline insulators (TCIs). Both the SOTI and the TCI are protected by the mirror and inversion symmetries, for which we define the bulk topological numbers of the same type. When an in-plane magnetic field is introduced parallel to one of the helical edges, the system becomes a TCI. The conductance along the edge is 1 in the unit of the conductance quantum e^{2}/h. When it becomes orthogonal to a diagonal line, two topological corner states emerge on its vertices, and the system becomes a SOTI. This may be used as a basis of a topological circuit-changing switch. Alternatively, the device may be used as a sensor to measure local magnetization on a sample surface with a resolution of 10 nm.

Higher-Order Topological Insulators and Semimetals on the Breathing Kagome and Pyrochlore Lattices.

A second-order topological insulator in d dimensions is an insulator which has no d-1 dimensional topological boundary states but has d-2 dimensional topological boundary states. It is an extended notion of the conventional topological insulator. Higher-order topological insulators have been investigated in square and cubic lattices. In this Letter, we generalize them to breathing kagome and pyrochlore lattices. First, we construct a second-order topological insulator on the breathing Kagome lattice. Three topological boundary states emerge at the corner of the triangle, realizing a 1/3 fractional charge at each corner. Second, we construct a third-order topological insulator on the breathing pyrochlore lattice. Four topological boundary states emerge at the corners of the tetrahedron with a 1/4 fractional charge at each corner. These higher-order topological insulators are characterized by the quantized polarization, which constitutes the bulk topological index. Finally, we study a second-order topological semimetal by stacking the breathing kagome lattice.

Loop-Nodal and Point-Nodal Semimetals in Three-Dimensional Honeycomb Lattices.

A honeycomb structure has a natural extension to three dimensions. Simple examples are hyperhoneycomb and stripy-honeycomb lattices, which are realized in ß-Li_{2}IrO_{3} and γ-Li_{2}IrO_{3}, respectively. We propose a wide class of three-dimensional (3D) honeycomb lattices which are loop-nodal semimetals. Their edge states have intriguing properties similar to the two-dimensional honeycomb lattice in spite of a dimensional difference. Partial flat bands emerge at the zigzag or bearded edge of the 3D honeycomb lattice, whose boundary is given by the Fermi loop in the bulk spectrum. On the other hand, perfect flat bands emerge in the zigzag-bearded edge or when the anisotropy is large. The loop-nodal structure is destroyed once staggered potential or antiferromagnetic order is introduced. All these 3D honeycomb lattices become strong topological insulators with the inclusion of the spin-orbit interaction (SOI). Furthermore, point-nodal semimetals may be realized in the presence of both antiferromagnetic order and the SOI. We construct the effective four-band theory with the SOI to understand the physics near the Fermi level, based upon which the density of states and the dc conductivity are calculated.

Antiferromagnetic topological superconductor and electrically controllable Majorana fermions.

We investigate the realization of a topological superconductor in a generic bucked honeycomb system equipped with four types of mass-generating terms, where the superconductor gap is introduced by attaching the honeycomb system to an s-wave superconductor. Constructing the topological phase diagram, we show that Majorana modes are formed in the phase boundary. In particular, we analyze the honeycomb system with antiferromagnetic order in the presence of perpendicular electric field E(z). It becomes topological for |E(z)|>E(z)(cr) and trivial for |E(z)|

All-magnetic control of skyrmions in nanowires by a spin wave.

Magnetic skyrmions are topologically protected nanoscale objects, which are promising building blocks for novel magnetic and spintronic devices. Here, we investigate the dynamics of a skyrmion driven by a spin wave in a magnetic nanowire. It is found that (i) the skyrmion is first accelerated and then decelerated exponentially; (ii) it can turn L-corners with both right and left turns; and (iii) it always turns left (right) when the skyrmion number is positive (negative) in the T- and Y-junctions. Our results will be the basis of skyrmionic devices driven by a spin wave.

Photoinduced topological phase transition and a single Dirac-cone state in silicene.

Silicene (a monolayer of silicon atoms) is a two-dimensional topological insulator (TI) that undergoes a topological phase transition to a band insulator under external electric field E(z). We investigate a photoinduced topological phase transition from a TI to another TI by changing its topological class by irradiating circular polarized light at fixed E(z). The band structure is modified by photon dressing with a new dispersion, where the topological property is altered. By increasing the intensity of light at E(z)=0, a photoinduced quantum Hall insulator is realized. Its edge modes are anisotropic chiral, in which the velocities of up and down spins are different. At E(z)>E(cr) with a certain critical field E(cr), a photoinduced spin-polarized quantum Hall insulator emerges. This is a new state of matter, possessing one Chern number and one-half spin-Chern numbers. We newly discover a single Dirac-cone state along a phase boundary. A distinctive hallmark of the state is that one of the two Dirac valleys is closed and the other open.

Valley-polarized metals and quantum anomalous Hall effect in silicene.

Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, which shares almost every remarkable property with graphene. The low-energy structure of silicene is described by Dirac electrons with relatively large spin-orbit interactions due to its buckled structure. The key observation is that the band structure is controllable by applying electric field to silicene. We explore the phase diagram of silicene together with exchange field M and by applying electric field E(z). A quantum anomalous Hall (QAH) insulator, valley polarized metal (VPM), marginal valley polarized metal (M-VPM), quantum spin Hall insulator, and band insulator appear. They are characterized by the Chern numbers and/or by the edge modes of a nanoribbon. It is intriguing that electrons have been moved from a conduction band at the K point to a valence band at the K' point for E(z) > 0 in the VPM. We find in the QAH phase that almost flat gapless edge modes emerge and that spins form a momentum-space Skyrmion to yield the Chern number. It is remarkable that a topological quantum phase transition can be induced simply by changing electric field in a single silicene sheet.

Complex structure of triangular graphene: electronic, magnetic and electromechanical properties.

We have investigated electronic and magnetic properties of graphene nanodisks (nanosize triangular graphene) as well as electromechanical properties of graphene nanojunctions. Nanodisks are nanomagnets made of graphene, which are robust against perturbation such as impurities and lattice defects, where the ferromagnetic order is assured by Lieb's theorem. We can generate a spin current by spin filter, and manipulate it by a spin valve, a spin switch and other spintronic devices made of graphene nanodisks. We have analyzed nanodisk arrays, which have multi-degenerate perfect flat bands and are ferromagnet. By connecting two triangular graphene corners, we propose a nanomechanical switch and rotator, which can detect a tiny angle rotation by measuring currents between the two corners. By making use of the strain induced Peierls transition of zigzag nanoribbons, we also propose a nanomechanical stretch sensor, in which the conductance can be switched off by a nanometer scale stretching.

Variational quantum support vector machine based on [Formula: see text] matrix expansion and variational universal-quantum-state generator.

We analyze a binary classification problem by using a support vector machine based on variational quantum-circuit model. We propose to solve a linear equation of the support vector machine by using a [Formula: see text] matrix expansion. In addition, it is shown that an arbitrary quantum state is prepared by optimizing a universal quantum circuit representing an arbitrary [Formula: see text] based on the steepest descent method. It may be a quantum generalization of Field-Programmable-Gate Array (FPGA).

Transcription and logic operations of magnetic skyrmions in bilayer cross structures.

Magnetic skyrmions are potential building blocks for future information storage and computing devices. Here, we computationally study the skyrmion dynamics in a cross structure made of two ferromagnetic nanotracks. We show that by controlling the skyrmion motion in the cross structure using spin currents, it is possible to realize the transcription of skyrmion at the intersection of the cross structure at certain conditions. Based on the transcription of skyrmion, we computationally demonstrate the AND, OR and NOT logical gates using the cross structures with modified geometries and appropriate magnetic parameters. Our results may provide guidelines to design future three-dimensional spintronics devices based on magnetic skyrmions.

Giant Skyrmions stabilized by dipole-dipole interactions in thin ferromagnetic films.

Motivated by a recent magnetization reversal experiment on a TbFeCo thin film, we study a topological excitation in the anisotropic nonlinear sigma model together with the Zeeman and magnetic dipole-dipole interactions. Dipole-dipole interactions turn a ferromagnet into a frustrated spin system, which allows a nontrivial spin texture such as a giant Skyrmion. We derive an analytic formula for the Skyrmion radius. The radius is controllable by the external magnetic field. It is intriguing that a Skyrmion may have already been observed as a magnetic domain. A salient feature is that a single Skyrmion can be created or destroyed experimentally. An analysis is made also on Skyrmions in chiral magnets.

Skyrmion-electronics: writing, deleting, reading and processing magnetic skyrmions toward spintronic applications.

The field of magnetic skyrmions has been actively investigated across a wide range of topics during the last decades. In this topical review, we mainly review and discuss key results and findings in skyrmion research since the first experimental observation of magnetic skyrmions in 2009. We particularly focus on the theoretical, computational and experimental findings and advances that are directly relevant to the spintronic applications based on magnetic skyrmions, i.e. their writing, deleting, reading and processing driven by magnetic field, electric current and thermal energy. We then review several potential applications including information storage, logic computing gates and non-conventional devices such as neuromorphic computing devices. Finally, we discuss possible future research directions on magnetic skyrmions, which also cover rich topics on other topological textures such as antiskyrmions and bimerons in antiferromagnets and frustrated magnets.

Current-Induced Helicity Reversal of a Single Skyrmionic Bubble Chain in a Nanostructured Frustrated Magnet.

Helicity indicates the in-plane magnetic-moment swirling direction of a skyrmionic configuration. The ability to reverse the helicity of a skyrmionic bubble via purely electrical means has been predicted in frustrated magnetic systems; however, it has been challenging to observe this experimentally. The current-driven helicity reversal of the skyrmionic bubble in a nanostructured frustrated Fe3 Sn2 magnet is experimentally demonstrated. The critical current density required to trigger the helicity reversal is 109 -1010 A m-2 , with a corresponding pulse-width varying from 1 µs to 100 ns. Computational simulations reveal that both the pinning effect and dipole-dipole interaction play a crucial role in the helicity reversal process.