Fermi Surface Spin Texture and Topological Superconductivity in Spin-Orbit Free Noncollinear Antiferromagnets.

We explore the relationship among the magnetic ordering in real space, the resulting spin texture on the Fermi surface, and the related superconducting gap structure in noncollinear antiferromagnetic metals without spin-orbit coupling. Via a perturbative approach, we show that noncollinear magnetic ordering in a metal can generate momentum-dependent spin texture on its Fermi surface, even in the absence of spin-orbit coupling, if the metal has more than three sublattices in its magnetic unit cell. Thus, our theory naturally extends the idea of altermagnetism to noncollinear spin structures. When superconductivity is developed in a magnetic metal, as the gap-opening condition is strongly constrained by the spin texture, the nodal structure of the superconducting state is also enforced by the magnetism-induced spin texture. Taking the noncollinear antiferromagnet on the kagome lattice as a representative example, we demonstrate how the Fermi surface spin texture induced by noncollinear antiferromagnetism naturally leads to odd-parity spin-triplet superconductivity with nontrivial topological properties.

Transverse Magnetization in Spin-Orbit Coupled Antiferromagnets.

Some antiferromagnets under a magnetic field develop magnetization perpendicular to the field as well as more conventional ones parallel to the field. So far, the transverse magnetization (TM) has been attributed to either the spin canting effect or the presence of cluster magnetic multipolar ordering. However, a general theory of TM based on microscopic understanding is still missing. Here, we construct a general microscopic theory of TM in antiferromagnets with cluster magnetic multipolar ordering by considering classical spin Hamiltonians with spin anisotropy that arises from the spin-orbit coupling. First, from general symmetry analysis, we show that TM can appear only when all crystalline symmetries are broken other than the antiunitary mirror, antiunitary twofold rotation, and inversion symmetries. Moreover, by analyzing spin Hamiltonians, we show that TM always appears when the degenerate ground state manifold of the spin Hamiltonian is discrete, as long as it is not prohibited by symmetry. On the other hand, when the degenerate ground state manifold is continuous, TM generally does not appear except when the magnetic field direction and the spin configuration satisfy specific geometric conditions under single-ion anisotropy. Finally, we show that TM can induce the anomalous planar Hall effect, a unique transport phenomenon that can be used to probe multipolar antiferromagnetic structures. We believe that our theory provides a useful guideline for understanding the anomalous magnetic responses of the antiferromagnets with complex magnetic structures.

Higher harmonics in planar Hall effect induced by cluster magnetic multipoles.

Antiferromagnetic (AFM) materials are attracting tremendous attention due to their spintronic applications and associated novel topological phenomena. However, detecting and identifying the spin configurations in AFM materials are quite challenging due to the absence of net magnetization. Herein, we report the practicality of utilizing the planar Hall effect (PHE) to detect and distinguish "cluster magnetic multipoles" in AFM Nd2Ir2O7 (NIO-227) fully strained films. By imposing compressive strain on the spin structure of NIO-227, we artificially induced cluster magnetic multipoles, namely dipoles and A2- and T1-octupoles. Importantly, under magnetic field rotation, each magnetic multipole exhibits distinctive harmonics of the PHE oscillation. Moreover, the planar Hall conductivity has a nonlinear magnetic field dependence, which can be attributed to the magnetic response of the cluster magnetic octupoles. Our work provides a strategy for identifying cluster magnetic multipoles in AFM systems and would promote octupole-based AFM spintronics.

Geometric characterization of anomalous Landau levels of isolated flat bands.

According to the Onsager's semiclassical quantization rule, the Landau levels of a band are bounded by its upper and lower band edges at zero magnetic field. However, there are two notable systems where the Landau level spectra violate this expectation, including topological bands and flat bands with singular band crossings, whose wave functions possess some singularities. Here, we introduce a distinct class of flat band systems where anomalous Landau level spreading (LLS) appears outside the zero-field energy bounds, although the relevant wave function is nonsingular. The anomalous LLS of isolated flat bands are governed by the cross-gap Berry connection that measures the wave-function geometry of multi bands. We also find that symmetry puts strong constraints on the LLS of flat bands. Our work demonstrates that an isolated flat band is an ideal system for studying the fundamental role of wave-function geometry in describing magnetic responses of solids.

Colossal angular magnetoresistance in ferrimagnetic nodal-line semiconductors.

Efficient magnetic control of electronic conduction is at the heart of spintronic functionality for memory and logic applications1,2. Magnets with topological band crossings serve as a good material platform for such control, because their topological band degeneracy can be readily tuned by spin configurations, dramatically modulating electronic conduction3-10. Here we propose that the topological nodal-line degeneracy of spin-polarized bands in magnetic semiconductors induces an extremely large angular response of magnetotransport. Taking a layered ferrimagnet, Mn3Si2Te6, and its derived compounds as a model system, we show that the topological band degeneracy, driven by chiral molecular orbital states, is lifted depending on spin orientation, which leads to a metal-insulator transition in the same ferrimagnetic phase. The resulting variation of angular magnetoresistance with rotating magnetization exceeds a trillion per cent per radian, which we call colossal angular magnetoresistance. Our findings demonstrate that magnetic nodal-line semiconductors are a promising platform for realizing extremely sensitive spin- and orbital-dependent functionalities.

Topological acoustic triple point.

Acoustic phonon is a classic example of triple degeneracy point in band structure. This triple point always appears in phonon spectrum because of the Nambu-Goldstone theorem. Here, we show that this triple point can carry a topological charge [Formula: see text] that is a property of three-band systems with space-time-inversion symmetry. The charge [Formula: see text] can equivalently be characterized by the skyrmion number of the longitudinal mode, or by the Euler number of the transverse modes. We call triple points with nontrivial [Formula: see text] the topological acoustic triple point (TATP). TATP can also appear at high-symmetry momenta in phonon and spinless electron spectrums when Oh or Th groups protect it. The charge [Formula: see text] constrains the nodal structure and wavefunction texture around TATP, and can induce anomalous thermal transport of phonons and orbital Hall effect of electrons. Gapless points protected by the Nambu-Goldstone theorem form a new platform to study the topology of band degeneracies.

Sign-tunable anomalous Hall effect induced by two-dimensional symmetry-protected nodal structures in ferromagnetic perovskite thin films.

Magnetism and spin-orbit coupling are two quintessential ingredients underlying topological transport phenomena in itinerant ferromagnets. When spin-polarized bands support nodal points/lines with band degeneracy that can be lifted by spin-orbit coupling, the nodal structures become a source of Berry curvature, leading to a large anomalous Hall effect. However, two-dimensional systems can possess stable nodal structures only when proper crystalline symmetry exists. Here we show that two-dimensional spin-polarized band structures of perovskite oxides generally support symmetry-protected nodal lines and points that govern both the sign and the magnitude of the anomalous Hall effect. To demonstrate this, we performed angle-resolved photoemission studies of ultrathin films of SrRuO3, a representative metallic ferromagnet with spin-orbit coupling. We show that the sign-changing anomalous Hall effect upon variation in the film thickness, magnetization and chemical potential can be well explained by theoretical models. Our work may facilitate new switchable devices based on ferromagnetic ultrathin films.

Emergence of topological superconductivity in doped topological Dirac semimetals under symmetry-lowering lattice distortions.

Recently, unconventional superconductivity having a zero-bias conductance peak is reported in doped topological Dirac semimetal (DSM) with lattice distortion. Motivated by the experiments, we theoretically study the possible symmetry-lowering lattice distortions and their effects on the emergence of unconventional superconductivity in doped topological DSM. We find four types of symmetry-lowering lattice distortions that reproduce the crystal symmetries relevant to experiments from the group-theoretical analysis. Considering inter-orbital and intra-orbital electron density-density interactions, we calculate superconducting phase diagrams. We find that the lattice distortions can induce unconventional superconductivity hosting gapless surface Andreev bound states (SABS). Depending on the lattice distortions and superconducting pairing interactions, the unconventional inversion-odd-parity superconductivity can be either topological nodal superconductivity hosting a flat SABS or topological crystalline superconductivity hosting a gapless SABS. Remarkably, the lattice distortions increase the superconducting critical temperature, which is consistent with the experiments. Our work opens a pathway to explore and control pressure-induced topological superconductivity in doped topological semimetals.

Correlated Magnetic Weyl Semimetal State in Strained Pr2 Ir2 O7.

Correlated topological phases (CTPs) with interplay between topology and electronic correlations have attracted tremendous interest in condensed matter physics. Therein, correlated Weyl semimetals (WSMs) are rare in nature and, thus, have so far been less investigated experimentally. In particular, the experimental realization of the interacting WSM state with logarithmic Fermi velocity renormalization has not been achieved yet. Here, experimental evidence of a correlated magnetic WSM state with logarithmic renormalization in strained pyrochlore iridate Pr2 Ir2 O7 (PIO) which is a paramagnetic Luttinger semimetal in bulk, is reported. Benefitting from epitaxial strain, "bulk-absent" all-in-all-out antiferromagnetic ordering can be stabilized in PIO film, which breaks time-reversal symmetry and leads to a magnetic WSM state. With further analysis of the experimental data and renormalization group calculations, an interacting Weyl liquid state with logarithmically renormalized Fermi velocity, similar to that in graphene, is found, dressed by long-range Coulomb interactions. This work highlights the interplay of strain, magnetism, and topology with electronic correlations, and paves the way for strain-engineering of CTPs in pyrochlore iridates.

Odd-Parity Spin-Triplet Superconductivity in Centrosymmetric Antiferromagnetic Metals.

We propose a route to achieve odd-parity spin-triplet (OPST) superconductivity in metallic collinear antiferromagnets with inversion symmetry. Owing to the existence of hidden antiunitary symmetry, which we call the effective time-reversal symmetry (eTRS), the Fermi surfaces of ordinary antiferromagnetic metals are generally spin degenerate, and spin-singlet pairing is favored. However, by introducing a local inversion symmetry breaking perturbation that also breaks the eTRS, we can lift the degeneracy to obtain spin-polarized Fermi surfaces. In the weak-coupling limit, the spin-polarized Fermi surfaces constrain the electrons to form spin-triplet Cooper pairs with odd parity. Interestingly, all the odd-parity superconducting ground states we obtained host nontrivial band topologies manifested as chiral topological superconductors, second-order topological superconductors, and nodal superconductors. We propose that double perovskite oxides with collinear antiferromagnetic or ferrimagnetic ordering, such as SrLaVMoO_{6}, are promising candidate systems where our theoretical ideas can be applied to.

Phonon Angular Momentum Hall Effect.

The spin Hall effect is the transverse flow of the electron spin in response to an external electric field. Similarly, the temperature gradient in magnets can drive a transverse flow of the magnon spin, which provides a thermal alternative for spin manipulation. Recently, phonon angular momentum (PAM), the angular momentum of atoms resulting from their orbital motion around their equilibrium positions, has garnered attention as a quantity analogous to the magnon spin. Here, we report that the temperature gradient generally induces a transverse flow of PAM, which we term the phonon angular momentum Hall effect (PAMHE). The PAMHE arises whenever there are transverse and longitudinal acoustic phonons, and it is therefore ubiquitous in condensed matter systems. As a consequence of the PAMHE, PAM accumulates at the crystal edges. When the atoms in the crystal carry a non-zero Born effective charge, the edge PAM induces edge magnetization, which can be observed through optical measurement.

Quantum distance and anomalous Landau levels of flat bands.

Semiclassical quantization of electronic states under a magnetic field, as proposed by Onsager, describes not only the Landau level spectrum but also the geometric responses of metals under a magnetic field1-5. Even in graphene with relativistic energy dispersion, Onsager's rule correctly describes the π Berry phase, as well as the unusual Landau level spectrum of Dirac particles6,7. However, it is unclear whether this semiclassical idea is valid in dispersionless flat-band systems, in which an infinite number of degenerate semiclassical orbits are allowed. Here we show that the semiclassical quantization rule breaks down for a class of dispersionless flat bands called 'singular flat bands'8. The singular flat band has a band crossing with another dispersive band that is enforced by the band-flatness condition, and shows anomalous magnetic responses. The Landau levels of a singular flat band develop in the empty region in which no electronic states exist in the absence of a magnetic field, and exhibit an unusual 1/n dependence on the Landau level index n, which results in diverging orbital magnetic susceptibility. The total energy spread of the Landau levels of a singular flat band is determined by the quantum geometry of the relevant Bloch states, which is characterized by their Hilbert-Schmidt quantum distance. We show that there is a universal and simple relationship between the total Landau level spread of a flat band and the maximum Hilbert-Schmidt quantum distance, which can be verified in various candidate materials. The results indicate that the anomalous Landau level spectrum of flat bands is promising for the direct measurement of the quantum geometry of wavefunctions in condensed matter.

Strain engineering of the magnetic multipole moments and anomalous Hall effect in pyrochlore iridate thin films.

The recent observation of the anomalous Hall effect (AHE) without notable magnetization in antiferromagnets has suggested that ferromagnetic ordering is not a necessary condition. Thus, recent theoretical studies have proposed that higher-rank magnetic multipoles formed by clusters of spins (cluster multipoles) can generate the AHE without magnetization. Despite such an intriguing proposal, controlling the unconventional AHE by inducing these cluster multipoles has not been investigated. Here, we demonstrate that strain can manipulate the hidden Berry curvature effect by inducing the higher-rank cluster multipoles in spin-orbit-coupled antiferromagnets. Observing the large AHE on fully strained antiferromagnetic Nd2Ir2O7 thin films, we prove that strain-induced cluster T 1-octupoles are the only source of observed AHE. Our results provide a previously unidentified pathway for generating the unconventional AHE via strain-induced magnetic structures and establish a platform for exploring undiscovered topological phenomena via strain in correlated materials.

Direct Observation of Flatband Loop States Arising from Nontrivial Real-Space Topology.

Topological properties of lattices are typically revealed in momentum space using concepts such as the Chern number. Here, we study unconventional loop states, namely, the noncontractible loop states (NLSs) and robust boundary modes, mediated by nontrivial topology in real space. While such states play a key role in understanding fundamental physics of flatband systems, their experimental observation has been hampered because of the challenge in realizing desired boundary conditions. Using a laser-writing technique, we optically establish photonic kagome lattices with both an open boundary by properly truncating the lattice, and a periodic boundary by shaping the lattice into a Corbino geometry. We thereby demonstrate the robust boundary modes winding around the entire edge of the open lattice and, more directly, the NLSs winding in a closed loop akin to that in a torus. We prove that the NLSs due to real-space topology persist in ideal Corbino-shaped kagome lattices of arbitrary size. Our results could be of great importance for our understanding of the singular flatbands and the intriguing physics phenomenon applicable for strongly interacting systems.

Thermal Hall Effect, Spin Nernst Effect, and Spin Density Induced by a Thermal Gradient in Collinear Ferrimagnets from Magnon-Phonon Interaction.

We theoretically study the intrinsic thermal Hall and spin Nernst effect in collinear ferrimagnets on a honeycomb lattice with broken inversion symmetry. The broken inversion symmetry allows in-plane Dzyaloshinskii-Moriya interaction between the nearest neighbors, which does not affect the linear spin wave theory. However, the Dzyaloshinskii-Moriya interaction induces large Berry curvature in the magnetoelastic excitations through the magnon-phonon interaction (MPI) to produce thermal Hall current. Furthermore, the magnetoelastic excitations transport spin, which is inherited from the magnons. Therefore, spin Nernst current accompanies the thermal Hall current. Because the MPI does not conserve the spin, we examine the spatial distribution of spin induced by a thermal gradient in the system having a stripe geometry. We find that spin is accumulated at the edges, reflecting the spin Nernst current. We also find that the total spin of the system-and, therefore, the magnetization-is changed, because of the thermal gradient and MPI.

Band Topology and Linking Structure of Nodal Line Semimetals with Z_{2} Monopole Charges.

We study the band topology and the associated linking structure of topological semimetals with nodal lines carrying Z_{2} monopole charges, which can be realized in three-dimensional systems invariant under the combination of inversion P and time reversal T when spin-orbit coupling is negligible. In contrast to the well-known PT-symmetric nodal lines protected only by the π Berry phase, in which a single nodal line can exist, the nodal lines with Z_{2} monopole charges should always exist in pairs. We show that a pair of nodal lines with Z_{2} monopole charges is created by a double band inversion process and that the resulting nodal lines are always linked by another nodal line formed between the two topmost occupied bands. It is shown that both the linking structure and the Z_{2} monopole charge are the manifestation of the nontrivial band topology characterized by the second Stiefel-Whitney class, which can be read off from the Wilson loop spectrum. We show that the second Stiefel-Whitney class can serve as a well-defined topological invariant of a PT-invariant two-dimensional insulator in the absence of Berry phase. Based on this, we propose that pair creation and annihilation of nodal lines with Z_{2} monopole charges can mediate a topological phase transition between a normal insulator and a three-dimensional weak Stiefel-Whitney insulator. Moreover, using first-principles calculations, we predict ABC-stacked graphdiyne as a nodal line semimetal (NLSM) with Z_{2} monopole charges having the linking structure. Finally, we develop a formula for computing the second Stiefel-Whitney class based on parity eigenvalues at inversion-invariant momenta, which is used to prove the quantized bulk magnetoelectric response of NLSMs with Z_{2} monopole charges under a T-breaking perturbation.

Large anomalous Hall current induced by topological nodal lines in a ferromagnetic van der Waals semimetal.

Topological semimetals host electronic structures with several band-contact points or lines and are generally expected to exhibit strong topological responses. Up to now, most work has been limited to non-magnetic materials and the interplay between topology and magnetism in this class of quantum materials has been largely unexplored. Here we utilize theoretical calculations, magnetotransport and angle-resolved photoemission spectroscopy to propose Fe3GeTe2, a van der Waals material, as a candidate ferromagnetic (FM) nodal line semimetal. We find that the spin degree of freedom is fully quenched by the large FM polarization, but the line degeneracy is protected by crystalline symmetries that connect two orbitals in adjacent layers. This orbital-driven nodal line is tunable by spin orientation due to spin-orbit coupling and produces a large Berry curvature, which leads to a large anomalous Hall current, angle and factor. These results demonstrate that FM topological semimetals hold significant potential for spin- and orbital-dependent electronic functionalities.

Two-Dimensional Dirac Fermions Protected by Space-Time Inversion Symmetry in Black Phosphorus.

We report the realization of novel symmetry-protected Dirac fermions in a surface-doped two-dimensional (2D) semiconductor, black phosphorus. The widely tunable band gap of black phosphorus by the surface Stark effect is employed to achieve a surprisingly large band inversion up to ∼0.6 eV. High-resolution angle-resolved photoemission spectra directly reveal the pair creation of Dirac points and their movement along the axis of the glide-mirror symmetry. Unlike graphene, the Dirac point of black phosphorus is stable, as protected by space-time inversion symmetry, even in the presence of spin-orbit coupling. Our results establish black phosphorus in the inverted regime as a simple model system of 2D symmetry-protected (topological) Dirac semimetals, offering an unprecedented opportunity for the discovery of 2D Weyl semimetals.

Magnetic-field induced multiple topological phases in pyrochlore iridates with Mott criticality.

The interplay between electron correlation and spin-orbit coupling in solids has been proven to be an abundant gold mine for emergent topological phases. Here we report the results of systematic magnetotransport study on bandwidth-controlled pyrochlore iridates R2Ir2O7 near quantum metal-insulator transition (MIT). The application of a magnetic field along [001] crystallographic direction (H//[001]) significantly decreases resistivity while producing a unique Hall response, which indicates the emergence of the novel semi-metallic state in the course of the magnetic transformation from all-in all-out (AIAO, 4/0) to 2-in 2-out (2/2) spin configuration. For H//[111] that favours 3-in 1-out (3/1) configuration, by contrast, the resistivity exhibits saturation at a relatively high value typical of a semimetal. The observed properties can be identified to reflect the emergence of multiple Weyl semimetal states with varying numbers of Weyl points and line nodes in respective spin configurations. With tuning effective bandwidth, all these states appear to concentrate around the quantum MIT region, which may open a promising venue for topological phenomena and functions.