Kekulé Lattice in Graphdiyne: Coexistence of Phononic and Electronic Second-Order Topological Insulator

Real Topological Phonons in 3D Carbon Allotropes

There has been a significant focus on real topological systems that enjoy space-time inversion symmetry and lack spin-orbit coupling. While the theoretical classification of the real topology has been established, more progress has yet to be made in the materials realization of real topological phononic states in 3D. To address this crucial issue, high-throughput computing is performed to inspect the real topology in the phonon spectrums of the 3D carbon allotropes. Among 1661 carbon allotropes listed in the Samara Carbon Allotrope Database (SACADA), 79 candidates host a phononic real Chern insulating (PRCI) state, 2 candidates host a phononic real nodal line (PRNL) state, 12 candidates host a phononic real Dirac point (PRDP) state, and 10 candidates host a phononic real triple-point pair (PRTPP) state. The PRCI, PRNL, PRTPP, and PRDP states of 27-SG. 166-pcu-h, 1081-SG. 194-42T13-CA, 52-SG. 141-gis, and 132-SG. 191-3,4T157 are exhibited as illustrative examples, and the second-order phononic hinge modes are explored. This study broadens the understanding of 3D topological phonons and expands the material candidates with phononic hinge modes and phononic real topology.

Coupled Electronic and Magnonic Topological States in Two-Dimensional Ferromagnets

Magnetic materials offer a fertile playground for fundamental physics discovery, with not only electronic but also magnonic topological states intensively explored. However, one natural material with both electronic and magnonic nontrivial topologies is still unknown. Here, we demonstrate the coexistence of first-order topological magnon insulators (TMIs) and electronic second-order topological insulators (SOTIs) in 2D honeycomb ferromagnets, giving rise to the nontrivial corner states being connected by the charge-free magnonic edge states. We show that, with C 3 symmetry, the phase factor ± ϕ caused by the next nearest-neighbor Dzyaloshinskii-Moriya interaction breaks the pseudo-spin time-reversal symmetry T , which leads to the split of magnon bands, i.e., the emergence of TMIs with a nonzero Chern number of C = - 1 , in experimentally feasible candidates of MoI3, CrSiTe3, and CrGeTe3 monolayers. Moreover, protected by the C 3 symmetry, the electronic SOTIs characterized by nontrivial corner states are obtained, bridging the topological aspect of fermions and bosons with a high possibility of innovative applications in spintronics devices.

Layer-coupled corner states in two-dimensional topological multiferroics

The structural diversity and controllability in two-dimensional (2D) materials offers an intriguing platform for exploring a wide range of topological phenomena. The layer degree of freedom, as a novel technique for material manipulation, requires further investigation regarding its association with topological states. Here, using first-principles calculations and a tight-binding model, we propose a novel mechanism that couples the second-order topological corner states with the layer degree of freedom. By analyzing the edge states, topological indices, and spectra of nanoflakes, we identify ferromagnetic H'-Co2XF2 (X = C, N) as 2D second-order topological insulators with intrinsic ferroelectricity. Moreover, the topological corner states strongly couple with the layer degree of freedom, and, remarkably, ferroelectricity provides a nonvolatile handle to manipulate the layer-polarized corner states. These findings open an avenue for the manipulation of second-order topological states and establish a bridge between ferroelectricity and nontrivial topology.

Higher-order topological phases in crystalline and non-crystalline systems: a review

In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases due to the higher-order bulk-boundary correspondence. In this review, we summarize current research progress on higher-order topological phases in both crystalline and non-crystalline systems. We firstly introduce prototypical models of higher-order topological phases in crystals and their topological characterizations. We then discuss effects of quenched disorder on higher-order topology and demonstrate disorder-induced higher-order topological insulators. We also review the theoretical studies on higher-order topological insulators in amorphous systems without any crystalline symmetry and higher-order topological phases in non-periodic lattices including quasicrystals, hyperbolic lattices, and fractals, which have no crystalline counterparts. We conclude the review by a summary of experimental realizations of higher-order topological phases and discussions on potential directions for future study.

Exploring the Potential of Chemically Modified Graphyne Nanodots as an Efficient Adsorbent and Sensitive Detector of Environmental Contaminants: A First Principles Study

In this study, we investigated the reactivity of γ-graphyne (Gp) and its derivatives, Gp-CH3, Gp-COOH, Gp-CN, Gp-NO2, and Gp-SOH, for the removal of toxic heavy metal ions (Hg+ 2, Pb+ 2, and Cd+ 2) from wastewater. From the analysis of the optimized structures, it was observed that all the compounds exhibited planar geometry. The dihedral angles (C9-C2-C1-C6 and C9-C2-C1-C6) were approximately 180.00°, indicating planarity in all molecular arrangements. To understand the electronic properties of the compounds, the HOMO (EH) and LUMO (EL) energies were calculated, and their energy gaps (Eg) were determined. The EH and EL values ranged between - 6.502 and - 8.192 eV and - 1.864 and - 3.773 eV, respectively, for all the compounds. Comparing the EH values, Gp-NO2 exhibited the most stable HOMO, while Gp-CH3 had the least stable structure. In terms of EL values, Gp-NO2 had the most stable LUMO, while Gp-CH3 was the least stable. The Eg values followed the order: Gp-NO2 < Gp-COOH < Gp-CN < Gp-SOH < Gp-CH3 < Gp, with Gp-NO2 (4.41 eV) having the smallest energy gap. The density of states (DOS) analysis showed that the shape and functional group modifications affected the energy levels. Functionalization with electron-withdrawing (CN, NO2, COOH, SOH) or electron-donating (CH3) groups reduced the energy gap. To specifically target the removal of heavy metal ions, the Gp-NO2 ligand was selected for its high binding energy. Complexes of Gp-NO2-Cd, Gp-NO2-Hg, and Gp-NO2-Pb were optimized, and their properties were analyzed. The complexes were found to be planar, with metal-ligand bond distances within the range of 2.092→3.442 Å. The Gp-NO2-Pb complex exhibited the shortest bond length, indicating a stronger interaction due to the smaller size of Pb+ 2. The computed adsorption energy values (Eads) indicated the stability of the complexes, with values ranging from - 0.035 to -4.199 eV. Non-covalent interaction (NCI) analysis was employed to investigate intermolecular interactions in Gp-NO2 complexes. The analysis revealed distinct patterns of attractive and repulsive interactions, providing valuable insights into the binding preferences and steric effects of heavy metals.

Graphyne and graphdiyne nanoribbons: from their structures and properties to potential applications

Graphyne (GY) and graphdiyne (GDY) have properties including unique sp- and sp2-hybrid carbon atomic structures, natural non-zero band gaps, and highly conjugated π electrons. GY and GDY have good application prospects in many fields, including catalysis, solar cells, sensors, and modulators. Under the influence of the boundary effect and quantum size effect, quasi-one-dimensional graphyne nanoribbons (GYNRs) and graphdiyne nanoribbons (GDYNRs) show novel physical properties. The various structures available give GYNRs and GDYNRs greater band structure and electronic properties, and their excellent physical and chemical properties differ from those of two-dimensional GY and GDY. However, the development of GYNRs and GDYNRs still faces problems, including issues with accurate synthesis, advanced structural characterization, the structure-performance correlation of materials, and potential applications. In this review, the structures and physical properties of quasi-one-dimensional GYNRs and GDYNRs are reviewed, their advantages and disadvantages are summarized, and their potential applications are highlighted. This review provides a meaningful basis and research foundation for the design and development of high-performance materials and devices based on GYNRs and GDYNRs in the field of energy.

Robust Second-Order Topological Insulators with Giant Valley Polarization in Two-Dimensional Honeycomb Ferromagnets

Magnetic topological states have attracted great attention that provide exciting platforms for exploring prominent physical phenomena and applications of topological spintronics. Here, using a tight-binding model and first-principles calculations, we put forward that, in contrast to previously reported magnetic second-order topological insulators (SOTIs), robust SOTIs can emerge in two-dimensional ferromagnets regardless of magnetization directions. Remarkably, we identify intrinsic ferromagnetic 2H-RuCl₂ and Janus VSSe monolayers as experimentally feasible candidates of predicted robust SOTIs with the emergence of nontrivial corner states along different magnetization directions. Moreover, under out-of-plane magnetization, we unexpectedly point out that the valley polarization of SOTIs can be huge and much larger than that of the known ferrovalley materials, opening up a technological avenue to bridge the valleytronics and higher-order topology with high possibility of innovative applications in topological spintronics and valleytronics.

Intrinsic Second-Order Topological Insulator in Two-Dimensional Covalent Organic Frameworks

As an intriguing topological phase, higher-order topological insulators have attracted tremendous attention, but the candidate materials are limited in artificial and inorganic systems. In this work, we propose a universal approach to search for two-dimensional (2D) second-order topological insulators (SOTIs) in covalent organic frameworks (COFs) with C₃ symmetric cores. The underlying mechanism is illustrated through tight-binding calculations in a star lattice, showing the 2D SOTI in an overlooked energy window between two Kagome-bands with four types of nontrivial band structures. The emergence of the unique topological edge and corner states can be understood from the Su-Schrieffer-Heeger model. Furthermore, using the frontier orbital of the monomer building block as an indicator, the 2D SOTI is directly confirmed in three realistic COFs by first-principles calculations. Our results not only extend the concept of organic topological insulators from first-order to second-order but also demonstrate the universal existence of intrinsic higher-order topology in 2D COFs.