Even-Odd Layer-Dependent Exchange Bias Effect in MnBi2Te4 Chern Insulator Devices.

Magnetic topological materials with coexisting magnetism and nontrivial band structures exhibit many novel quantum phenomena, including the quantum anomalous Hall effect, the axion insulator state, and the Weyl semimetal phase. As a stoichiometric layered antiferromagnetic topological insulator, thin films of MnBi2Te4 show fascinating even-odd layer-dependent physics. In this work, we fabricate a series of thin-flake MnBi2Te4 devices using stencil masks and observe the Chern insulator state at high magnetic fields. Upon magnetic field training, a large exchange bias effect is observed in odd but not in even septuple layer (SL) devices. Through theoretical calculations, we attribute the even-odd layer-dependent exchange bias effect to the contrasting surface and bulk magnetic properties of MnBi2Te4 devices. Our findings reveal the microscopic magnetic configuration of MnBi2Te4 thin flakes and highlight the challenges in replicating the zero magnetic field quantum anomalous Hall effect in odd SL MnBi2Te4 devices.

Dynamically tunable moiré exciton Rydberg states in a monolayer semiconductor on twisted bilayer graphene.

Moiré excitons are emergent optical excitations in two-dimensional semiconductors with moiré superlattice potentials. Although these excitations have been observed on several platforms, a system with dynamically tunable moiré potential to tailor their properties is yet to be realized. Here we present a continuously tunable moiré potential in monolayer WSe2, enabled by its proximity to twisted bilayer graphene (TBG) near the magic angle. By tuning local charge density via gating, TBG provides a spatially varying and dynamically tunable dielectric superlattice for modulation of monolayer WSe2 exciton wave functions. We observed emergent moiré exciton Rydberg branches with increased energy splitting following doping of TBG due to exciton wave function hybridization between bright and dark Rydberg states. In addition, emergent Rydberg states can probe strongly correlated states in TBG at the magic angle. Our study provides a new platform for engineering moiré excitons and optical accessibility to electronic states with small correlation gaps in TBG.

(Mg,Mn,Fe,Co,Ni)O: A rocksalt high-entropy oxide containing divalent Mn and Fe.

High-entropy oxides (HEOs) have aroused growing interest due to fundamental questions relating to their structure formation, phase stability, and the interplay between configurational disorder and physical and chemical properties. Introducing Fe(II) and Mn(II) into a rocksalt HEO is considered challenging, as theoretical analysis suggests that they are unstable in this structure under ambient conditions. Here, we develop a bottom-up method for synthesizing Mn- and Fe-containing rocksalt HEO (FeO-HEO). We present a comprehensive investigation of its crystal structure and the random cation-site occupancy. We show the improved structural robustness of this FeO-HEO and verify the viability of an oxygen sublattice as a buffer layer. Compositional analysis reveals the valence and spin state of the iron species. We further report the antiferromagnetic order of this FeO-HEO below the transition temperature ~218 K and predict the conditions of phase stability of Mn- and Fe-containing HEOs. Our results provide fresh insights into the design and property tailoring of emerging classes of HEOs.

Extrinsic Nonlinear Kerr Rotation in Topological Materials under a Magnetic Field.

Topological properties in quantum materials are often governed by symmetry and tuned by crystal structure and external fields, and hence, symmetry-sensitive nonlinear optical measurements in a magnetic field are a valuable probe. Here, we report nonlinear magneto-optical second harmonic generation (SHG) studies of nonmagnetic topological materials including bilayer WTe2, monolayer WSe2, and bulk TaAs. The polarization-resolved patterns of optical SHG under a magnetic field show nonlinear Kerr rotation in these time-reversal symmetric materials. For materials with 3-fold rotational symmetric lattice structure, the SHG polarization pattern rotates just slightly in a magnetic field, whereas in those with mirror or 2-fold rotational symmetry, the SHG polarization pattern rotates greatly and distorts. These different magneto-SHG characters can be understood by considering the superposition of the magnetic field-induced time-noninvariant nonlinear optical tensor and the crystal-structure-based time-invariant counterpart. The situation is further clarified by scrutinizing the Faraday rotation, whose subtle interplay with crystal symmetry accounts for the diverse behavior of the extrinsic nonlinear Kerr rotation in different materials. Our work illustrates the application of magneto-SHG techniques to directly probe nontrivial topological properties, and underlines the importance of minimizing extrinsic nonlinear Kerr rotation in polarization-resolved magneto-optical studies.

Atomic-Scale Andreev Probe of Unconventional Superconductivity.

Recent emergence of low-dimensional unconventional superconductors and their exotic interface properties calls for new approaches to probe the pairing symmetry, a fundamental and frequently elusive property of the superconducting condensate. Here, we introduce the unique capability of tunneling Andreev reflection (TAR) to probe unconventional pairing symmetry, utilizing the sensitivity of this technique to specific Andreev reflections. Specifically, suppression of the lowest-order Andreev reflection due to quantum interference but emergence of the higher-order Andreev processes provides direct evidence of the sign-changing order parameter in the paradigmatic FeSe superconductor. TAR spectroscopy also reveals two superconducting gaps, points to a possibility of a nodal gap structure, and directly confirms that superconductivity is locally suppressed along the nematic twin boundary, with preferential and near-complete suppression of the larger energy gap. Our findings therefore enable new, atomic-scale insight into microscopic, inhomogeneous, and interfacial properties of emerging quantum materials.

Polaritonic Probe of an Emergent 2D Dipole Interface.

The use of work-function-mediated charge transfer has recently emerged as a reliable route toward nanoscale electrostatic control of individual atomic layers. Using α-RuCl3 as a 2D electron acceptor, we are able to induce emergent nano-optical behavior in hexagonal boron nitride (hBN) that arises due to interlayer charge polarization. Using scattering-type scanning near-field optical microscopy (s-SNOM), we find that a thin layer of α-RuCl3 adjacent to an hBN slab reduces the propagation length of hBN phonon polaritons (PhPs) in significant excess of what can be attributed to intrinsic optical losses. Concomitant nano-optical spectroscopy experiments reveal a novel resonance that aligns energetically with the region of excess PhP losses. These experimental observations are elucidated by first-principles density-functional theory and near-field model calculations, which show that the formation of a large interfacial dipole suppresses out-of-plane PhP propagation. Our results demonstrate the potential utility of charge-transfer heterostructures for tailoring optoelectronic properties of 2D insulators.

Current-Phase Relation of a WTe2 Josephson Junction.

When a topological insulator is incorporated into a Josephson junction, the system is predicted to reveal the fractional Josephson effect with a 4π-periodic current-phase relation. Here, we report the measurement of a 4π-periodic switching current through an asymmetric SQUID, formed by the higher-order topological insulator WTe2. Contrary to the established opinion, we show that a high asymmetry in critical current and negligible loop inductance are not sufficient by themselves to reliably measure the current-phase relation. Instead, we find that our measurement is heavily influenced by additional inductances originating from the self-formed PdTex inside the junction. We therefore develop a method to numerically recover the current-phase relation of the system and find the 1.5 µm long junction to be best described in the short ballistic limit. Our results highlight the complexity of subtle inductance effects that can give rise to misleading topological signatures in transport measurements.

Nematically Templated Vortex Lattices in Superconducting FeSe.

New pathways to controlling the morphology of superconducting vortex lattices─and their subsequent dynamics─are required to guide and scale vortex world-lines into a computing platform. We have found that the nematic twin boundaries align superconducting vortices in the adjacent terraces due to the incommensurate potential between vortices surrounding twin boundaries and those trapped within them. With the varying density and morphology of twin boundaries, the vortex lattice assumes several distinct structural phases, including square, regular, and irregular one-dimensional lattices. Through concomitant analysis of vortex lattice models, we have inferred the characteristic energetics of the twin boundary potential and furthermore predicted the existence of geometric size effects as a function of increasing confinement by the twin boundaries. These findings extend the ideas of directed control over vortex lattices to intrinsic topological defects and their self-organized networks, which have direct implications for the future design and control of strain-based topological quantum computing architectures.

Intercell moiré exciton complexes in electron lattices.

Excitons, Coulomb-bound electron-hole pairs, play a crucial role in both optical excitation and correlated phenomena in solids. When excitons interact with other quasiparticles, few- and many-body excited states can appear. Here we report an interaction between exciton and charges enabled by unusual quantum confinement in two-dimensional moiré superlattices, which results in many-body ground states composed of moiré excitons and correlated electron lattices. In an H-stacked (60o-twisted) WS2/WSe2 heterobilayer, we found an interlayer moiré exciton whose hole is surrounded by its partner electron's wavefunction distributed among three adjacent moiré traps. This three-dimensional excitonic structure enables large in-plane electrical quadrupole moments in addition to the vertical dipole. Upon doping, the quadrupole facilitates the binding of interlayer moiré excitons to the charges in neighbouring moiré cells, forming intercell charged exciton complexes. Our work provides a framework for understanding and engineering emergent exciton many-body states in correlated moiré charge orders.

Every-other-layer dipolar excitons in a spin-valley locked superlattice.

Monolayer semiconducting transition metal dichalcogenides possess broken inversion symmetry and strong spin-orbit coupling, leading to a unique spin-valley locking effect. In 2H stacked pristine multilayers, spin-valley locking yields an electronic superlattice structure, where alternating layers correspond to barriers and quantum wells depending on the spin-valley indices. Here we show that the spin-valley locked superlattice hosts a kind of dipolar exciton with the electron and hole constituents separated in an every-other-layer configuration: that is, either in two even or two odd layers. Such excitons become optically bright via hybridization with intralayer excitons. This effect is also manifested by the presence of multiple anti-crossing patterns in the reflectance spectra, as the dipolar exciton is tuned through the intralayer resonance by an electric field. The reflectance spectra further reveal an excited state orbital of the every-other-layer exciton, pointing to a sizable binding energy in the same order of magnitude as the intralayer exciton. As layer thickness increases, the dipolar exciton can form a one-dimensional Bose-Hubbard chain displaying layer number-dependent fine spectroscopy structures.

Role of Magnetic Defects in Tuning Ground States of Magnetic Topological Insulators.

Magnetic defects play an important, but poorly understood, role in magnetic topological insulators (TIs). For example, topological surface transport and bulk magnetic properties are controlled by magnetic defects in Bi2 Se3 -based dilute ferromagnetic (FM) TIs and MnBi2 Te4 (MBT)-based antiferromagnetic (AFM) TIs. Despite its nascent ferromagnetism, the inelastic neutron scattering data show that a fraction of the Mn defects in Sb2 Te3 form strong AFM dimer singlets within a quintuple block. The AFM superexchange coupling occurs via Mn-Te-Mn linear bonds and is identical to the AFM coupling between antisite defects and the FM Mn layer in MBT, establishing common interactions in the two materials classes. It is also found that the FM correlations in (Sb1-x Mnx )2 Te3 are likely driven by magnetic defects in adjacent quintuple blocks across the van der Waals gap. In addition to providing answers to long-standing questions about the evolution of FM order in dilute TI, these results also show that the evolution of global magnetic order from AFM to FM in Sb-substituted MBT is controlled by defect engineering of the intrablock and interblock coupling.

Anomalous Second Harmonic Generation from Atomically Thin MnBi2Te4.

MnBi2Te4 is a van der Waals topological insulator with intrinsic intralayer ferromagnetic exchange and A-type antiferromagnetic interlayer coupling. Theoretically, it belongs to a class of structurally centrosymmetric crystals whose layered antiferromagnetic order breaks inversion symmetry for even layer numbers, making optical second harmonic generation (SHG) an ideal probe of the coupling between the crystal and magnetic structures. Here, we perform magnetic field and temperature-dependent SHG measurements on MnBi2Te4 flakes ranging from bulk to monolayer thickness. We find that the dominant SHG signal from MnBi2Te4 is unexpectedly unrelated to both magnetic state and layer number. We suggest that surface SHG is the likely source of the observed strong SHG, whose symmetry matches that of the MnBi2Te4-vacuum interface. Our results highlight the importance of considering the surface contribution to inversion symmetry-breaking in van der Waals centrosymmetric magnets.

Visualizing the interplay of Dirac mass gap and magnetism at nanoscale in intrinsic magnetic topological insulators.

In intrinsic magnetic topological insulators, Dirac surface-state gaps are prerequisites for quantum anomalous Hall and axion insulating states. Unambiguous experimental identification of these gaps has proved to be a challenge, however. Here, we use molecular beam epitaxy to grow intrinsic MnBi2Te4 thin films. Using scanning tunneling microscopy/spectroscopy, we directly visualize the Dirac mass gap and its disappearance below and above the magnetic order temperature. We further reveal the interplay of Dirac mass gaps and local magnetic defects. We find that, in high defect regions, the Dirac mass gap collapses. Ab initio and coupled Dirac cone model calculations provide insight into the microscopic origin of the correlation between defect density and spatial gap variations. This work provides unambiguous identification of the Dirac mass gap in MnBi2Te4 and, by revealing the microscopic origin of its gap variation, establishes a material design principle for realizing exotic states in intrinsic magnetic topological insulators.

Discrete scale invariance of the quasi-bound states at atomic vacancies in a topological material.

Recently, log-periodic quantum oscillations have been detected in the topological materials zirconium pentatelluride (ZrTe5) and hafnium pentatelluride (HfTe5), displaying an intriguing discrete scale invariance (DSI) characteristic. In condensed materials, the DSI is considered to be related to the quasi-bound states formed by massless Dirac fermions with strong Coulomb attraction, offering a feasible platform to study the long-pursued atomic-collapse phenomenon. Here, we demonstrate that a variety of atomic vacancies in the topological material HfTe5 can host the geometric quasi-bound states with a DSI feature, resembling an artificial supercritical atom collapse. The density of states of these quasi-bound states is enhanced, and the quasi-bound states are spatially distributed in the "orbitals" surrounding the vacancy sites, which are detected and visualized by low-temperature scanning tunneling microscope/spectroscopy. By applying the perpendicular magnetic fields, the quasi-bound states at lower energies become wider and eventually invisible; meanwhile, the energies of quasi-bound states move gradually toward the Fermi energy (EF). These features are consistent with the theoretical prediction of a magnetic field-induced transition from supercritical to subcritical states. The direct observation of geometric quasi-bound states sheds light on the deep understanding of the DSI in quantum materials.

Topological current divider in a Chern insulator junction.

A Chern insulator is a two-dimensional material that hosts chiral edge states produced by the combination of topology with time reversal symmetry breaking. Such edge states are perfect one-dimensional conductors, which may exist not only on sample edges, but on any boundary between two materials with distinct topological invariants (or Chern numbers). Engineering of such interfaces is highly desirable due to emerging opportunities of using topological edge states for energy-efficient information transmission. Here, we report a chiral edge-current divider based on Chern insulator junctions formed within the layered topological magnet MnBi2Te4. We find that in a device containing a boundary between regions of different thickness, topological domains with different Chern numbers can coexist. At the domain boundary, a Chern insulator junction forms, where we identify a chiral edge mode along the junction interface. We use this to construct topological circuits in which the chiral edge current can be split, rerouted, or switched off by controlling the Chern numbers of the individual domains. Our results demonstrate MnBi2Te4 as an emerging platform for topological circuits design.

Direct Visualization of Surface Spin-Flip Transition in MnBi_{4}Te_{7}.

We report direct visualization of spin-flip transition of the surface layer in antiferromagnet MnBi_{4}Te_{7}, a natural superlattice of alternating MnBi_{2}Te_{4} and Bi_{2}Te_{3} layers, using cryogenic magnetic force microscopy (MFM). The observation of magnetic contrast across domain walls and step edges confirms that the antiferromagnetic order persists to the surface layers. The magnetic field dependence of the MFM images reveals that the surface magnetic layer undergoes a first-order spin-flip transition at a magnetic field that is lower than the bulk transition, in excellent agreement with a revised Mills model. Our analysis suggests no reduction of the order parameter in the surface magnetic layer, implying robust ferromagnetism in the single-layer limit. The direct visualization of surface spin-flip transition not only opens up exploration of surface metamagnetic transitions in layered antiferromagnets, but also provides experimental support for realizing quantized transport in ultrathin films of MnBi_{4}Te_{7} and other natural superlattice topological magnets.

Hidden Local Symmetry Breaking in a Kagome-Lattice Magnetic Weyl Semimetal.

Exploring the relationship between intriguing physical properties and structural complexity is a central topic in studying modern functional materials. Co3Sn2S2, a newly discovered kagome-lattice magnetic Weyl semimetal, has triggered intense interest owing to the intimate coupling between topological semimetallic states and peculiar magnetic properties. However, the origins of the magnetic phase separation and spin glass state below TC in this ordered compound are two unresolved yet important puzzles in understanding its magnetism. Here, we report the discovery of local symmetry breaking surprisingly co-emerges with the onset of ferromagnetic order in Co3Sn2S2, by a combined use of neutron total scattering and half-polarized neutron diffraction. An anisotropic distortion of the cobalt kagome lattice at the atomic/nano level is also found, with distinct distortion directions among the two Co1 and four Co2 atoms. The mismatch of local and average symmetries occurs below TC, indicating that Co3Sn2S2 evolves to an intrinsically lattice disordered system when the ferromagnetic order is established. The local symmetry breaking with intrinsic lattice disorder provides new understanding of the puzzling magnetic properties. Our density functional theory (DFT) calculation indicates that the local symmetry breaking is expected to reorient local ferromagnetic moments, unveiling the existence of the ferromagnetic instability associated with the lattice instability. Furthermore, DFT calculation unveils that the local symmetry breaking could affect the Weyl property by breaking the mirror plane. Our findings highlight the fundamentally important role that the local symmetry breaking plays in advancing our understanding on the magnetic and topological properties in Co3Sn2S2, which may draw attention to explore the overlooked local symmetry breaking in Co3Sn2S2, its derivatives and more broadly in other topological Dirac/Weyl semimetals and kagome-lattice magnets.

Quantum Spin Hall Edge States and Interlayer Coupling in Twisted Bilayer WTe2.

The quantum spin Hall (QSH) effect, characterized by topologically protected spin-polarized edge states, was recently demonstrated in monolayers of the transition metal dichalcogenide (TMD) WTe2. However, the robustness of this topological protection remains largely unexplored in van der Waals heterostructures containing one or more layers of a QSH insulator. In this work, we use scanning tunneling microscopy and spectroscopy (STM/STS) to explore the topological nature of twisted bilayer (tBL) WTe2. At the tBL edges, we observe the characteristic spectroscopic signatures of the QSH edge states. For small twist angles, a rectangular moiré pattern develops, which results in local modifications of the band structure. Using first-principles calculations, we quantify the interactions in tBL WTe2 and its topological edge states as a function of interlayer distance and conclude that it is possible to engineer the topology of WTe2 bilayers via the twist angle as well as interlayer interactions.

Deterministic switching of a perpendicularly polarized magnet using unconventional spin-orbit torques in WTe2.

Spin-orbit torque (SOT)-driven deterministic control of the magnetic state of a ferromagnet with perpendicular magnetic anisotropy is key to next-generation spintronic applications including non-volatile, ultrafast and energy-efficient data-storage devices. However, field-free deterministic switching of perpendicular magnetization remains a challenge because it requires an out-of-plane antidamping torque, which is not allowed in conventional spin-source materials such as heavy metals and topological insulators due to the system's symmetry. The exploitation of low-crystal symmetries in emergent quantum materials offers a unique approach to achieve SOTs with unconventional forms. Here we report an experimental realization of field-free deterministic magnetic switching of a perpendicularly polarized van der Waals magnet employing an out-of-plane antidamping SOT generated in layered WTe2, a quantum material with a low-symmetry crystal structure. Our numerical simulations suggest that the out-of-plane antidamping torque in WTe2 is essential to explain the observed magnetization switching.

Magnons and magnetic fluctuations in atomically thin MnBi2Te4.

Electron band topology is combined with intrinsic magnetic orders in MnBi2Te4, leading to novel quantum phases. Here we investigate collective spin excitations (i.e. magnons) and spin fluctuations in atomically thin MnBi2Te4 flakes using Raman spectroscopy. In a two-septuple layer with non-trivial topology, magnon characteristics evolve as an external magnetic field tunes the ground state through three ordered phases: antiferromagnet, canted antiferromagnet, and ferromagnet. The Raman selection rules are determined by both the crystal symmetry and magnetic order while the magnon energy is determined by different interaction terms. Using non-interacting spin-wave theory, we extract the spin-wave gap at zero magnetic field, an anisotropy energy, and interlayer exchange in bilayers. We also find magnetic fluctuations increase with reduced thickness, which may contribute to a less robust magnetic order in single layers.