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Register a new userRealizing Corner States in Artificial Crystals Based on Topological Spin Textures
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The recent discovery of higher-order topological insulators (HOTIs) has significantly extended our understanding of topological phases of matter. Here, we predict that second-order corner states can emerge in the dipolar-coupled dynamics of topological spin textures in two-dimensional artificial crystals. Taking a breathing honeycomb lattice of magnetic vortices as an example, we derive the full phase diagram of collective vortex gyrations and identify three types of corner states that have not been discovered before. We show that the topological zero-energy corner modes are protected by a generalized chiral symmetry in the sexpartite lattice, leading to particular robustness against disorder and defects, although the conventional chiral symmetry of bipartite lattices is absent. We propose the use of the quantized $mathbb{Z}_{6}$ Berry phase to characterize the nontrivial topology. Interestingly, we observe corner states at either obtuse-angled or acute-angled corners, depending on whether the lattice boundary has an armchair or zigzag shape. Full micromagnetic simulations confirm the theoretical predictions with good agreement. Experimentally, we suggest using the recently developed ultrafast Lorentz microscopy technique [M{o}ller emph{et al}.,{arXiv:1907.04608}] to detect the topological corner states by tracking the nanometer-scale vortex orbits in a time-resolved manner. Our findings open up a promising route for realizing higher-order topologically protected corner states in magnetic systems and finally achieving topological spintronic memory and computing.
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Macroscopic two-dimensional sonic crystals with inversion symmetry are studied to reveal higher-order topological physics in classical wave systems. By tuning a single geometry parameter, the band topology of the bulk and the edges can be controlled simultaneously. The bulk band gap forms an acoustic analog of topological crystalline insulators with edge states which are gapped due to symmetry reduction on the edges. In the presence of mirror symmetry, the band topology of the edge states can be characterized by the Zak phase, illustrating the band topology in a hierarchy of dimensions, which is at the heart of higher-order topology. Moreover, the edge band gap can be closed without closing the bulk band gap, revealing an independent topological transition on the edges. The rich topological transitions in both bulk and edges can be well-described by the symmetry eigenvalues at the high-symmetry points in the bulk and surface Brillouin zones. We further analyze the higher-order topology in the shrunken sonic crystals where slightly different physics but richer corner and edge phenomena are revealed. In these systems, the rich, multidimensional topological transitions can be exploited for topological transfer among zero-, one- and two- dimensional acoustic modes by controlling the geometry.
We consider a system of weakly coupled Rashba nanowires in the strong spin-orbit interaction (SOI) regime. The nanowires are arranged into two tunnel-coupled layers proximitized by a top and bottom superconductor such that the superconducting phase difference between them is $pi$. We show that in such a system strong electron-electron interactions can stabilize a helical topological superconducting phase hosting Kramers partners of $mathbb{Z}_{2m}$ parafermion edge modes, where $m$ is an odd integer determined by the position of the chemical potential. Furthermore, upon turning on a weak in-plane magnetic field, the system is driven into a second-order topological superconducting phase hosting zero-energy $mathbb{Z}_{2m}$ parafermion bound states localized at two opposite corners of a rectangular sample. As a special case, zero-energy Majorana corner states emerge in the non-interacting limit $m=1$, where the chemical potential is tuned to the SOI energy of the single nanowires.
Magnonics is gaining momentum as an emerging technology for information processing. The wave character and Joule heating-free propagation of spin-waves hold promises for highly efficient analog computing platforms, based on integrated magnonic circuits. Miniaturization is a key issue but, so far, only few examples of manipulation of spin-waves in nanostructures have been demonstrated, due to the difficulty of tailoring the nanoscopic magnetic properties with conventional fabrication techniques. In this Letter, we demonstrate an unprecedented degree of control in the manipulation of spin-waves at the nanoscale by using patterned reconfigurable spin-textures. By space and time-resolved scanning transmission X-ray microscopy imaging, we provide direct evidence for the channeling and steering of propagating spin-waves in arbitrarily shaped nanomagnonic waveguides based on patterned domain walls, with no need for external magnetic fields or currents. Furthermore, we demonstrate a prototypic nanomagnonic circuit based on two converging waveguides, allowing for the tunable spatial superposition and interaction of confined spin-waves modes.
Recently, a new type of second-order topological insulator has been theoretically proposed by introducing an in-plane Zeeman field into the Kane-Mele model in the two-dimensional honeycomb lattice. A pair of topological corner states arise at the corners with obtuse angles of an isolated diamond-shaped flake. To probe the corner states, we study their transport properties by attaching two leads to the system. Dressed by incoming electrons, the dynamic corner state is very different from its static counterpart. Resonant tunneling through the dressed corner state can occur by tuning the in-plane Zeeman field. At the resonance, the pair of spatially well separated and highly localized corner states can form a dimer state, whose wavefunction extends almost the entire bulk of the diamond-shaped flake. By varying the Zeeman field strength, multiple resonant tunneling events are mediated by the same dimer state. This re-entrance effect can be understood by a simple model. These findings extend our understanding of dynamic aspects of the second-order topological corner states.
Theory of interference-induced quantum corrections to conductivity is developed for two dimensional systems with chiral spin textures including skyrmions. The effect of exchange interaction between electrons and spin textures on weak localization of electronic waves is studied. The spin dephasing rates are calculated as functions of the spin texture size. The anomalous magnetoresistance is shown to be governed by the size and magnetization spatial distribution of the spin textures. The effect of average magnetization-induced spin splitting on weak localization is analyzed. The sign-alternating weak-antilocalization magnetoresistance is demonstrated for skyrmion crystals. We argue that analysis of the low-field magnetoresistance serves as an independent tool for an experimental detection of chiral spin textures and, in particular, skyrmions.
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