Weyl semimetals and higher-order topological phases represent two fundamental yet distinct classes of topological matter. While both have been extensively studied in classical-wave systems, their coexistence and controllable transition remain largely unexplored. Meanwhile, emulating three-dimensional spin-orbit couplings, which are crucial for realizing abroad class of higher-dimensional synthetic topological phases, continues to pose significant experimental challenges. Here, we experimentally emulate three-dimensional spin-orbit coupling in a circuit metamaterial and show that tuning the coupling strength into a dimerized configuration enables the coexistence of and a controllable transition between a Weyl semimetal phase and a third-order topological insulator phase. We observe hallmark signatures of both phases, including Fermi arcs revealed by frequency-resolved spectroscopy and topological corner modes probed via local density-of-states measurements. Interestingly, the corner mode degeneracy doubles compared to that in the canonical Benalcazar-Bernevig-Hughes model, signaling an enriched topological structure. Our study establishes a fundamental connection between two paradigmatic topological phases and paves the way for further exploring spin-orbit-coupling-induced exotic higher-dimensional topological phases.

The study explores a novel class of unconventional superconductivity characterized by topologically obstructed pairing orders termed monopole pairing. This superconducting state emerges from the interplay of geometric phases, band topology, and electron interactions in systems such as doped magnetic Weyl semimetals. The analysis extends the concept of Berry phase from single-particle quantum states to Cooper pairs, revealing that pairing between Fermi surfaces with distinct monopole (Chern) charges induces a nonzero monopole charge for the Cooper pair. This topological feature enforces a nodal superconducting gap structure fundamentally distinct from known s-, p-, or d-wave symmetries, necessitating description via monopole harmonic functions rather than conventional spherical harmonics. The monopole pairing order exhibits a shifted angular momentum quantum number and breaks inversion symmetry, resulting in a total vorticity on the Fermi surface that differs from established unconventional superconductors. Proposed material realizations include magnetically doped Dirac semimetals where Weyl points and associated Fermi surfaces with opposite Chern numbers arise. Phase-sensitive Josephson junctions between monopole superconductors and conventional s-wave superconductors are designed to detect the unique angular momentum and topological signatures, including characteristic 2π and 4π periodicities linked to Majorana surface modes. The framework also predicts novel bulk-boundary correspondences, such as Majorana arcs connecting Fermi surface projections. This work provides a topological classification of superconducting orders beyond traditional paradigms and suggests experimental probes to identify monopole pairing, offering new avenues to investigate many-body effects in topological quantum materials.

Dirac material LaCuSb2 shows anisotropic superconducting response to applied magnetic fields.

Prussian blue analogs (PBAs) are widely recognized as promising candidates for aqueous zinc-ion batteries (AZIBs) due to their stable three-dimensional framework structure. However, their further development is limited by their low specific capacity and unsatisfactory cycling performance, primarily caused by phase transformation during charge-discharge cycles. Herein, we employed a high-entropy strategy to introduce five different metal elements (Fe, Co, Ni, Mn, and Cu) into the nitrogen-coordinated Ma sites of PBAs, forming a high-entropy Prussian blue analog (HEPBA). By leveraging the cocktail effect of the high-entropy strategy, the phase transformation in the HEPBA was significantly suppressed. Consequently, the HEPBA as an AZIB cathode delivered a high reversible specific capacity of 132.1 mAh g-1 at 0.1 A g-1, and showed exceptional cycling stability with 84.7% capacity retention after 600 cycles at 0.5 A g-1. This work provides innovative insights into the rational design of advanced cathode materials for AZIBs.

Distinct from familiar s-, p-, or d-wave pairings, the monopole superconducting order represents a novel class of pairing order arising from nontrivial monopole charge of the Cooper pair. In the weak-coupling regime, this order can emerge when pairing occurs between Fermi surfaces with different Chern numbers in, for example, doped Weyl semimetal systems. However, the phase of monopole pairing order is not well-defined over an entire Fermi surface, making it challenging to design experiments sensitive to both its symmetry and topology. To address this, we propose a scheme based on symmetry and topological principles to identify this elusive pairing order through a set of phase-sensitive Josephson experiments. By examining the discrepancy between global and local angular momentum of the pairing order, we can unveil the monopole charge of the pairing order, including for models with higher pair monopole charge |qp| = 1, 2, and 3. We demonstrate the proposed probe of monopole pairing order through analytic and numerical studies of Josephson coupling in models of monopole superconductor junctions. This work opens a promising avenue to uncover the unique topological properties of monopole pairing orders and to distinguish them from known pairing orders based on spherical harmonic symmetry.

Topological corner states are exotic topological boundary states that are bounded to zero-dimensional geometry even the dimension of systems is large than one. As an elegant physical correspondence, their numbers are dictated by the bulk topological invariants. So far, all previous realizations of HOTIs are hallmarked by ℤ_2 topological invariants and therefore have only one corner state at each corner. Here we report an experimental demonstration of ℤ-class HOTI phases in electric circuits, hosting N corner modes at each single corner structure. By measuring the impedance spectra and distributions, we clearly demonstrate the ℤ-class HOTI phases, including the zero-energy corner modes and their density distributions. Moreover, we reveal that the local density of states (LDOS) at each corner for N=4 are equally distributed at four corner unit cells, prominently differing from ℤ_2-class case where the LDOS only dominates over one corner unit cell. Our results extend the observation of HOTIs from ℤ_2 class to ℤ class and the coexistence of spatially overlapped large number of corner modes which may enable exotic topological devices that require high degeneracy boundary states.

When superconducting pairing occurs between Fermi surfaces with different Chern numbers, the Cooper pairs experience a nontrivial pair Berry phase and effective pair monopole charge that enforces nodal monopole harmonic superconducting order beyond the familiar s -, p -, and d -wave superconductors. When magnetically doped, the Dirac semimetal Cd 3 As 2 features Fermi pockets enclosing Weyl nodes with chiralities χ = ± 1 , ± 2. This material serves as a candidate platform for realizing monopole superconductivity with pair monopole charges q p = 1 or 2, depending on the chemical potential. We demonstrate the distinctions in the superconducting phase winding due to pairing with different pair monopole charges and due to pairings in different irreducible representations of the C 4 h symmetry of magnetically doped Cd 3 As 2 . In all cases, the phase winding patterns are subject to the topologically invariant total phase winding, which depends only on the pair monopole charge and guarantees nodes in the superconducting order for q p > 0.

Conventional BCS superconductors are expected to exhibit a conductivity with vanishing dissipation with decreasing temperature. While bulk physical properties measurements indicate PdPb$_{2}$ is a conventional superconductor with a $T_c$ of 3.0 K, measurements of surface impedance through the microwave cavity perturbation technique indicate a large, non-vanishing dissipative component below $T_c$ that is at odds with conventional superconductivity. We demonstrate PdPb$_2$ to be a possible topological superconductor with a fully gapped bulk and a dissipative Majorana fluid surface.

We consider a two-layer multi-orbital system consisting of a $p_x$, $p_y$-orbital honeycomb lattice layer and an $f$-orbital triangular lattice layer with sites aligned with the centers of the honeycomb plaquettes. With an appropriately tuned chemical potential difference between these two layers, the system exhibits a flat band with provably ferromagnetic ground states at half filling of the band in the presence of intra-orbital Hubbard interactions and Hund's coupling. Away from half filling, the interacting system admits a percolation representation, where the ground state space is spanned by maximum-spin clusters of localized single-particle states. A paramagnetic-ferromagnetic transition occurs as the band approaches half filling and the ground states become dominated by states with a large cluster.

We study a class of topological charge density wave states exhibiting monopole harmonic symmetries. The density wave ordering is equivalent to pairing in the particle-hole channel due to Fermi surface nesting under interactions. When electron and hole Fermi surfaces carry different Chern numbers, the particle-hole pairing exhibits a nontrivial Berry phase inherited from band-structure topology independent of the concrete density wave ordering mechanism. The associated density wave gap functions become nodal, and the net nodal vorticity is determined by the monopole charge of the pairing Berry phase. The gap function nodes become zero-energy Weyl nodes of the bulk spectra of quasiparticle excitations. These states can occur in doped Weyl semimetals with nested electron and hole Fermi surfaces enclosing Weyl nodes of the same chirality in the weak-coupling regime. Topologically nontrivial low-energy Fermi arc surface states appear in the density wave ordering state as a consequence of the emergent zero-energy Weyl nodes.

We report the magnetic structure and electronic properties of the honeycomb antiferromagnet NaNi2BiO5.66. We find magnetic order with moments along the c axis for temperatures below T-c1 = 6.3(1) K and then in the honeycomb plane for T < T-c2 = 4.8(1) K with a counterrotating pattern and an ordering wave vector q = (1/3, 1/3, 0.15(1)). Density functional theory and electron spin resonance indicate this is high-spin Ni3+ magnetism 3 1, near a high to low spin transition. The ordering wave vector, in-plane magnetic correlations, missing entropy, spin state, and superexchange pathways are all consistent with bond-dependent Kitaev-Gamma-Heisenberg exchange interactions in NaNi2BiO6-delta.

We generalize the concept of Berry connection of the single-electron band structure to that of a two-particle Cooper pairing state between two Fermi surfaces with opposite Chern numbers. Because of underlying Fermi surface topology, the pairing Berry phase acquires nontrivial monopole structure. Consequently, pairing gap functions have topologically protected nodal structure as vortices in the momentum space with the total vorticity solely determined by the pair monopole charge q_{p}. The nodes of gap function behave as the Weyl-Majorana points of the Bogoliubov-de Gennes pairing Hamiltonian. Their relation with the connection patterns of the surface modes from the Weyl band structure and the Majorana surface modes inside the pairing gap is also discussed. Under the approximation of spherical Fermi surfaces, the pairing symmetry are represented by monopole harmonic functions. The lowest possible pairing channel carries angular momentum number j=|q_{p}|, and the corresponding gap functions are holomorphic or antiholomorphic functions on Fermi surfaces. After projected on the Fermi surfaces with nontrivial topology, all the partial-wave channels of pairing interactions acquire the monopole charge q_{p} independent of concrete pairing mechanism.

We report the magnetic structure and electronic properties of the honeycomb antiferromagnet NaNi_2BiO_5.66. We find magnetic order with moments along the c axis for temperatures below T_c1=6.3(1) K and then in the honeycomb plane for T < T_c2=4.8(1) K with a counterrotating pattern and an ordering wave vector q=(1/3,1/3, 0.15(1)). Density functional theory and electron spin resonance indicate this is high-spin Ni^3+ magnetism near a high to low spin transition. The ordering wave vector, in-plane magnetic correlations, missing entropy, spin state, and superexchange pathways are all consistent with bond-dependent Kitaev-Γ-Heisenberg exchange interactions in NaNi_2BiO_6-δ.

In conventional superconductors an external magnetic field generally suppresses superconductivity. This results from a simple thermodynamic competition of the superconducting and magnetic free energies. In this study, we report the unconventional features in the superconducting epitaxial thin film tungsten telluride (WTe2). Measuring the electrical transport properties of Molecular Beam Epitaxy (MBE) grown WTe2 thin films with a high precision rotation stage, we map the upper critical field Hc2 at different temperatures T. We observe the superconducting transition temperature T c is enhanced by in-plane magnetic fields. The upper critical field Hc2 is observed to establish an unconventional non-monotonic dependence on temperature. We suggest that this unconventional feature is due to the lifting of inversion symmetry, which leads to the enhancement of Hc2 in Ising superconductors.

We apply a result from graph theory to prove exact results about itinerant ferromagnetism. Nagaoka's theorem is extended to all nonseparable graphs except single polygons with more than four vertices by applying the solution to the generalized 15-puzzle problem, which studies whether the hole's motion can connect all possible tile configurations. This proves that the ground state of a $U\ensuremath{\rightarrow}\ensuremath{\infty}$ Hubbard model with one hole away from the half filling on a two-dimensional honeycomb lattice or a three-dimensional diamond lattice is fully spin polarized. Furthermore, the condition of connectivity for $N$-component fermions is presented, and Nagaoka's theorem is also generalized to $\text{SU}(N)$-symmetric fermion systems on nonseparable graphs.

We generalize the previous exact results of the Nagaoka-type itinerant ferromagnetic states in a three dimensional $t_{2g}$-orbital system to allow for multiple holes. The system is a simple cubic lattice with each site possessing $d_{xy}$, $d_{yz}$, and $d_{xz}$ orbitals, which allow two-dimensional hopping within each orbital plane. In the strong coupling limit of $U\to \infty$, the orbital-generalized Nagaoka ferromagnetic states are proved degenerate with the ground state in the thermodynamic limit when the hole number per orbital layer scales slower than $L^{\frac{1}{2}}$. This result is valid for arbitrary values of the ferromagnetic Hund's coupling $J>0$ and inter-orbital repulsion $V\ge 0$. The stability of the Nagaoka-type state at finite electron densities with respect to a single spin-flip is investigated. These results provide helpful guidance for studying the mechanism of itinerant ferromagnetism for the $t_{2g}$-orbital materials.

We systematically generalize the exotic He-B phase, which not only exhibits unconventional symmetry but is also isotropic and topologically non-trivial, to arbitrary partial-wave channels with multi-component fermions. The concrete example with four-component fermions is illustrated including the isotropic f , p and d-wave pairings in the spin septet, triplet, and quintet channels, respectively. The odd partial-wave channel pairings are topologically non-trivial, while pairings in even partial-wave channels are topologically trivial. The topological index reaches the largest value of N in the p-wave channel (N is half of the fermion component number). The surface spectra exhibit multiple linear and even high order Dirac cones. Applications to multi-orbital condensed matter systems and multi-component ultra-cold large spin fermion systems are discussed.

We report the magnetic structure of the honeycomb antiferromagnet $rm NaNi_2BiO_6$. We find magnetic order with moments along the $c$ axis below $T_{c1}=6.3u003e{rm K}$ and then in the honeycomb plane below $T_{c2}=4.8u003e{rm K}$ with a counterrotating pattern and an incommensurate ordering wave vector ${bf q}=(frac{1}{3},u003e frac{1}{3},u003e 0.154 pm 0.011)$. Neutron scattering shows half of the expected static magnetic moment remains fluctuating at low temperatures, suggesting proximity to a quantum disordered phase. The ordering wave vector, in-plane magnetic correlations, and superexchange pathways are all consistent with a bond-dependent 120textdegree compass model exchange in $rm NaNi_2BiO_6$. %lying close to a quantum critical point. %arising through orbital contributions to Ni magnetism.

The sign problem is a major obstacle in quantum Monte Carlo simulations for many-body fermion systems. We examine this problem with a new perspective based on the Majorana reflection positivity and Majorana Kramers positivity. Two sufficient conditions are proven for the absence of the fermion sign problem. Our proof provides a unified description for all the interacting lattice fermion models previously known to be free of the sign problem based on the auxiliary field quantum Monte Carlo method. It also allows us to identify a number of new sign-problem-free interacting fermion models including, but not limited to, lattice fermion models with repulsive interactions but without particle-hole symmetry, and interacting topological insulators with spin-flip terms.

We study the topological configurations of the two-component condensates of bosons with the three-dimensional (3D)(sigma) over right arrow.(p) over right arrow Weyl-type spin-orbit coupling subject to a harmonic trapping potential. The topology of the condensate wave functions manifests in the quaternionic representation. In comparison to the U(1) complex phase, the quaternionic phase manifold is S-3 and the spin orientations form the S-2 Bloch sphere through the first Hopf mapping. The spatial distributions of the quaternionic phases exhibit the 3D skyrmion configurations, and the spin distributions possess nontrivial Hopf invariants. Spin textures evolve from the concentric distributions at the weak spin-orbit coupling regime to the rotation symmetry-breaking patterns at the intermediate spin-orbit coupling regime. In the strong spin-orbit coupling regime, the single-particle spectra exhibit the Landau-level-type quantization. In this regime, the three-dimensional skyrmion lattice structures are formed when interactions are below the energy scale of Landau-level mixings. Sufficiently strong interactions can change condensates into spin-polarized plane-wave states or superpositions of two plane waves exhibiting helical spin spirals.