Antiferromagnetic Topological Insulator with Nonsymmorphic Protection in Two Dimensions

Design of Antiferromagnetic Second-Order Band Topology with Rotation Topological Invariants in Two Dimensions

The existence of fractionally quantized topological corner charge serves as a key indicator for two-dimensional (2D) second-order topological insulators (SOTIs), yet it has not been experimentally observed in realistic materials. Here, based on effective model analysis and symmetry arguments, we propose a strategy for achieving SOTI phases with in-gap corner states in 2D systems with antiferromagnetic (AFM) order. We discover that the band topology originates from the interplay between intrinsic spin-orbital coupling and interlayer AFM exchange interactions. Using first-principles calculations, we show that the 2D AFM SOTI phase can be realized in (MnBi2Te4)(Bi2Te3)m films. Moreover, we demonstrate that the SOTI states are linked to rotation topological invariants under 3-fold rotation symmetry C3, resulting in fractionally quantized corner charge, i.e., n 3 | e | (mod e). Due to the great achievements in (MnBi2Te4)(Bi2Te3)m systems, our results providing reliable material candidates for experimentally accessible AFM SOTIs should draw intense attention.

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.

Engineering Gapless Edge States from Antiferromagnetic Chern Homobilayer

We put forward that stacked Chern insulators with opposite chiralities offer a strategy to achieve gapless helical edge states in two dimensions. We employ the square lattice as an example and elucidate that the gapless chiral and helical edge states emerge in the monolayer and antiferromagnetically stacked bilayer, characterized by Chern number C = - 1 and spin Chern number C S = - 1 , respectively. Particularly, for a topological phase transition to the normal insulator in the stacked bilayer, a band gap closing and reopening procedure takes place accompanied by helical edge states disappearing, where the Chern insulating phase in the monolayer vanishes at the same time. Moreover, EuO is revealed as a suitable candidate for material realization. This work is not only valuable to the research of the quantum anomalous Hall effect but also offers a favorable platform to realize magnetic topologically insulating materials for spintronics applications.

Emerging Nontrivial Topology in Ultrathin Films of Rare-Earth Pnictides

Thin films of rare-earth monopnictide (RE-V) semimetals are expected to turn into semiconductors due to quantum confinement effects (QCE), lifting the overlap between electron pockets at Brillouin zone edges (X) and hole pockets at the zone center (Γ). Instead, using LaSb as an example, we find the emergence of the quantum spin Hall (QSH) insulator phase in (001)-oriented films as the thickness is reduced to 7, 5, or 3 monolayers (MLs). This is attributed to a strong QCE on the in-plane electron pockets and the lack of quantum confinement on the out-of-plane pocket projected onto the zone center, resulting in a band inversion. Spin-orbit coupling (SOC) opens a sizable nontrivial gap in the band structure of ultrathin films. Such effect is anticipated to be general in rare-earth monopnictides and may lead to interesting phenomena when coupled with the 4f magnetic moments present in other members of this family of materials.

Phase Engineering of 2D Materials

Polymorphic 2D materials allow structural and electronic phase engineering, which can be used to realize energy-efficient, cost-effective, and scalable device applications. The phase engineering covers not only conventional structural and metal-insulator transitions but also magnetic states, strongly correlated band structures, and topological phases in rich 2D materials. The methods used for the local phase engineering of 2D materials include various optical, geometrical, and chemical processes as well as traditional thermodynamic approaches. In this Review, we survey the precise manipulation of local phases and phase patterning of 2D materials, particularly with ideal and versatile phase interfaces for electronic and energy device applications. Polymorphic 2D materials and diverse quantum materials with their layered, vertical, and lateral geometries are discussed with an emphasis on the role and use of their phase interfaces. Various phase interfaces have demonstrated superior and unique performance in electronic and energy devices. The phase patterning leads to novel homo- and heterojunction structures of 2D materials with low-dimensional phase boundaries, which highlights their potential for technological breakthroughs in future electronic, quantum, and energy devices. Accordingly, we encourage researchers to investigate and exploit phase patterning in emerging 2D materials.

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

Manipulating spin polarization in wide-gap wurtzite semiconductors is crucial for the development of high-temperature spintronics applications. A topological insulator revealed recently in wurtzite quantum wells (QWs) provides a platform to mediate spin-polarized transport through the polarization field-driven topological edges and large Rashba spin-orbit coupling (SOC). Here, we propose a spin-polarized device in a quantum point contact (QPC) structure based on ZnO/CdO wurtzite topological QWs. The results show that the QPC width can sufficiently control the lateral spin-orbit coupling (SOC) as well as the band gap of the edge states through the quantum size effect. As a result, the spin-polarized conductance exhibits oscillation due to the spin precession, which can be controlled by adjusting the voltage imposed on the split gate. The QPC-induced large spin splitting is highly nonlinear and becomes strong close to the gap. The spin splitting of the edge states will be suppressed for QPC widths greater than 50 nm, and thus lead to an extremely long spin precession length. This QPC width-dependent lateral SOC effect provides an emerging electrical approach to manipulate spin-polarized electron transport in topological wurtzite systems.

Magnetic Weyl Semimetal in BaCrSe2 with Long-Distance Distribution of Weyl Points

Weyl semimetals (WSMs) have attracted great attentions that provide intriguing platforms for exploring fundamental physical phenomena and future topotronics applications. Despite the fact that numerous WSMs are achieved, WSMs with long-distance distribution of Weyl points (WPs) in given material candidates remain elusive. Here, the emergence of intrinsic ferromagnetic WSMs in BaCrSe₂ with the nontrivial nature explicitly confirmed by the Chern number and Fermi arc surface states analysis is theoretically demonstrated. Remarkably, unlike previous WSMs for which opposite chirality WPs are located very close to each other, the WPs of BaCrSe₂ host a long-distance distribution, as much as half of the reciprocal space vector, suggesting that the WPs are highly robust and difficult to be annihilated by perturbations. The presented results not only advance the general understanding of magnetic WSMs but also put forward potential applications in topotronics.

Emergent Majorana zero-modes in an intrinsic anti-ferromagnetic topological superconductor Mn2B2 monolayer

Topological superconductors (TSCs) are an exotic field due to the existence of Majorana zero-modes (MZM) in the edge states that obey non-Abelian statistics and can be used to implement topological quantum computations, especially for two-dimensional (2D) materials. Here we predict manganese diboride (Mn₂B₂) as an intrinsic 2D anti-ferromagnetic (AFM) TSC based on the magnetic and electronic structures of Mn and B atoms. Once Mn₂B₂ ML enters a superconducting state, MZM will be induced by the spin-polarized helical gapless edge states. The Z₂ topological non-trivial properties are confirmed by Wannier charge centers (WCC) and the platform of the spin Hall conductivity near the Fermi level. Phonon-electron coupling (EPC) implies s-wave superconductivity and the critical temperature (T_c) is 6.79 K.

Electronic structure and layer-dependent magnetic order of a new high-mobility layered antiferromagnet KMnBi

Room-temperature two-dimensional antiferromagnetic (AFM) materials are highly desirable for various device applications. In this letter, we report the low-energy electronic structure of KMnBi measured by angle-resolved photoemission spectroscopy, which confirms an AFM ground state with the valence band maximum located at -100 meV below the Fermi level and small hole effective masses associated with the sharp band dispersion. Using complementary Raman, atomic force microscope and electric transport measurement, we systematically study the evolution of electric transport characteristics of micro-mechanically exfoliated KMnBi with varied flake thicknesses, which all consistently reveal the existence of a probable AFM ground state down to the quintuple-layer regime. The AFM phase transition temperature ranges from 220 K to 275 K, depending on the thickness. Our results suggest that with proper device encapsulation, multilayer KMnBi is indeed a promising 2D AFM platform for testing various theoretical proposals for device applications.

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 Ferroelectric Quantum Spin Hall Insulator in Monolayer Na3Bi with Surface Trimerization

Two-dimensional (2D) ferroelectric quantum spin Hall (FEQSH) insulator, which features coexisting ferroelectric and topologically insulating orders in two-dimension, is generally considered available only in engineered 2D systems. This is detrimental to the synthesis and application of next generation nonvolatile functional candidates. Therefore, exploring the intrinsic 2D FEQSH insulator is crucial. Here, by means of first-principles, we report a long-thought intrinsic 2D FEQSH insulator in monolayer Na₃Bi with surface trimerization. The material harbors merits including large ferroelectric polarization, sizable nontrivial band gap, and low switching barrier, which are particularly beneficial for the detection and observation of ferroelectric topologically insulating states. Also, it is capable of nonvolatile switching of nontrivial spin textures via inherent ferroelectricity. The fantastic combination of excellent ferroelectric and topological phases in intrinsic the Na₃Bi monolayer serves as an alluring platform for accelerating both scientific discoveries and innovative applications.

Chiral Majorana fermions in two-dimensional square lattice antiferromagnet with proximity-induced superconductivity

Combination of proximity-induced superconductivity and ferromagnetic exchange field in a two-dimensional square-lattice antiferromagnet with spin-orbit coupling and nonsymmorphic symmetry can induce a topological superconductor phase with chiral Majorana edge states. The lattice model of the Bogoliubov-de Gennes (BdG) Hamiltonian was applied to study the phase diagram of bulks and chiral Majorana edge states in nanoribbons. By numerically studying the phase diagram, we found that the non-uniformity of either the superconducting pairing parameters or the exchange field at the two sublattices is necessary to induce a topological superconductor phase with chiral Majorana edge states. The BdG Chern number of certain topological superconductor phases is ±1 or ±3, such that the corresponding nanoribbons have one or three pairs of chiral Majorana edge states, respectively.

Helical Luttinger Liquid on the Edge of a Two-Dimensional Topological Antiferromagnet

A boundary helical Luttinger liquid (HLL) with broken bulk time-reversal symmetry belongs to a unique topological class that may occur in antiferromagnets (AFM). Here, we search for signatures of HLL on the edge of a recently discovered topological AFM, MnBi₂Te₄ even-layer. Using a scanning superconducting quantum interference device, we directly image helical edge current in the AFM ground state appearing at its charge neutral point. Such a helical edge state accompanies an insulating bulk which is topologically distinct from the ferromagnetic Chern insulator phase, as revealed in a magnetic field driven quantum phase transition. The edge conductance of the AFM order follows a power law as a function of temperature and source-drain bias which serves as strong evidence for HLL. Such HLL scaling is robust at finite fields below the quantum critical point. The observed HLL in a layered AFM semiconductor represents a highly tunable topological matter compatible with future spintronics and quantum computation.

Guiding antiferromagnetic transitions in Ca[Formula: see text]RuO[Formula: see text]

Understanding and controlling the transition between antiferromagnetic states having different symmetry content with respect to time-inversion and space-group operations are fundamental challenges for the design of magnetic phases with topologically nontrivial character. Here, we consider a paradigmatic antiferromagnetic oxide insulator, Ca[Formula: see text]RuO[Formula: see text], with symmetrically distinct magnetic ground states and unveil a novel path to guide the transition between them. The magnetic changeover results from structural and orbital reconstruction at the transition metal site that in turn arise as a consequence of substitutional doping. By means of resonant X-ray diffraction we track the evolution of the structural, magnetic, and orbital degrees of freedom for Mn doped Ca[Formula: see text]RuO[Formula: see text] to demonstrate the mechanisms which drive the antiferromagnetic transition. While our analysis focuses on a specific case of substitution, we show that any perturbation that can impact in a similar way on the crystal structure, by reconstructing the induced spin-orbital exchange, is able to drive the antiferromagnetic reorganization.

Controllable Synthesis Quadratic-Dependent Unsaturated Magnetoresistance of Two-Dimensional Nonlayered Fe7S8 with Robust Environmental Stability

Two-dimensional (2D) iron chalcogenides (FeX, X = S, Se, Te) are emerging as an appealing class of materials for a wide range of research topics, including electronics, spintronics, and catalysis. However, the controlled syntheses and intrinsic property explorations of such fascinating materials still remain daunting challenges, especially for 2D nonlayered Fe₇S₈ with mixed-valence states and high conductivity. Herein, we design a general and temperature-mediated chemical vapor deposition (CVD) approach to synthesize ultrathin and large-domain Fe₇S₈ nanosheets on mica substrates, with the thickness down to ∼4.4 nm (2 unit-cell). Significantly, we uncover a quadratic-dependent unsaturated magnetoresistance (MR) with out-of-plane anisotropy in 2D Fe₇S₈, thanks to its ultrahigh crystalline quality and high conductivity (∼2.7 × 10⁵ S m^-1 at room temperature and ∼1.7 × 10⁶ S m^-1 at 2 K). More interestingly, the CVD-synthesized 2D Fe₇S₈ nanosheets maintain robust environmental stability for more than 8 months. These results hereby lay solid foundations for synthesizing 2D nonlayered iron chalcogenides with mixed-valence states and exploring fascinating quantum phenomena.

Generalization of piezoelectric quantum anomalous Hall insulator based on monolayer Fe2I2: a first-principles study

To easily synthesize a piezoelectric quantum anomalous Hall insulator (PQAHI), the Janus monolayer Fe₂IBr (FeI_0.5Br_0.5) as a representative PQAHI, is generalized to monolayer FeI_1-xBr_x (x = 0.25 and 0.75) with α and β phases. By first-principles calculations, it is proved that monolayer FeI_1-xBr_x (x = 0.25 and 0.75) are dynamically, mechanically and thermally stable. They are excellent room-temperature PQAHIs with high Curie temperatures, sizable gaps and high Chern number (C = 2). Because the considered crystal structures of α and β phases possess M_x and M_y mirror symmetries, the topological properties of monolayer FeI_1-xBr_x (x = 0.25 and 0.75) are maintained. Namely, if the constructed structures have M_x and M_y mirror symmetries, the mixing ratio of Br and I atoms can be generalized for other proportions. It is also found that different crystal phases have important effects on the out-of-plane piezoelectric response, and the piezoelectric strain coefficient, d₃₂, of the β phase is higher than or comparable with those of other known two-dimensional (2D) materials. To further confirm this idea, the physical and chemical properties of monolayer LiFeSe_0.75S_0.25 with α and β phases, as a generalization of PQAHI LiFeSe_0.5S_0.5, is investigated, as it has a similar electronic structure, magnetic and topological properties as LiFeSe_0.5S_0.5. Our work provides a practical guide to achieve PQAHIs experimentally, and the combination of piezoelectricity, topological and ferromagnetic (FM) orders makes Fe₂I₂-based monolayers a potential platform for multi-functional spintronics and piezoelectric electronics.

A theoretical investigation of quantum spin Hall state in ordered M'2M″2C3MXenes (M'V, Nb, Ta and M″Ti, Zr, Hf)

MXenes have attracted lots of attention because of the potential applications in electronic devices and energy storage. A variety of transition metals in MXenes give rise to distinct properties and trigger more interests. Depending on the exfoliation processes from the MAX phase, the surfaces of MXenes can be terminated by O, F, Cl, OH groups. Theoretical calculations reveal that the electronic properties of MXenes can be tuned by different surface terminations. For example, some F and O terminated MXenes are predicted to be topological insulators with the quantum spin hall states. In OH terminated MXene multilayers, the image potential states are close to the Fermi level. The energies of these states are sensitive to the interlayer distances. Consequently, the topology of the energy bands can be modulated. Here, based on the density functional theory, we study the electronic structures of the ordered double transition metal MXenes M'₂M″₂C₃T₂(where M' = V, Nb, Ta, M″ = Ti, Zr, Hf and T = F, Cl). We propose that these materials are topologically nontrivial insulators or semimetals. The topologicalZ2index is 1 and the presence of the conducting helical edge states is demonstrated. Their dynamical stabilities are confirmed by the phonon spectra. We expect that our prediction can facilitate the future application of MXenes as the topological insulating devices.

A magnetic topological insulator in two-dimensional EuCd2Bi2: giant gap with robust topology against magnetic transitions

Magnetic topological states open up exciting opportunities for exploring fundamental topological quantum physics and innovative design of topological spintronics devices. However, the nontrivial topologies, for most known magnetic topological states, are usually associated with and may be heavily deformed by fragile magnetism. Here, using a tight-binding model and first-principles calculations, we demonstrate that a highly robust magnetic topological insulator phase, which remains intact under both ferromagnetic and antiferromagnetic configurations, can emerge in two-dimensional EuCd₂Bi₂ quintuple layers. Because of spin-orbital coupling, an inverted gap with intrinsic band inversions occuring simultaneously for up and down spin channels is obtained, accompanied by a nonzero spin Chern number and a pair of gapless edge states, and remarkably the magnitude of the nontrivial band gap for EuCd₂Bi₂ reaches as much as 750 meV. Moreover, the robustness of the magnetic TI phase is further confirmed by rotating the magnetization directions, indicating that EuCd₂Bi₂ represents a promising material for understanding and utilizing the topological insulating states in two-dimensional spin-orbit magnets.

Exciton manipulation in rippled transition metal dichalcogenides

Two-dimensional (2D) transition metal dichalcogenides (TMDs) have shown tremendous potential for applications in optoelectronics due to strong light-matter coupling. However, little is known about how to alter and control the excitonic properties in TMD monolayers. Here, based on many-body perturbation theory via the GW approach and Bethe-Salpeter equation, we systematically investigate exciton manipulation in rippled TMD monolayers. Our results demonstrate that local strain induced by structure deformation plays an important role in determining the electronic and optical properties of TMD materials. Instead of delocalizing in flat monolayers, excitons are pushed to accumulate at the regions with high tensile stress in rippled structure, which can be ascribed to the excitonic funnel effect. In addition, when build-in electric field is also applied, the localized excitons are spatially separated along the zigzag direction, resulting in long exciton lifetime, thus facilitating their future applications in light detecting and harvesting. Our findings provide a way to tailor the excitonic properties in 2D materials and promote their performance in optoelectronic and photovoltaic devices.

Optically induced topological phase transition in two dimensional square lattice antiferromagnet

The two dimensional square lattice antiferromagnet with spin-orbit coupling and nonsymmorphic symmetry is recently found to be topological insulator (TI). We theoretically studied the Floquet states of the antiferromagnetic crystal with optical irradiation, which could be applicable in opto-spintronic. An optical irradiation with circular polarization induces topological phase transition into quantum Anomalous Hall phase with varying Chern number. At the phase boundaries, the Floquet systems could be semimetal with one, two or three band valleys. A linear polarized optical field induces effective antiferromagnetic exchange field, which change the phase regime of the TI. At the intersection of two phase boundaries, the bulk band structure is nearly flat along one of the high symmetry line in the first Brillouin zone, which result in large density of states near to the Fermi energy in bulk and nanoribbons.