Engineering Second‐Order Corner States in 2D Multiferroics

Abstract

Z topological phase is destroyed because the Zeeman field breaks the time-reversal symmetry. [29] Therefore, an outstanding question arises as to whether and how the (d − 2)-dimensional boundaries can be effectively tuned without magnetism, especially for 2D SOTIs in experimentally feasible candidates.In recent years, ferroelectric and ferroelastic in 2D materials have received extensive attentions. [30,31] Ferroelastic and/ or ferroelectric transitions enable controllable switches for lots of exciting physical properties, which holds great potential for applications in piezoelectric sensors, mechanical switches, and nonvolatile memory devices. [32] A material has ferroelasticity when it refers to the spontaneous structural polarization and strain-induced transition between the identical stable phases, and has ferroelectricity with switchable electrical polarization through the application of the external electric field. [33,34] Recently, the research on ferroelasticity and ferroelectricity started to reach out to 2D systems with the material candidates been theoretically proposed in LiMgBi, phosphorene, transition metal dichalcogenides, boron pentaphosphide, and so on, but only with conventional TIs characterized by (d-1)-dimenional boundary states. [35][36][37][38][39][40][41][42][43][44][45][46] Although many efforts have been carried out, so far, the 2D ferroelasticity and ferroelectricity remain poorly understood. [47] One major issue is the combination of 2D ferroelasticity and ferroelectricity, or even with both of them, with SOTIs, which would open bright avenues in engineering the nontrivial corner states and in exploiting universal arguments of 2D multiferroics in topological spintronic device applications.In the present work, we identify the manipulation of secondorder corner states in 2D multiferroics of SbAs and BP 5 monolayers. Unlike conventional TIs, gapped edge bands emerge on their typical 1D edges. However, the zero-dimensional (0D) corner states appear as illustrated by performing the calculations of energy discrete spectra in finite-size nanoflakes. We show that the charge spatial distribution is well located at the corners of nanoflakes for both SbAs and BP 5 when they possess the in-plane polarization, revealing the hallmark of 2D SOTIs with ferroelectricity. Surprisingly, under a ferroelastic switching from the initial to final states, the spatial distribution of the corner states are effectively rotated by 90 o . Moreover, by using nudged elastic band (NEB) method, the energy pathway for both the ferroelectric and ferroelastic switching are investigated with the results reveal that the signal of switching is strong. The SOTIs engineered by ferroelasticity

3D Carbon Allotropes: Topological Quantum Materials with Obstructed Atomic Insulating Phases, Multiple Bulk‐Boundary Correspondences, and Real Topology

“…Note that the study of topological matters has recently revolutionized with the finding of second-order topological phases. [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59] Second-order topological phases in 3D induce unconventional bulk-boundary correspondence because they exhibit boundary states in two dimensions lower than the 3D bulk, as opposed to the previous first-order topological phases, which contained topological boundary states in one dimension lower than the 3D bulk. The second-order topological phases in 3D are manifested in the hinge modes located at the hinges of the sample materials with a tube geometry.…”

Topology-Engineered Orbital Hall Effect in Two-Dimensional Ferromagnets

“…Band inversions occur in the + K and − K valleys sequentially, revealing TPTs with increasing ϵ 2 . For ϵ 2 = 3.2 eV, a floating edge state emerges in the insulating gap, which is usually considered as a key signature of the SOTI. − To identify its band topology, a triangular nanoflake with C 3 rotational symmetry is constructed and the energy spectrum is presented in Figure (c). Obviously, around the Fermi level, one observes three states (red dots) with their spatial distribution well localized at the three corners of the nanoflake, verifying the SOTI phase.…”

Spin polarization in quantum point contact based on wurtzite topological quantum well

“…18 For example, the spatial distribution of nontrivial corner states in second-order TI SbAs and BP 5 can be sufficiently engineered by ferroelasticity and ferroelectricity. 17 Manipulating the spin polarization of edge states, which is crucial for spin transistors, relies intrinsically on the Zeeman effect, exchange interaction or spin–orbit coupling (SOC). In particular, the combination of band topology and SOC is able to support the intriguing transport properties in QPC devices, 19–21 where the topological edge states can interact in a one-dimensional (1D) channel.…”

“…3–7 The 2D TI hosts dissipationless metallic edge states protected by the time-reversal symmetry of a bulk insulator. Based on this distinctive property, quantum transport through edge states has been widely studied in different platforms, such as graphene, 8–10 superconductors, 11,12 ferromagnets, 13,14 and ferroelectric 15–17 and antiferromagnetic materials. 18 For example, the spatial distribution of nontrivial corner states in second-order TI SbAs and BP 5 can be sufficiently engineered by ferroelasticity and ferroelectricity.…”