Layer-Number-Dependent Magnetism and Anomalous Hall Effect in van der Waals Ferromagnet Fe5GeTe2.

Realization of ferromagnetism in the two-dimensional (2D) van der Waals (vdW) crystals opens up a vital route to understand the magnetic ordering in the 2D limit and to design novel spintronics. Here, we report enriched layer-number-dependent magnetotransport properties in the vdW ferromagnet Fe5GeTe2. By studying the magnetoresistance and anomalous Hall effect (AHE) in nanoflakes with thicknesses down to monolayer, we demonstrate that while the bulk crystals exhibit soft ferromagnetism with an in-plane magnetic anisotropy, hard ferromagnetism develops upon thinning, and a perpendicular easy-axis anisotropy is realized in bilayer flakes, which is accompanied by a pronounced enhancement of AHE because of extrinsic mechanisms. For the monolayer flakes, the hard ferromagnetism is replaced by spin-glass-like behavior, in accordance with the localization effect in the 2D limit. Our results highlight the thickness-based tunability of the magnetotransport properties in the atomically thin vdW magnets that promises engineering of high-performance spintronic devices.

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.

Unveiling Weyl-related optical responses in semiconducting tellurium by mid-infrared circular photogalvanic effect.

Elemental tellurium, conventionally recognized as a narrow bandgap semiconductor, has recently aroused research interests for exploiting Weyl physics. Chirality is a unique feature of Weyl cones and can support helicity-dependent photocurrent generation, known as circular photogalvanic effect. Here, we report circular photogalvanic effect with opposite signs at two different mid-infrared wavelengths which provides evidence of Weyl-related optical responses. These two different wavelengths correspond to two critical transitions relating to the bands of different Weyl cones and the sign of circular photogalvanic effect is determined by the chirality selection rules within certain Weyl cone and between two different Weyl cones. Further experimental evidences confirm the observed response is an intrinsic second-order process. With flexibly tunable bandgap and Fermi level, tellurium is established as an ideal semiconducting material to manipulate and explore chirality-related Weyl physics in both conduction and valence bands. These results are also directly applicable to helicity-sensitive optoelectronics devices.

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

Topological physics has been extensively studied in different kinds of bosonic and Fermionic systems, but the coexistence of topological phonons and electrons in one single material has seldom been reported. Recently, graphdiyne has been proposed as a two-dimensional (2D) electronic second-order topological insulator (SOTI). In this work, we found that graphdiyne is equivalent to Kekulé lattice, also realizing a 2D phononic SOTI in both out-of-plane and in-plane modes. Depending on edge terminations, the characterized topological corner states can be either inside or outside the bulk gap and are tunable by the local corner potential. Most remarkably, a unique selectivity of space and symmetry is revealed in the electron-phonon coupling between the localized phononic and electronic topological corner states. Our results not only demonstrate the phononic higher-order band topology in a real carbon material but also provide an opportunity to investigate the interplay between phononic and electronic higher-order topological states.

Higher-Order Band Topology in Twisted Moiré Superlattice.

The two-dimensional (2D) twisted bilayer materials with van der Waals coupling have ignited great research interests, paving a new way to explore the emergent quantum phenomena by twist degree of freedom. Generally, with the decreasing of twist angle, the enhanced interlayer coupling will gradually flatten the low-energy bands and isolate them by two high-energy gaps at zero and full filling, respectively. Although the correlation and topological physics in the low-energy flat bands have been intensively studied, little information is available for these two emerging gaps. In this Letter, we predict a 2D second-order topological insulator (SOTI) for twisted bilayer graphene and twisted bilayer boron nitride in both zero and full filling gaps. Employing a tight-binding Hamiltonian based on first-principles calculations, three unique fingerprints of 2D SOTI are identified, that is, nonzero bulk topological index, gapped topological edge state, and in-gap topological corner state. Most remarkably, the 2D SOTI exists in a wide range of commensurate twist angles, which is robust to microscopic structure disorder and twist center, greatly facilitating the possible experimental measurement. Our results not only extend the higher-order band topology to massless and massive twisted moiré superlattice, but also demonstrate the importance of high-energy bands for fully understanding the nontrivial electronics.

Folding Graphene into a Chern Insulator with Light Irradiation.

Recently, the precise folding of flexible graphene is reported experimentally [ Science, 2019, 365, 1036-1040], demonstrating an efficient approach to manipulate its electronic and optoelectronic properties. Here, we propose a light-induced high-Chern-number Chern insulator (CI) in the folded graphene. Along both armchair and zigzag folding directions, we demonstrate that there are two-handedness-dependent chiral interface states localized at the curved region. Physically, they can be attributed to the light-induced mass-term inversion across the folded graphene. Most remarkably, by rationally designing the folding processes, 2D and 3D CIs are also realizable in a single-wall carbon nanotube and periodic folded graphene, respectively, illustrating a high tunability of the folding degree of freedom. We envision that this intriguing form of "foldtronics" will provide a new platform for investigating the topological state in 2D materials to draw immediate experimental attention.