Fractional quantum anomalous Hall effect in multilayer graphene.

The fractional quantum anomalous Hall effect (FQAHE), the analogue of the fractional quantum Hall effect1 at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking2-6. The demonstration of FQAHE could lead to non-Abelian anyons that form the basis of topological quantum computation7-9. So far, FQAHE has been observed only in twisted MoTe2 at a moiré filling factor v > 1/2 (refs. 10-13). Graphene-based moiré superlattices are believed to host FQAHE with the potential advantage of superior material quality and higher electron mobility. Here we report the observation of integer and fractional QAH effects in a rhombohedral pentalayer graphene-hBN moiré superlattice. At zero magnetic field, we observed plateaus of quantized Hall resistance [Formula: see text] at v = 1, 2/3, 3/5, 4/7, 4/9, 3/7 and 2/5 of the moiré superlattice, respectively, accompanied by clear dips in the longitudinal resistance Rxx. Rxy equals [Formula: see text] at v = 1/2 and varies linearly with v, similar to the composite Fermi liquid in the half-filled lowest Landau level at high magnetic fields14-16. By tuning the gate-displacement field D and v, we observed phase transitions from composite Fermi liquid and FQAH states to other correlated electron states. Our system provides an ideal platform for exploring charge fractionalization and (non-Abelian) anyonic braiding at zero magnetic field7-9,17-19, especially considering a lateral junction between FQAHE and superconducting regions in the same device20-22.

Signatures of hybridization of multiple Majorana zero modes in a vortex.

Majorana zero modes (MZMs) are emergent zero-energy topological quasiparticles that are their own antiparticles1,2. Detected MZMs are spatially separated and electrically neutral, so producing hybridization between MZMs is extremely challenging in superconductors3,4. Here, we report the magnetic field response of vortex bound states in superconducting topological crystalline insulator SnTe (001) films. Several MZMs were predicted to coexist in a single vortex due to magnetic mirror symmetry. Using a scanning tunnelling microscope equipped with a three-axis vector magnet, we found that the zero-bias peak (ZBP) in a single vortex exhibits an apparent anisotropic response even though the magnetic field is weak. The ZBP can robustly extend a long distance of up to approximately 100 nm at the (001) surface when the magnetic field is parallel to the ( 1 1 ¯ 0 )-type mirror plane, otherwise it displays an asymmetric splitting. Our systematic simulations demonstrate that the anisotropic response cannot be reproduced with trivial ZBPs. Although the different MZMs cannot be directly distinguished due to the limited energy resolution in our experiments, our comparisons between experimental measurements and theoretical simulations strongly support the existence and hybridization of symmetry-protected multiple MZMs. Our work demonstrates a way to hybridize different MZMs by controlling the orientation of the magnetic field and expands the types of MZM available for tuning topological states.

Dual quantum spin Hall insulator by density-tuned correlations in TaIrTe4.

The convergence of topology and correlations represents a highly coveted realm in the pursuit of new quantum states of matter1. Introducing electron correlations to a quantum spin Hall (QSH) insulator can lead to the emergence of a fractional topological insulator and other exotic time-reversal-symmetric topological order2-8, not possible in quantum Hall and Chern insulator systems. Here we report a new dual QSH insulator within the intrinsic monolayer crystal of TaIrTe4, arising from the interplay of its single-particle topology and density-tuned electron correlations. At charge neutrality, monolayer TaIrTe4 demonstrates the QSH insulator, manifesting enhanced nonlocal transport and quantized helical edge conductance. After introducing electrons from charge neutrality, TaIrTe4 shows metallic behaviour in only a small range of charge densities but quickly goes into a new insulating state, entirely unexpected on the basis of the single-particle band structure of TaIrTe4. This insulating state could arise from a strong electronic instability near the van Hove singularities, probably leading to a charge density wave (CDW). Remarkably, within this correlated insulating gap, we observe a resurgence of the QSH state. The observation of helical edge conduction in a CDW gap could bridge spin physics and charge orders. The discovery of a dual QSH insulator introduces a new method for creating topological flat minibands through CDW superlattices, which offer a promising platform for exploring time-reversal-symmetric fractional phases and electromagnetism2-4,9,10.

Orbital multiferroicity in pentalayer rhombohedral graphene.

Ferroic orders describe spontaneous polarization of spin, charge and lattice degrees of freedom in materials. Materials exhibiting multiple ferroic orders, known as multiferroics, have important parts in multifunctional electrical and magnetic device applications1-4. Two-dimensional materials with honeycomb lattices offer opportunities to engineer unconventional multiferroicity, in which the ferroic orders are driven purely by the orbital degrees of freedom and not by electron spin. These include ferro-valleytricity corresponding to the electron valley5 and ferro-orbital-magnetism6 supported by quantum geometric effects. These orbital multiferroics could offer strong valley-magnetic couplings and large responses to external fields-enabling device applications such as multiple-state memory elements and electric control of the valley and magnetic states. Here we report orbital multiferroicity in pentalayer rhombohedral graphene using low-temperature magneto-transport measurements. We observed anomalous Hall signals Rxy with an exceptionally large Hall angle (tanΘH > 0.6) and orbital magnetic hysteresis at hole doping. There are four such states with different valley polarizations and orbital magnetizations, forming a valley-magnetic quartet. By sweeping the gate electric field E, we observed a butterfly-shaped hysteresis of Rxy connecting the quartet. This hysteresis indicates a ferro-valleytronic order that couples to the composite field E · B (where B is the magnetic field), but not to the individual fields. Tuning E would switch each ferroic order independently and achieve non-volatile switching of them together. Our observations demonstrate a previously unknown type of multiferroics and point to electrically tunable ultralow-power valleytronic and magnetic devices.

Observation of fractionally quantized anomalous Hall effect.

The integer quantum anomalous Hall (QAH) effect is a lattice analogue of the quantum Hall effect at zero magnetic field1-3. This phenomenon occurs in systems with topologically non-trivial bands and spontaneous time-reversal symmetry breaking. Discovery of its fractional counterpart in the presence of strong electron correlations, that is, the fractional QAH effect4-7, would open a new chapter in condensed matter physics. Here we report the direct observation of both integer and fractional QAH effects in electrical measurements on twisted bilayer MoTe2. At zero magnetic field, near filling factor ν = -1 (one hole per moiré unit cell), we see an integer QAH plateau in the Hall resistance Rxy quantized to h/e2 ± 0.1%, whereas the longitudinal resistance Rxx vanishes. Remarkably, at ν = -2/3 and -3/5, we see plateau features in Rxy at [Formula: see text] and [Formula: see text], respectively, whereas Rxx remains small. All features shift linearly versus applied magnetic field with slopes matching the corresponding Chern numbers -1, -2/3 and -3/5, precisely as expected for integer and fractional QAH states. Additionally, at zero magnetic field, Rxy is approximately 2h/e2 near half-filling (ν = -1/2) and varies linearly as ν is tuned. This behaviour resembles that of the composite Fermi liquid in the half-filled lowest Landau level of a two-dimensional electron gas at high magnetic field8-14. Direct observation of the fractional QAH and associated effects enables research in charge fractionalization and anyonic statistics at zero magnetic field.

Superconductivity and strong interactions in a tunable moiré quasicrystal.

Electronic states in quasicrystals generally preclude a Bloch description1, rendering them fascinating and enigmatic. Owing to their complexity and scarcity, quasicrystals are underexplored relative to periodic and amorphous structures. Here we introduce a new type of highly tunable quasicrystal easily assembled from periodic components. By twisting three layers of graphene with two different twist angles, we form two mutually incommensurate moiré patterns. In contrast to many common atomic-scale quasicrystals2,3, the quasiperiodicity in our system is defined on moiré length scales of several nanometres. This 'moiré quasicrystal' allows us to tune the chemical potential and thus the electronic system between a periodic-like regime at low energies and a strongly quasiperiodic regime at higher energies, the latter hosting a large density of weakly dispersing states. Notably, in the quasiperiodic regime, we observe superconductivity near a flavour-symmetry-breaking phase transition4,5, the latter indicative of the important role that electronic interactions play in that regime. The prevalence of interacting phenomena in future systems with in situ tunability is not only useful for the study of quasiperiodic systems but may also provide insights into electronic ordering in related periodic moiré crystals6-12. We anticipate that extending this platform to engineer quasicrystals by varying the number of layers and twist angles, and by using different two-dimensional components, will lead to a new family of quantum materials to investigate the properties of strongly interacting quasicrystals.

Signatures of fractional quantum anomalous Hall states in twisted MoTe2.

The interplay between spontaneous symmetry breaking and topology can result in exotic quantum states of matter. A celebrated example is the quantum anomalous Hall (QAH) state, which exhibits an integer quantum Hall effect at zero magnetic field owing to intrinsic ferromagnetism1-3. In the presence of strong electron-electron interactions, fractional QAH (FQAH) states at zero magnetic field can emerge4-8. These states could host fractional excitations, including non-Abelian anyons-crucial building blocks for topological quantum computation9. Here we report experimental signatures of FQAH states in a twisted molybdenum ditelluride (MoTe2) bilayer. Magnetic circular dichroism measurements reveal robust ferromagnetic states at fractionally hole-filled moiré minibands. Using trion photoluminescence as a sensor10, we obtain a Landau fan diagram showing linear shifts in carrier densities corresponding to filling factor v = -2/3 and v = -3/5 ferromagnetic states with applied magnetic field. These shifts match the Streda formula dispersion of FQAH states with fractionally quantized Hall conductance of [Formula: see text] and [Formula: see text], respectively. Moreover, the v = -1 state exhibits a dispersion corresponding to Chern number -1, consistent with the predicted QAH state11-14. In comparison, several non-ferromagnetic states on the electron-doping side do not disperse, that is, they are trivial correlated insulators. The observed topological states can be electrically driven into topologically trivial states. Our findings provide evidence of the long-sought FQAH states, demonstrating MoTe2 moiré superlattices as a platform for exploring fractional excitations.

Quantum anomalous Hall effect from intertwined moiré bands.

Electron correlation and topology are two central threads of modern condensed matter physics. Semiconductor moiré materials provide a highly tuneable platform for studies of electron correlation1-12. Correlation-driven phenomena, including the Mott insulator2-5, generalized Wigner crystals2,6,9, stripe phases10 and continuous Mott transition11,12, have been demonstrated. However, non-trivial band topology has remained unclear. Here we report the observation of a quantum anomalous Hall effect in AB-stacked MoTe2 /WSe2 moiré heterobilayers. Unlike in the AA-stacked heterobilayers11, an out-of-plane electric field not only controls the bandwidth but also the band topology by intertwining moiré bands centred at different layers. At half band filling, corresponding to one particle per moiré unit cell, we observe quantized Hall resistance, h/e2 (with h and e denoting the Planck's constant and electron charge, respectively), and vanishing longitudinal resistance at zero magnetic field. The electric-field-induced topological phase transition from a Mott insulator to a quantum anomalous Hall insulator precedes an insulator-to-metal transition. Contrary to most known topological phase transitions13, it is not accompanied by a bulk charge gap closure. Our study paves the way for discovery of emergent phenomena arising from the combined influence of strong correlation and topology in semiconductor moiré materials.

Continuous Mott transition in semiconductor moiré superlattices.

The evolution of a Landau Fermi liquid into a non-magnetic Mott insulator with increasing electronic interactions is one of the most puzzling quantum phase transitions in physics1-6. The vicinity of the transition is believed to host exotic states of matter such as quantum spin liquids4-7, exciton condensates8 and unconventional superconductivity1. Semiconductor moiré materials realize a highly controllable Hubbard model simulator on a triangular lattice9-22, providing a unique opportunity to drive a metal-insulator transition (MIT) via continuous tuning of the electronic interactions. Here, by electrically tuning the effective interaction strength in MoTe2/WSe2 moiré superlattices, we observe a continuous MIT at a fixed filling of one electron per unit cell. The existence of quantum criticality is supported by the scaling collapse of the resistance, a continuously vanishing charge gap as the critical point is approached from the insulating side, and a diverging quasiparticle effective mass from the metallic side. We also observe a smooth evolution of the magnetic susceptibility across the MIT and no evidence of long-range magnetic order down to ~5% of the Curie-Weiss temperature. This signals an abundance of low-energy spinful excitations on the insulating side that is further corroborated by the Pomeranchuk effect observed on the metallic side. Our results are consistent with the universal critical theory of a continuous Mott transition in two dimensions4,23.

Layer Hall effect in a 2D topological axion antiferromagnet.

Whereas ferromagnets have been known and used for millennia, antiferromagnets were only discovered in the 1930s1. At large scale, because of the absence of global magnetization, antiferromagnets may seem to behave like any non-magnetic material. At the microscopic level, however, the opposite alignment of spins forms a rich internal structure. In topological antiferromagnets, this internal structure leads to the possibility that the property known as the Berry phase can acquire distinct spatial textures2,3. Here we study this possibility in an antiferromagnetic axion insulator-even-layered, two-dimensional MnBi2Te4-in which spatial degrees of freedom correspond to different layers. We observe a type of Hall effect-the layer Hall effect-in which electrons from the top and bottom layers spontaneously deflect in opposite directions. Specifically, under zero electric field, even-layered MnBi2Te4 shows no anomalous Hall effect. However, applying an electric field leads to the emergence of a large, layer-polarized anomalous Hall effect of about 0.5e2/h (where e is the electron charge and h is Planck's constant). This layer Hall effect uncovers an unusual layer-locked Berry curvature, which serves to characterize the axion insulator state. Moreover, we find that the layer-locked Berry curvature can be manipulated by the axion field formed from the dot product of the electric and magnetic field vectors. Our results offer new pathways to detect and manipulate the internal spatial structure of fully compensated topological antiferromagnets4-9. The layer-locked Berry curvature represents a first step towards spatial engineering of the Berry phase through effects such as layer-specific moiré potential.

SWATH-MS-based proteogenomic analysis reveals the involvement of alternative splicing in poplar upon lead stress.

Alternative splicing (AS) regulates gene expression and increases proteomic diversity for the fine tuning of stress responses in plants, but the exact mechanism through which AS functions in plant stress responses is not thoroughly understood. Here, we investigated how AS functions in poplar (Populus trichocarpa), a popular plant for bioremediation, in response to lead (Pb) stress. Using a proteogenomic analysis, we determine that Pb stress induced alterations in AS patterns that are characterized by an increased use of nonconventional splice sites and a higher abundance of Pb-responsive splicing factors (SFs) associated with Pb-responsive transcription factors. A strong Pb(II)-inducible chaperone protein, PtHSP70, that undergoes AS was further characterized. Overexpression of its two spliced isoforms, PtHSP70-AS1 and PtHSP70-AS2, in poplar and Arabidopsis significantly enhances the tolerance to Pb. Further characterization shows that both isoforms can directly bind to Pb(II), and PtHSP70-AS2 exhibits 10-fold higher binding capacities and a greater increase in expression under Pb stress, thereby reducing cellular toxicity through Pb(II) extrusion and conferring Pb tolerance. AS of PtHSP70 is found to be regulated by PtU1-70K, a Pb(II)-inducible core SF involved in 5'-splice site recognition. Because the same splicing pattern is also found in HSP70 orthologs in other plant species, AS of HSP70 may be a common regulatory mechanism to cope with Pb(II) toxicity. Overall, we have revealed a novel post-transcriptional machinery that mediates heavy metal tolerance in diverse plant species. Our findings offer new molecular targets and bioengineering strategies for phytoremediation and provide new insight for future directions in AS research.

Unconventional ferroelectricity in moiré heterostructures.

The constituent particles of matter can arrange themselves in various ways, giving rise to emergent phenomena that can be surprisingly rich and often cannot be understood by studying only the individual constituents. Discovering and understanding the emergence of such phenomena in quantum materials-especially those in which multiple degrees of freedom or energy scales are delicately balanced-is of fundamental interest to condensed-matter research1,2. Here we report on the surprising observation of emergent ferroelectricity in graphene-based moiré heterostructures. Ferroelectric materials show electrically switchable electric dipoles, which are usually formed by spatial separation between the average centres of positive and negative charge within the unit cell. On this basis, it is difficult to imagine graphene-a material composed of only carbon atoms-exhibiting ferroelectricity3. However, in this work we realize switchable ferroelectricity in Bernal-stacked bilayer graphene sandwiched between two hexagonal boron nitride layers. By introducing a moiré superlattice potential (via aligning bilayer graphene with the top and/or bottom boron nitride crystals), we observe prominent and robust hysteretic behaviour of the graphene resistance with an externally applied out-of-plane displacement field. Our systematic transport measurements reveal a rich and striking response as a function of displacement field and electron filling, and beyond the framework of conventional ferroelectrics. We further directly probe the ferroelectric polarization through a non-local monolayer graphene sensor. Our results suggest an unconventional, odd-parity electronic ordering in the bilayer graphene/boron nitride moiré system. This emergent moiré ferroelectricity may enable ultrafast, programmable and atomically thin carbon-based memory devices.

Colossal room-temperature non-reciprocal Hall effect.

Non-reciprocal charge transport has gained significant attention due to its potential in exploring quantum symmetry and its promising applications. Traditionally, non-reciprocal transport has been observed in the longitudinal direction, with non-reciprocal resistance being a small fraction of the ohmic resistance. Here we report a transverse non-reciprocal transport phenomenon featuring a quadratic current-voltage characteristic and divergent non-reciprocity, termed the non-reciprocal Hall effect. This effect is observed in microscale Hall devices fabricated from platinum (Pt) deposited by a focused ion beam on silicon substrates. The transverse non-reciprocal Hall effect arises from the geometrically asymmetric scattering of textured Pt nanoparticles within the focused-ion-beam-deposited Pt structures. Notably, the non-reciprocal Hall effect generated in focused-ion-beam-deposited Pt electrodes can propagate to adjacent conductors such as Au and NbP through Hall current injection. Additionally, this pronounced non-reciprocal Hall effect facilitates broadband frequency mixing. These findings not only validate the non-reciprocal Hall effect concept but also open avenues for its application in terahertz communication, imaging and energy harvesting.

Angle-resolved transport non-reciprocity and spontaneous symmetry breaking in twisted trilayer graphene.

The identification and characterization of spontaneous symmetry breaking is central to our understanding of strongly correlated two-dimensional materials. In this work, we utilize the angle-resolved measurements of transport non-reciprocity to investigate spontaneous symmetry breaking in twisted trilayer graphene. By analysing the angular dependence of non-reciprocity in both longitudinal and transverse channels, we are able to identify the symmetry axis associated with the underlying electronic order. We report that a hysteretic rotation in the mirror axis can be induced by thermal cycles and a large current bias, supporting the spontaneous breaking of rotational symmetry. Moreover, the onset of non-reciprocity with decreasing temperature coincides with the emergence of orbital ferromagnetism. Combined with the angular dependence of the superconducting diode effect, our findings uncover a direct link between rotational and time-reversal symmetry breaking. These symmetry requirements point towards exchange-driven instabilities in momentum space as a possible origin for transport non-reciprocity in twisted trilayer graphene.

Observation of the nonlinear Hall effect under time-reversal-symmetric conditions.

The electrical Hall effect is the production, upon the application of an electric field, of a transverse voltage under an out-of-plane magnetic field. Studies of the Hall effect have led to important breakthroughs, including the discoveries of Berry curvature and topological Chern invariants1,2. The internal magnetization of magnets means that the electrical Hall effect can occur in the absence of an external magnetic field2; this 'anomalous' Hall effect is important for the study of quantum magnets2-7. The electrical Hall effect has rarely been studied in non-magnetic materials without external magnetic fields, owing to the constraint of time-reversal symmetry. However, only in the linear response regime-when the Hall voltage is linearly proportional to the external electric field-does the Hall effect identically vanish as a result of time-reversal symmetry; the Hall effect in the nonlinear response regime is not subject to such symmetry constraints8-10. Here we report observations of the nonlinear Hall effect10 in electrical transport in bilayers of the non-magnetic quantum material WTe2 under time-reversal-symmetric conditions. We show that an electric current in bilayer WTe2 leads to a nonlinear Hall voltage in the absence of a magnetic field. The properties of this nonlinear Hall effect are distinct from those of the anomalous Hall effect in metals: the nonlinear Hall effect results in a quadratic, rather than linear, current-voltage characteristic and, in contrast to the anomalous Hall effect, the nonlinear Hall effect results in a much larger transverse than longitudinal voltage response, leading to a nonlinear Hall angle (the angle between the total voltage response and the applied electric field) of nearly 90 degrees. We further show that the nonlinear Hall effect provides a direct measure of the dipole moment10 of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe2. Our results demonstrate a new type of Hall effect and provide a way of detecting Berry curvature in non-magnetic quantum materials.

Spin-triplet superconductivity from excitonic effect in doped insulators.

SignificanceWe present a mechanism for unconventional superconductivity in doped band insulators, where short-ranged pairing interaction arises from Coulomb repulsion due to virtual interband or excitonic processes. Remarkably, electron pairing is found upon infinitesimal doping, giving rise to Bose-Einstein condensate (BEC)-Bardeen-Cooper-Schrieffer (BCS) crossover at low density. Our theory explains puzzling behaviors of superconductivity and predicts spin-triplet pairing in electron-doped ZrNCl and WTe2.

Supercurrent diode effect and finite-momentum superconductors.

SignificanceOur work shows a fascinating application of finite-momentum superconductivity, the supercurrent diode effect, which is being reported in a growing number of experiments. We show that, under external magnetic field, Cooper pairs can acquire finite momentum so that critical currents in the direction parallel and antiparallel to the Cooper pair momentum become unequal.

Exploring the oncogenic potential of circSOD2 in clear cell renal cell carcinoma: a novel positive feedback loop.

BACKGROUND: Existing studies have found that circular RNAs (circRNAs) act as sponges for micro RNAs (miRNAs) to control downstream genes. However, the specific functionalities and mechanisms of circRNAs in human clear cell renal cell carcinoma (ccRCC) have yet to be thoroughly investigated. METHODS: Patient cohorts from online databases were used to screen candidate circRNAs, while another cohort from our hospital was obtained for validation. CircSOD2 was identified as a potential oncogenic target, and its relevant characteristics were investigated during ccRCC progression through various assays. A positive feedback loop containing downstream miRNA and its target gene were identified using bioinformatics and validated by luciferase reporter assays, RNA pull-down, and high-throughput sequencing. RESULTS: CircSOD2 expression was elevated in tumor samples and significantly correlated with overall survival (OS) and the tumor stage of ccRCC patients, which appeared in the enhanced proliferation, invasion, and migration of tumor cells. Through competitive binding to circSOD2, miR-532-3p can promote the expression of PAX5 and the progression of ccRCC, and such regulation can be salvaged by miR-532-3p inhibitor. CONCLUSION: A novel positive feedback loop, PAX5/circSOD2/miR-532-3p/PAX5 was identified in the study, indicating that the loop may play an important role in the diagnosis and prognostic prediction in ccRCC patients.

Tunable spin and valley excitations of correlated insulators in Γ-valley moiré bands.

Moiré superlattices formed from transition metal dichalcogenides support a variety of quantum electronic phases that are highly tunable using applied electromagnetic fields. While the valley degree of freedom affects optoelectronic properties in the constituent transition metal dichalcogenides, it has yet to be fully explored in moiré systems. Here we establish twisted double-bilayer WSe2 as an experimental platform to study electronic correlations within Γ-valley moiré bands. Through local and global electronic compressibility measurements, we identify charge-ordered phases at multiple integer and fractional moiré fillings. By measuring the magnetic field dependence of their energy gaps and the chemical potential upon doping, we reveal spin-polarized ground states with spin-polaron quasiparticle excitations. In addition, an applied displacement field induces a metal-insulator transition driven by tuning between Γ- and K-valley moiré bands. Our results demonstrate control over the spin and valley character of the correlated ground and excited states in this system.

Strong-Coupling Phases of Trions and Excitons in Electron-Hole Bilayers at Commensurate Densities.

We introduce density imbalanced electron-hole bilayers at a commensurate 2:1 density ratio as a platform for realizing novel phases of electrons, excitons, and trions. Through the independently tunable carrier densities and interlayer spacing, competition between kinetic energy, intralayer repulsion, and interlayer attraction yields a rich phase diagram. By a combination of theoretical analysis and numerical calculation, we find a variety of strong-coupling phases in different parameter regions, including quantum crystals of electrons, excitons, and trions. We also propose an "electron-exciton supersolid" phase that features electron crystallization and exciton superfluidity simultaneously. The material realization and experimental signature of these phases are discussed in the context of semiconductor transition metal dichalcogenide bilayers.