A hybrid topological quantum state in an elemental solid.

Topology1-3 and interactions are foundational concepts in the modern understanding of quantum matter. Their nexus yields three important research directions: (1) the competition between distinct interactions, as in several intertwined phases, (2) the interplay between interactions and topology that drives the phenomena in twisted layered materials and topological magnets, and (3) the coalescence of several topological orders to generate distinct novel phases. The first two examples have grown into major areas of research, although the last example remains mostly unexplored, mainly because of the lack of a material platform for experimental studies. Here, using tunnelling microscopy, photoemission spectroscopy and a theoretical analysis, we unveil a 'hybrid' topological phase of matter in the simple elemental-solid arsenic. Through a unique bulk-surface-edge correspondence, we uncover that arsenic features a conjoined strong and higher-order topology that stabilizes a hybrid topological phase. Although momentum-space spectroscopy measurements show signs of topological surface states, real-space microscopy measurements unravel a unique geometry of topologically induced step-edge conduction channels revealed on various natural nanostructures on the surface. Using theoretical models, we show that the existence of gapless step-edge states in arsenic relies on the simultaneous presence of both a non-trivial strong Z2 invariant and a non-trivial higher-order topological invariant, which provide experimental evidence for hybrid topology. Our study highlights pathways for exploring the interplay of different band topologies and harnessing the associated topological conduction channels in engineered quantum or nano-devices.

Writing and Detecting Topological Charges in Exfoliated Fe5-xGeTe2.

Fe5-xGeTe2 is a promising two-dimensional (2D) van der Waals (vdW) magnet for practical applications, given its magnetic properties. These include Curie temperatures above room temperature, and topological spin textures─TST (both merons and skyrmions), responsible for a pronounced anomalous Hall effect (AHE) and its topological counterpart (THE), which can be harvested for spintronics. Here, we show that both the AHE and THE can be amplified considerably by just adjusting the thickness of exfoliated Fe5-xGeTe2, with THE becoming observable even in zero magnetic field due to a field-induced unbalance in topological charges. Using a complementary suite of techniques, including electronic transport, Lorentz transmission electron microscopy, and micromagnetic simulations, we reveal the emergence of substantial coercive fields upon exfoliation, which are absent in the bulk, implying thickness-dependent magnetic interactions that affect the TST. We detected a "magic" thickness t ≈ 30 nm where the formation of TST is maximized, inducing large magnitudes for the topological charge density (∼6.45 × 1020 cm-2), and the concomitant anomalous (ρxyA,max ≃22.6 µΩ cm) and topological (ρxyu,T 1≃5 µΩ cm) Hall resistivities at T ≈ 120 K. These values for ρxyA,max and ρxyu,T are higher than those found in magnetic topological insulators and, so far, the largest reported for 2D magnets. The hitherto unobserved THE under zero magnetic field could provide a platform for the writing and electrical detection of TST aiming at energy-efficient devices based on vdW ferromagnets.

Weyl nodal ring states and Landau quantization with very large magnetoresistance in square-net magnet EuGa4.

Magnetic topological semimetals allow for an effective control of the topological electronic states by tuning the spin configuration. Among them, Weyl nodal line semimetals are thought to have the greatest tunability, yet they are the least studied experimentally due to the scarcity of material candidates. Here, using a combination of angle-resolved photoemission spectroscopy and quantum oscillation measurements, together with density functional theory calculations, we identify the square-net compound EuGa4 as a magnetic Weyl nodal ring semimetal, in which the line nodes form closed rings near the Fermi level. The Weyl nodal ring states show distinct Landau quantization with clear spin splitting upon application of a magnetic field. At 2 K in a field of 14 T, the transverse magnetoresistance of EuGa4 exceeds 200,000%, which is more than two orders of magnitude larger than that of other known magnetic topological semimetals. Our theoretical model suggests that the non-saturating magnetoresistance up to 40 T arises as a consequence of the nodal ring state.

Coexistence of Merons with Skyrmions in the Centrosymmetric Van Der Waals Ferromagnet Fe5- x GeTe2.

Fe5- x GeTe2 is a centrosymmetric, layered van der Waals (vdW) ferromagnet that displays Curie temperatures Tc (270-330 K) that are within the useful range for spintronic applications. However, little is known about the interplay between its topological spin textures (e.g., merons, skyrmions) with technologically relevant transport properties such as the topological Hall effect (THE) or topological thermal transport. Here, via high-resolution Lorentz transmission electron microscopy, it is shown that merons and anti-meron pairs coexist with Néel skyrmions in Fe5- x GeTe2 over a wide range of temperatures and probe their effects on thermal and electrical transport. A THE is detected, even at room T, that senses merons at higher T's, as well as their coexistence with skyrmions as T is lowered, indicating an on-demand thermally driven formation of either type of spin texture. Remarkably, an unconventional THE is also observed in absence of Lorentz force, and it is attributed to the interaction between charge carriers and magnetic field-induced chiral spin textures. These results expose Fe5-x GeTe2 as a promising candidate for the development of applications in skyrmionics/meronics due to the interplay between distinct but coexisting topological magnetic textures and unconventional transport of charge/heat carriers.

Evidence of a room-temperature quantum spin Hall edge state in a higher-order topological insulator.

Room-temperature realization of macroscopic quantum phases is one of the major pursuits in fundamental physics1,2. The quantum spin Hall phase3-6 is a topological quantum phase that features a two-dimensional insulating bulk and a helical edge state. Here we use vector magnetic field and variable temperature based scanning tunnelling microscopy to provide micro-spectroscopic evidence for a room-temperature quantum spin Hall edge state on the surface of the higher-order topological insulator Bi4Br4. We find that the atomically resolved lattice exhibits a large insulating gap of over 200 meV, and an atomically sharp monolayer step edge hosts an in-gap gapless state, suggesting topological bulk-boundary correspondence. An external magnetic field can gap the edge state, consistent with the time-reversal symmetry protection inherent in the underlying band topology. We further identify the geometrical hybridization of such edge states, which not only supports the Z2 topology of the quantum spin Hall state but also visualizes the building blocks of the higher-order topological insulator phase. Our results further encourage the exploration of high-temperature transport quantization of the putative topological phase reported here.

Paramagnetic Molecular Semiconductors Combining Anisotropic Magnetic Ions with TCNQ Radical Anions.

We report the synthesis, magnetic properties, and transport properties of paramagnetic metal complexes, [Co(DMF)4(TCNQ)2](TCNQ)2 (1), [La(DMF)8(TCNQ)](TCNQ)5 (2), and [Nd(DMF)7(TCNQ)](TCNQ)5 (3) (DMF = N,N-dimethylformamide, TCNQ = 7,7,8,8-tetracyanoquinodimethane). All three compounds contain fractionally charged TCNQδ- anions (0 < δ < 1) and mononuclear complex cations in which the coordination environment of a metal center includes several DMF molecules and one or two terminally coordinated TCNQδ- anions. The coordinated TCNQδ- anions participate in π-π stacking interactions with noncoordinated TCNQδ- anions, forming columnar substructures that provide efficient charge-transporting pathways. As a result, temperature-dependent conductivity measurements demonstrate that all three compounds exhibit semiconducting behavior.

Observation of Quantum Anomalous Hall Effect and Exchange Interaction in Topological Insulator/Antiferromagnet Heterostructure.

Integration of a quantum anomalous Hall insulator with a magnetically ordered material provides an additional degree of freedom through which the resulting exotic quantum states can be controlled. Here, an experimental observation is reported of the quantum anomalous Hall effect in a magnetically-doped topological insulator grown on the antiferromagnetic insulator Cr2 O3 . The exchange coupling between the two materials is investigated using field-cooling-dependent magnetometry and polarized neutron reflectometry. Both techniques reveal strong interfacial interaction between the antiferromagnetic order of the Cr2 O3 and the magnetic topological insulator, manifested as an exchange bias when the sample is field-cooled under an out-of-plane magnetic field, and an exchange spring-like magnetic depth profile when the system is magnetized within the film plane. These results identify antiferromagnetic insulators as suitable candidates for the manipulation of magnetic and topological order in topological insulator films.

Probing the low-temperature limit of the quantum anomalous Hall effect.

Quantum anomalous Hall effect has been observed in magnetically doped topological insulators. However, full quantization, up until now, is limited within the sub-1 K temperature regime, although the material's magnetic ordering temperature can go beyond 100 K. Here, we study the temperature limiting factors of the effect in Cr-doped (BiSb)2Te3 systems using both transport and magneto-optical methods. By deliberate control of the thin-film thickness and doping profile, we revealed that the low occurring temperature of quantum anomalous Hall effect in current material system is a combined result of weak ferromagnetism and trivial band involvement. Our findings may provide important insights into the search for high-temperature quantum anomalous Hall insulator and other topologically related phenomena.

Topological Transitions Induced by Antiferromagnetism in a Thin-Film Topological Insulator.

Magnetism in topological insulators (TIs) opens a topologically nontrivial exchange band gap, providing an exciting platform for manipulating the topological order through an external magnetic field. Here, we show that the surface of an antiferromagnetic thin film can magnetize the top and the bottom TI surface states through interfacial couplings. During the magnetization reversal, intermediate spin configurations are ascribed from unsynchronized magnetic switchings. This unsynchronized switching develops antisymmetric magnetoresistance spikes during magnetization reversals, which might originate from a series of topological transitions. With the high Néel ordering temperature provided by the antiferromagnetic layers, the signature of the induced topological transition persists up to ∼90 K.