Tuning the Chern number in quantum anomalous Hall insulators.

A quantum anomalous Hall (QAH) state is a two-dimensional topological insulating state that has a quantized Hall resistance of h/(Ce2) and vanishing longitudinal resistance under zero magnetic field (where h is the Planck constant, e is the elementary charge, and the Chern number C is an integer)1,2. The QAH effect has been realized in magnetic topological insulators3-9 and magic-angle twisted bilayer graphene10,11. However, the QAH effect at zero magnetic field has so far been realized only for C = 1. Here we realize a well quantized QAH effect with tunable Chern number (up to C = 5) in multilayer structures consisting of alternating magnetic and undoped topological insulator layers, fabricated using molecular beam epitaxy. The Chern number of these QAH insulators is determined by the number of undoped topological insulator layers in the multilayer structure. Moreover, we demonstrate that the Chern number of a given multilayer structure can be tuned by varying either the magnetic doping concentration in the magnetic topological insulator layers or the thickness of the interior magnetic topological insulator layer. We develop a theoretical model to explain our experimental observations and establish phase diagrams for QAH insulators with high, tunable Chern number. The realization of such insulators facilitates the application of dissipationless chiral edge currents in energy-efficient electronic devices, and opens up opportunities for developing multi-channel quantum computing and higher-capacity chiral circuit interconnects.

Electrical switching of the edge current chirality in quantum anomalous Hall insulators.

A quantum anomalous Hall (QAH) insulator is a topological phase in which the interior is insulating but electrical current flows along the edges of the sample in either a clockwise or counterclockwise direction, as dictated by the spontaneous magnetization orientation. Such a chiral edge current eliminates any backscattering, giving rise to quantized Hall resistance and zero longitudinal resistance. Here we fabricate mesoscopic QAH sandwich Hall bar devices and succeed in switching the edge current chirality through thermally assisted spin-orbit torque (SOT). The well-quantized QAH states before and after SOT switching with opposite edge current chiralities are demonstrated through four- and three-terminal measurements. We show that the SOT responsible for magnetization switching can be generated by both surface and bulk carriers. Our results further our understanding of the interplay between magnetism and topological states and usher in an easy and instantaneous method to manipulate the QAH state.

Engineering Plateau Phase Transition in Quantum Anomalous Hall Multilayers.

The plateau phase transition in quantum anomalous Hall (QAH) insulators corresponds to a quantum state wherein a single magnetic domain gives way to multiple domains and then reconverges back to a single magnetic domain. The layer structure of the sample provides an external knob for adjusting the Chern number C of the QAH insulators. Here, we employ molecular beam epitaxy to grow magnetic topological insulator multilayers and realize the magnetic field-driven plateau phase transition between two QAH states with odd Chern number change ΔC. We find that critical exponents extracted for the plateau phase transitions with ΔC = 1 and ΔC = 3 in QAH insulators are nearly identical. We construct a four-layer Chalker-Coddington network model to understand the consistent critical exponents for the plateau phase transitions with ΔC = 1 and ΔC = 3. This work will motivate further investigations into the critical behaviors of plateau phase transitions with different ΔC in QAH insulators.

Electrically Controlled Anomalous Hall Effect and Orbital Magnetization in Topological Magnet MnBi_{2}Te_{4}.

We propose an intrinsic mechanism to understand the even-odd effect, namely, opposite signs of anomalous Hall resistance and different shapes of hysteresis loops for even and odd septuple layers (SLs), of MBE-grown MnBi_{2}Te_{4} thin films with electron doping. The nonzero hysteresis loops in the anomalous Hall effect and magnetic circular dichroism for even-SLs MnBi_{2}Te_{4} films originate from two different antiferromagnetic (AFM) configurations with different zeroth Landau level energies of surface states. The complex form of the anomalous Hall hysteresis loop can be understood from two magnetic transitions, a transition between two AFM states followed by a second transition to the ferromagnetic state. Our model also clarifies the relationship and distinction between axion parameter and magnetoelectric coefficient, and shows an even-odd oscillation behavior of magnetoelectric coefficients in MnBi_{2}Te_{4} films.

Crossover from Ising- to Rashba-type superconductivity in epitaxial Bi2Se3/monolayer NbSe2 heterostructures.

A topological insulator (TI) interfaced with an s-wave superconductor has been predicted to host topological superconductivity. Although the growth of epitaxial TI films on s-wave superconductors has been achieved by molecular-beam epitaxy, it remains an outstanding challenge for synthesizing atomically thin TI/superconductor heterostructures, which are critical for engineering the topological superconducting phase. Here we used molecular-beam epitaxy to grow Bi2Se3 films with a controlled thickness on monolayer NbSe2 and performed in situ angle-resolved photoemission spectroscopy and ex situ magnetotransport measurements on these heterostructures. We found that the emergence of Rashba-type bulk quantum-well bands and spin-non-degenerate surface states coincides with a marked suppression of the in-plane upper critical magnetic field of the superconductivity in Bi2Se3/monolayer NbSe2 heterostructures. This is a signature of a crossover from Ising- to Rashba-type superconducting pairings, induced by altering the Bi2Se3 film thickness. Our work opens a route for exploring a robust topological superconducting phase in TI/Ising superconductor heterostructures.

Confinement-Induced Chiral Edge Channel Interaction in Quantum Anomalous Hall Insulators.

In quantum anomalous Hall (QAH) insulators, the interior is insulating but electrons can travel with zero resistance along one-dimensional (1D) conducting paths known as chiral edge channels (CECs). These CECs have been predicted to be confined to the 1D edges and exponentially decay in the two-dimensional (2D) bulk. In this Letter, we present the results of a systematic study of QAH devices fashioned in a Hall bar geometry of different widths under gate voltages. At the charge neutral point, the QAH effect persists in a Hall bar device with a width of only ∼72 nm, implying the intrinsic decaying length of CECs is less than ∼36 nm. In the electron-doped regime, we find that the Hall resistance deviates quickly from the quantized value when the sample width is less than 1 µm. Our theoretical calculations suggest that the wave function of CEC first decays exponentially and then shows a long tail due to disorder-induced bulk states. Therefore, the deviation from the quantized Hall resistance in narrow QAH samples originates from the interaction between two opposite CECs mediated by disorder-induced bulk states in QAH insulators, consistent with our experimental observations.

Delicate Ferromagnetism in MnBi6Te10.

Tailoring magnetic orders in topological insulators is critical to the realization of topological quantum phenomena. An outstanding challenge is to find a material where atomic defects lead to tunable magnetic orders while maintaining a nontrivial topology. Here, by combining magnetization measurements, angle-resolved photoemission spectroscopy, and transmission electron microscopy, we reveal disorder-enabled, tunable magnetic ground states in MnBi6Te10. In the ferromagnetic phase, an energy gap of 15 meV is resolved at the Dirac point on the MnBi2Te4 termination. In contrast, antiferromagnetic MnBi6Te10 exhibits gapless topological surface states on all terminations. Transmission electron microscopy and magnetization measurements reveal substantial Mn vacancies and Mn migration in ferromagnetic MnBi6Te10. We provide a conceptual framework where a cooperative interplay of these defects drives a delicate change of overall magnetic ground state energies and leads to tunable magnetic topological orders. Our work provides a clear pathway for nanoscale defect-engineering toward the realization of topological quantum phases.

Momentum-Space Spin Antivortex and Spin Transport in Monolayer Pb.

Nontrivial momentum-space spin texture of electrons can be induced by spin-orbit coupling and underpins various spin transport phenomena, such as current-induced spin polarization and the spin Hall effect. In this work, we find a nontrivial spin texture, spin antivortex, can appear at certain momenta on the Γ-K line in a 2D monolayer Pb on top of SiC. Different from spin vortex due to the band degeneracy in the Rashba model, the existence of this spin antivortex is guaranteed by the Poincaré-Hopf theorem and thus topologically stable. Accompanied with this spin antivortex, a Lifshitz transition of Fermi surfaces occurs at certain momenta on the K-M line, and both phenomena are originated from the anticrossing between the j=1/2 and j=3/2 bands. A rapid variation of the response coefficients for both the current-induced spin polarization and spin Hall conductivity is found when the Fermi energy is tuned around the spin antivortex. Our work demonstrates the monolayer Pb as a potentially appealing platform for spintronic applications.

Competing Vortex Topologies in Iron-Based Superconductors.

In this Letter, we establish a new theoretical paradigm for vortex Majorana physics in the recently discovered topological iron-based superconductors (TFeSCs). While TFeSCs are widely accepted as an exemplar of topological insulators (TIs) with intrinsic s-wave superconductivity, our theory implies that such a common belief could be oversimplified. Our main finding is that the normal-state bulk Dirac nodes, usually ignored in TI-based vortex Majorana theories for TFeSCs, will play a key role of determining the vortex state topology. In particular, the interplay between TI and Dirac nodal bands will lead to multiple competing topological phases for a superconducting vortex line in TFeSCs, including an unprecedented hybrid topological vortex state that carries both Majorana bound states and a gapless dispersion. Remarkably, this exotic hybrid vortex phase generally exists in the vortex phase diagram for our minimal model for TFeSCs and is directly relevant to TFeSC candidates such as LiFeAs. When the fourfold rotation symmetry is broken by vortex-line tilting or curving, the hybrid vortex gets topologically trivialized and becomes Majorana free, which could explain the puzzle of ubiquitous trivial vortices observed in LiFeAs. The origin of the Majorana signal in other TFeSC candidates such as FeTe_{x}Se_{1-x} and CaKFe_{4}As_{4} is also interpreted within our theory framework. Our theory sheds new light on theoretically understanding and experimentally engineering Majorana physics in high-temperature iron-based systems.

Zero Magnetic Field Plateau Phase Transition in Higher Chern Number Quantum Anomalous Hall Insulators.

The plateau-to-plateau transition in quantum Hall effect under high magnetic fields is a celebrated quantum phase transition between two topological states. It can be achieved by either sweeping the magnetic field or tuning the carrier density. The recent realization of the quantum anomalous Hall (QAH) insulators with tunable Chern numbers introduces the channel degree of freedom to the dissipation-free chiral edge transport and makes the study of the quantum phase transition between two topological states under zero magnetic field possible. Here, we synthesized the magnetic topological insulator (TI)/TI pentalayer heterostructures with different Cr doping concentrations in the middle magnetic TI layers using molecular beam epitaxy. By performing transport measurements, we found a potential plateau phase transition between C=1 and C=2 QAH states under zero magnetic field. In tuning the transition, the Hall resistance monotonically decreases from h/e^{2} to h/2e^{2}, concurrently, the longitudinal resistance exhibits a maximum at the critical point. Our results show that the ratio between the Hall resistance and the longitudinal resistance is greater than 1 at the critical point, which indicates that the original chiral edge channel from the C=1 QAH state coexists with the dissipative bulk conduction channels. Subsequently, these bulk conduction channels appear to self-organize and form the second chiral edge channel in completing the plateau phase transition. Our study will motivate further investigations of this novel Chern number change-induced quantum phase transition and advance the development of the QAH chiral edge current-based electronic and spintronic devices.

Even-Odd Layer-Dependent Anomalous Hall Effect in Topological Magnet MnBi2Te4 Thin Films.

Recently, MnBi2Te4 has been demonstrated to be an intrinsic magnetic topological insulator and the quantum anomalous Hall (QAH) effect was observed in exfoliated MnBi2Te4 flakes. Here, we used molecular beam epitaxy (MBE) to grow MnBi2Te4 films with thickness down to 1 septuple layer (SL) and performed thickness-dependent transport measurements. We observed a nonsquare hysteresis loop in the antiferromagnetic state for films with thickness greater than 2 SL. The hysteresis loop can be separated into two AH components. We demonstrated that one AH component with the larger coercive field is from the dominant MnBi2Te4 phase, whereas the other AH component with the smaller coercive field is from the minor Mn-doped Bi2Te3 phase. The extracted AH component of the MnBi2Te4 phase shows a clear even-odd layer-dependent behavior. Our studies reveal insights on how to optimize the MBE growth conditions to improve the quality of MnBi2Te4 films.

Phonon Helicity Induced by Electronic Berry Curvature in Dirac Materials.

In two-dimensional insulators with time-reversal (TR) symmetry, a nonzero local Berry curvature of low-energy massive Dirac fermions can give rise to nontrivial spin and charge responses, even though the integral of the Berry curvature over all occupied states is zero. In this Letter, we present a new effect induced by the electronic Berry curvature. By studying electron-phonon interactions in BaMnSb_{2}, a prototype two-dimensional Dirac material possessing two TR-related massive Dirac cones, we find that the nonzero local Berry curvature of electrons can induce a phonon angular momentum. The direction of this phonon angular momentum is locked to the phonon propagation direction, and thus we refer to it as "phonon helicity" in a way that is reminiscent of electron helicity in spin-orbit-coupled electronic systems. We discuss possible experimental probes of such phonon helicity.

Gapless Criterion for Crystals from Effective Axion Field.

Gapless criteria that can efficiently determine whether a crystal is gapless or not are particularly useful for identifying topological semimetals. In this work, we propose a sufficient gapless criterion for three-dimensional noninteracting crystals, based on the simplified expressions for the bulk average value of the static axion field. The brief logic is that two different simplified expressions give the same value in an insulator, and thus the gapless phase can be detected by the mismatch of them. We demonstrate the effectiveness of the gapless criterion in the magnetic systems with space groups 26 and 13, where mirror, glide, and inversion symmetries provide the simplified expressions. In particular, the gapless criterion can identify gapless phases that are missed by the symmetry-representation approach, as illustrated by space group 26. Our proposal serves as a guiding principle for future discovery of topological semimetals.

Anomalous Quantum Oscillations of Interacting Electron-Hole Gases in Inverted Type-II InAs/GaSb Quantum Wells.

We report magnetotransport studies of InAs/GaSb bilayer quantum wells in a regime where the interlayer tunneling between the electron and hole gases is suppressed. When the chemical potential is tuned close to the charge neutrality point, we observe anomalous quantum oscillations that are inversely periodic in magnetic field and that have an extremely high frequency despite the highly insulating regime where they are observed. The seemingly contradictory coexistence of a high sheet resistance and high frequency quantum oscillations in the charge neutrality regime cannot be understood within the single-particle picture. We propose an interpretation that attributes our experimental observation to the Coulomb drag between the electron and hole gases, thus providing strong evidence of the significance of Coulomb interaction in this topological insulator.

Lattice-Symmetry-Assisted Second-Order Topological Superconductors and Majorana Patterns.

We propose a realization of the lattice-symmetry-assisted second-order topological superconductors with corner Majorana zero modes (MZM) based on two-dimensional topological insulators (2DTI). The lattice symmetry can naturally lead to the anisotropic coupling of edge states along different directions to the in-plane magnetic field and conventional s-wave pairings, thus leading to a single MZM located at the corners for various lattice patterns. In particular, we focus on the 2DTI with D_{3d} lattice symmetry and found different types of gap opening for the edge states along the armchair and zigzag edges in a broad range of parameters. As a consequence, a single MZM exists at the corner between the zigzag and armchair edges, and is robust against weakly broken lattice symmetry. We propose to realize such corner MZMs in a variety of polygon patterns, such as triangles and quadrilaterals. We further show their potentials in building the Majorana network through constructing the Majorana Y junction under an in-plane magnetic field.

Observation of Hourglass Nodal Lines in Photonics.

Nodal line semimetals exhibiting line degeneracies in three-dimensional momentum space have been demonstrated recently. In general, the presence of nodal line semimetals is protected by special symmetries, such as mirror symmetry. However, these symmetries are usually necessary but not sufficient conditions, as nodal lines can be annihilated even without breaking them. Very recently, nodal line semimetal possessing an hourglass-shaped band structure emerges as a more robust candidate, where line degeneracies cannot be annihilated while preserving all underlying spatial symmetries. Here, for the first time, we experimentally demonstrate the presence of an hourglass nodal line (HNL) in photonic metacrystal at microwave frequency. We observe the HNL through near-field scanning of the spatial fields, followed by subsequent Fourier transformations. The observed photonic HNL resides in a clean and large frequency interval and is immune to symmetry preserving perturbation, which provides an ideal robust platform for photonic applications, such as anomalous quantum oscillation, spontaneous emission and resonant scattering.

Crystalline Symmetry-Protected Majorana Mode in Number-Conserving Dirac Semimetal Nanowires.

One of the cornerstones for topological quantum computations is the Majorana zero mode, which has been intensively searched in fractional quantum Hall systems and topological superconductors. Several recent works suggest that such an exotic mode can also exist in a one-dimensional (1D) interacting double-wire setup even without long-range superconductivity. A notable instability in these proposals comes from interchannel single-particle tunneling that spoils the topological ground state degeneracy. Here we show that a 1D Dirac semimetal (DSM) nanowire is an ideal number-conserving platform to realize such Majorana physics. By inserting magnetic flux, a DSM nanowire is driven into a 1D crystalline-symmetry-protected semimetallic phase. Interaction enables the emergence of boundary Majorana zero modes, which is robust as a result of crystalline symmetry protection. We also explore several experimental consequences of Majorana signals.

Cucurbit[7]uril-Driven Host-Guest Chemistry for Reversible Intervention of 5-Formylcytosine-Targeted Biochemical Reactions.

5-Formylcytosine (5fC) is identified as one of the key players in active DNA demethylation and also as an epigenetic mark in mammals, thus representing a novel attractive target to chemical intervention. The current study represents an attempt to develop a reversible 5fC-targeted intervention tool. A supramolecular aldehyde reactive probe was therefore introduced for selective conversion of the 5fC to 5fC-AD nucleotide. Using various methods, we demonstrate that cucurbit[7]uril (CB7) selectively targets the 5fC-AD nucleotide in DNA, however, the binding of CB7 to 5fC-AD does not affect the hydrogen bonding properties of natural nucleobases in duplex DNA. Importantly, CB7-driven host-guest chemistry has been applied for reversible intervention of a variety of 5fC-targeted biochemical reactions, including restriction endonuclease digestion, DNA polymerase elongation, and polymerase chain reaction. On the basis of the current study, the macrocyclic CB7 creates obstructions that, through steric hindrance, prevent the enzyme from binding to the substrate, whereas the CB7/5fC-AD host-guest interactions can be reversed by treatment with adamantanamine. Moreover, fragment- and site-specific identification of 5fC modification in DNA has been accomplished without sequence restrictions. These findings thus show promising potential of host-guest chemistry for DNA/RNA epigenetics.

Unconventional Superconductivity in Bilayer Transition Metal Dichalcogenides.

Bilayer transition metal dichalcogenides (TMDs) belong to a class of materials with two unique features, the coupled spin-valley-layer degrees of freedom and the crystal structure that is globally centrosymmetric but locally noncentrosymmetric. In this Letter, we will show that the combination of these two features can lead to a rich phase diagram for unconventional superconductivity, including intralayer and interlayer singlet pairings and interlayer triplet pairings, in bilayer superconducting TMDs. In particular, we predict that the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov state can exist in bilayer TMDs under an in-plane magnetic field. We also discuss the experimental relevance of our results and possible experimental signatures.

Fingerprints of a Bosonic Symmetry-Protected Topological State in a Quantum Point Contact.

In this work, we study the transport through a quantum point contact for bosonic helical liquid that exists at the edge of a bilayer graphene under a strong magnetic field. We identify "smoking gun" transport signatures to distinguish a bosonic symmetry-protected topological (BSPT) state from a fermionic two-channel quantum spin Hall (QSH) state in this system. In particular, a novel charge-insulator-spin-conductor phase is found for the BSPT state, while either the charge-insulator-spin-insulator or the charge-conductor-spin-conductor phase is expected for the two-channel QSH state. Consequently, a simple transport measurement will reveal the fingerprint of bosonic topological physics in bilayer graphene systems.