Higher-order topological solitonic insulators

Abstract

Pursuing topological phase and matter in a variety of systems is one central issue in current physical sciences and engineering. Motivated by the recent experimental observation of corner states in acoustic and photonic structures, we theoretically study the dipolar-coupled gyration motion of magnetic solitons on the twodimensional breathing kagome lattice. We calculate the phase diagram and predict both the Tamm-Shockley edge modes and the second-order corner states when the ratio between alternate lattice constants is greater than a critical value. We show that the emerging corner states are topologically robust against both structure defects and moderate disorders. Micromagnetic simulations are implemented to verify the theoretical predictions with an excellent agreement. Our results pave the way for investigating higher-order topological insulators based on magnetic solitons. arXiv:1909.11511v1 [cond-mat.mes-hall]

Disorder-induced quantum phase transitions in three-dimensional second-order topological insulators

“…When the surface states of a 3DFOTI are gapped, the intersection of two surfaces of different topological classes, i.e., a hinge, has topologically nontrivial chiral hinge states, leading to a so-called 3D second-order topological insulator (3DSOTI). The well-accepted paradigm is that a d-dimensional material can be a (d − n)th-order topological insulator with 1 n d so that all states in submanifolds, whose dimensions are greater than (d − n + 1), are gapped whereas states are gapless on, at least, one submanifold of dimension (d − n) [19][20][21][22][23][24][25][26][27].…”

Second-order topological solitonic insulator in a breathing square lattice of magnetic vortices

“…Firstly, the spring constant K can be obtained from the relation K = ω 0 |G|, with ω 0 the gyrotropic frequency of a single vortex. For Permalloy (Py) [64,65] nanodisk of vortex state with thickness w = 10 nm and radius r = 50 nm, the gyrotropic frequency ω 0 = 2π × 0.939 GHz, gyroscopic constant G = −3.0725 × 10 −13 J s rad −1 m −2 (Q = 1/2) [53], we have K = 1.8128 × 10 −3 J m −2 . Secondly, the analytical expressions of I and I ⊥ on the distance d between vortices have been obtained in a simplified two-nanodisk system [53].…”

Unsupervised Machine Learning to Distill Structural-Property Insights from 4D-STEM

“…With extracted patterns from unsupervised learning algorithms, follow-up experiment designs can be conducted for deeper investigation of the system under study.As an example, we show how manifold learning on a simulated 4D-STEM dataset for single-layer graphene automatically reveals real-space neighbor effects on electron deflection patterns recorded on the pixelated detector, that relate to both individual atomic sites and sublattice structures. Additional examples and detailed study on experimental datasets can be found in [7]. In layman's terms, for straightforward visualization purpose, manifold learning will project the whole diffraction patterns into a 2D space based on pair-wise similarity, with a one-to-one mapping between the points in the 2D manifold plane and the diffraction patterns.…”

“…Much information in 4D-STEM is currently unexploited. To address this fundamental issue, recently developed unsupervised learning algorithms based on graph-analytics and manifold learning [6,7] will allow subtle details, such local symmetry or defects, to be automatically identified, without any prior bias regarding the material structure and instrumental modality. With extracted patterns from unsupervised learning algorithms, follow-up experiment designs can be conducted for deeper investigation of the system under study.…”