We present the realization of a spin-$\frac{1}{2}$ hexagonal-plaquette chain with Ising anisotropy, an unexplored quantum spin model that serves as a platform for investigating anisotropic quantum magnetism. Specific heat at zero field reveals a sharp peak at $T_{\mathrm{N}}=1.0$ K, indicating a phase transition to a $\mathrm{N}\acute{\mathrm{e}}\mathrm{el}$ order stabilized by interchain couplings. A perturbative analysis maps the system onto an effective spin-$\frac{1}{2}$ Ising-like chain, supporting the presence of an anisotropy-induced excitation gap. Furthermore, the interchain interactions may induce discrete excitations in the spinon continuum, reminiscent of Zeeman ladder physics observed in related one-dimensional Ising-like systems. These results establish a well-defined model system for correlated spin phenomena in anisotropic magnets and highlight a route for engineering Ising-like quantum states in molecular-based frameworks.

We systematically investigate three body-centred cubic (bcc) high-entropy alloys (HEAs) with an identical valence electron count (VEC = 4.375): ${\left(\mathrm{NbHf}\right)}_{0.75}{\left(\mathrm{TiZr}\right)}_{0.25}$, ${\left(\mathrm{NbZr}\right)}_{0.75}{\left(\mathrm{TiHf}\right)}_{0.25}$, and ${(\mathrm{NbTi})}_{0.75}{\left(\mathrm{ZrHf}\right)}_{0.25}$. Despite their isoelectronic nature, it was found that these alloys exhibit markedly different superconducting properties. Critical temperatures $T_{\mathrm{c}}$ range from 7.14(5) K to 8.17(5) K, while upper critical fields ${\mu }_0{H}_{\mathrm{c}2}\left(0\right)$ exceed 12 T, reaching 14.0(9) T for the Ti-rich alloy ${\left(\mathrm{NbTi}\right)}_{0.75}{\left(\mathrm{ZrHf}\right)}_{0.25}$. These variations highlight the limited predictive power of the Matthias rule in HEA design. Furthermore, the exceptional properties observed in the Ti-rich composition suggest that Nb and Ti are critical elements for the development of new HEAs for next-generation superconducting magnets.

Metal-doped AlN (i.e., $\mathrm{A}{\mathrm{l}}_{1-x}\mathrm{S}{\mathrm{c}}_x\mathrm{N}$) has emerged as a promising ferroelectric material due to its excellent compatibility with conventional Si semiconductors. Understanding how individual cations contribute to the overall ferroelectric polarization and piezoelectric response is crucial for the rational design of high-performance devices. In this work, we take the recently synthesized wurtzite-derived ternary nitrides $\mathrm{Z}{\mathrm{n}}_3\mathrm{M}{\mathrm{N}}_4$ (M = W, Mo) as an example and employ first-principles calculations to investigate the atomic sublattice decomposition of their ferroelectric polarization and longitudinal piezoelectric coefficient. Our results reveal that the polarization value in $\mathrm{Z}{\mathrm{n}}_3\mathrm{M}{\mathrm{N}}_4$ is primarily dominated by the more electronegative W/Mo cation due to the strong hybridization between W 5dz²/Mo 4dz² and N 2p orbitals. Furthermore, the piezoelectric coefficient $e_{33}$ is primarily governed by the bond between the more electronegative W/Mo cation and the N anion within the $\mathrm{M}{\mathrm{N}}_4$ tetrahedron along the $c$ axis. This is attributed to the large absolute value of Born effective charge and $\frac{\mathrm{d}{u}_3}{\mathrm{d}{\eta }_3}$ of the N atom at the tetrahedral vertex along the $c$ direction. We further confirm that these findings can be extended to other wurtzite-derived ternary nitrides with different chemical formulas. Our study provides valuable theoretical insights for the future experimental design of wurtzite nitride semiconductors with excellent ferroelectric and piezoelectric properties.

Ferromagnetic resonance (FMR) serves as a powerful probe of magnetization dynamics and anisotropy in percolating ferromagnets, where short-range interactions govern long-range magnetic order. We apply this approach to ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{N}$ ($x\simeq 8\%$), a dilute ferromagnetic semiconductor, combining FMR and superconducting quantum interference device magnetometry. Our results confirm the percolative nature of ferromagnetism in (Ga,Mn)N, with a Curie temperature $T_{\mathrm{C}}=12\mathrm{K}$, and reveal that despite magnetic dilution, key features of conventional ferromagnets are retained. FMR measurements establish a robust uniaxial anisotropy, dictated by ${\mathrm{Mn}}^{3+}$ single-ion anisotropy, with an easy-plane character at low Mn content. While excessive line broadening suppresses FMR signals below 9 K, they persist up to 70 K, indicating the presence of nonpercolating ferromagnetic clusters well above $T_{\mathrm{C}}$. The temperature dependence of the FMR intensity follows that of the magnetization, underscoring the stability of these clusters. We quantitatively describe both FMR and SQUID observables using atomistic spin model operating on a common set of parameters. The level of agreement, achieved without tuning parameters between datasets, demonstrates the robustness and practical applicability of the approach in capturing the essential physics of spin-diluted, percolating ferromagnets. This study advances the understanding of percolating ferromagnetic systems, demonstrating that FMR is a key technique for probing their unique dynamic and anisotropic properties. Our findings contribute to the broader exploration of dilute ferromagnets and provide new insights into percolating ferromagnetic systems, which will be relevant for spintronic opportunities.

Charge creation via quantum tunneling, i.e., dielectric breakdown, is one of the most fundamental and significant phenomena arising from strong light(field)-matter coupling. In this work, we conduct a systematic numerical analysis of quantum tunneling in one-dimensional Mott insulators described by the extended $\left(U\text{−}V\right)$ Hubbard model. We discuss the applicability of the analytical formula for doublon-holon (DH) pair production, previously derived for the one-dimensional Hubbard model, which highlights the relationship between the tunneling threshold, the charge gap, and the correlation length. We test the formula's ability to predict both DH pair production and energy increase rate. Using tensor-network-based approaches, we demonstrate that the formula provides accurate predictions in the absence of excitonic states facilitated by the nearest-neighbor interaction $V$. However, when excitonic states emerge, the formula more accurately describes the rate of energy increase than the DH pair creation rate and in both cases gets improved by incorporating the exciton energy as the effective gap.

In the presence of crystalline symmetry, topologically ordered states can acquire a host of symmetry-protected invariants. These determine the patterns of crystalline symmetry fractionalization of the anyons in addition to fractionally quantized responses to lattice defects. Here we show how ground state expectation values of partial rotations centered at high symmetry points can be used to extract crystalline invariants. Using methods from conformal field theory and G-crossed braided tensor categories, we develop a theory of invariants obtained from partial rotations which apply to both Abelian and non-Abelian topological orders. We then perform numerical Monte Carlo calculations for projected parton wave functions of fractional Chern insulators, demonstrating remarkable agreement between theory and numerics. For the topological orders we consider, we show that the Hall conductivity, filling fraction, and partial rotation invariants fully characterize the crystalline invariants of the system. Our results also yield invariants of continuum fractional quantum Hall states protected by spatial rotational symmetry.

The exciton states in wurtzite CdSe nanocrystals (NCs) embedded in a glass matrix are examined by spin-flip Raman scattering using resonant excitation at magnetic fields up to 8 T. The Landé $g$ factors of the bright excitons of about 2.2 are found to be weakly dependent on the NC diameter in the range of $4.1–6.1\mathrm{nm}$. For an explanation of the experimental results, a theory of acoustic phonon-assisted exciton spin flips is developed, and the exciton spin relaxation rates are calculated. The theory is used to model the spin-flip Raman spectra of spherical CdSe NCs, taking into account their random orientation and size dispersion in the ensemble. Our calculations show that, despite the strong anisotropy of the exciton $g$ factors and the random NC orientation, the spin-flip Raman shifts are determined by the NCs whose wurtzite $c$ axis is oriented along the magnetic field. The model results are in good agreement with our experimental data. From fitting the experimental data, the hole $g$ factor $g_h=-1.17$ is extracted.

We consider a generic quantum many-body system initiated at thermal equilibrium and driven by an external parameter, and discuss the prospect for measuring the work done by the varying parameter on the system. While existing methods are based on a full control of the system's Hamiltonian and are thus limited to few-level quantum systems, measuring work in many-body quantum systems remains challenging. Our approach relies on transforming the external parameter into a dynamical “work agent”, for which we consider a harmonic oscillator in a semiclassical coherent state with a large photon number. We define a work generating function, which coincides with the standard two-point measurement protocol for work measurement in the limit of a large photon number. While in principle it allows one to relate the moments of work $\langle W^n\rangle$ to observables of the work agent, we focus on the average work, which is obtained from energy conservation by the change of the energy of the agent, which can be measured using photon number detection. We illustrate this concept on a transmon-microcavity system, which displays various quantum coherent effects including Landau-Zener Stükelberg interference and collapse and revival of Rabi oscillations. We discuss how our setup allows to measure work in a variety of quantum many-body systems.

We present a comprehensive study of topological phases in $\mathrm{SO}\left(n\right)$ spin chains using a combination of analytical parton construction and numerical techniques. For even $n=2l$, we identify a unique symmetry-protected topological phase, dubbed ${\mathrm{SPT}}^2$ phase characterized by two distinct topological sectors, exhibiting exact degeneracy at the matrix product state exactly solvable point. Through Gutzwiller-projected mean-field theory and density matrix renormalization group (DMRG) calculations, we demonstrate that these sectors remain topologically degenerate in close chains throughout the ${\mathrm{SPT}}^2$ phase, with energy gaps decaying exponentially with system size. For odd $n=2l+1$, we show that the ground state remains unique in close chains. We precisely characterize critical states using entanglement entropy scaling, confirming the central charges predicted by conformal field theories. Our results reveal fundamental differences between even and odd $n$ cases, provide numerical verification of topological protection, and establish reliable methods for studying high-symmetry quantum systems. The Gutzwiller-guided DMRG is demonstrated to be notably efficient in targeting specific topological sectors.

Featuring exotic quantum transport and surface states, topological semimetals can be classified into nodal-point, nodal-line, and nodal-surface semimetals according to the degeneracy and dimensionality of their nodes. However, a topological semimetal that possesses both nodal points and nodal lines is rarely reported. Here, we propose a scheme to construct this type of topological semimetal, which simultaneously exhibits hinge Fermi arcs and drumhead surface states. Then, by applying periodic driving on the system, we find a hybrid-order topological semimetal with nodal points and rich nodal-line structures and its conversion into a first-order topological semimetal, which are absent in a static system. Our results enrich the family of topological semimetals, and establish a foundation for further exploration of their potential applications.

Quantitative growth studies using surface diffraction and scanning tunneling microscopy are carried out to determine the intercalation conditions for Pb under Gr/SiC, with initial phase a mixture of buffer-layer and single-layer graphene. Intercalation is a kinetically complex, multistage process with intercalated Pb moving between different subsurface locations with annealing, eventually to the location of higher stability. The transfer is determined by monitoring the difference of a given spot intensity from its clean value, as a function of growth parameters. In addition, a broad, low-intensity ${(10\times 10)}_{\mathrm{gr}}$ moiré phase is observed exclusively originating from intercalated Pb. Well-defined growth conditions are identified for the moiré spot to be observed reversibly. The ${(10\times 10)}_{\mathrm{gr}}$ phase follows changes of the Pb(10) spot during growth and annealing experiments, instead of changes of the other Gr/SiC spots indicating preferred nucleation of Pb islands on the ${(10\times 10)}_{\mathrm{gr}}$ domains. These structural results are discussed in connection to different models proposed for the ${(10\times 10)}_{\mathrm{gr}}$ supercell and the subsurface Pb coverage. Mass transport of subsurface Pb is unusually high, possibly because of the very high compression of the intercalated Pb, when compared to metallic Pb(111).

The coherent lattice dynamics in the three-dimensional (3D) Dirac semimetal ${\mathrm{Cd}}_3{\mathrm{As}}_2$ is investigated in the nonperturbative regime of light-matter interaction using coherent two-dimensional terahertz (THz) spectroscopy, as a function of time delay and field strength. The phase-resolved nonlinear signal reveals a coherent phonon mode at 1.48 THz, corresponding to the $B_{2g}$ Raman-active mode, characterized by the periodic motion of two cadmium atoms in the substructure toward and away from two cadmium-vacant sites. The interaction of a strong THz electric field with the 3D Dirac semimetal ${\mathrm{Cd}}_3{\mathrm{As}}_2$ leads to transient charge carrier imbalance via tunneling ionization, which results in a displacive force that drives the lattice dynamics of a noninteracting Raman-active mode. The selective excitation of otherwise inaccessible phonon modes enables precise control over the material's properties at the atomic level, opening new pathways to manipulate its topological characteristics.

$\mathrm{B}{\mathrm{C}}_2\mathrm{N}$ is an important class of experimentally synthesizable superhard materials, typically explained by the distribution of B/C/N within a diamondlike framework, which provides a good explanation for their x-ray diffraction (XRD) patterns and hardness. However, there is still a lack of systematic theoretical investigations on the 1:2:1 distribution of B, C, and N atoms in the diamond framework. In this work, based on a 2 × 2 × 2 diamond supercell, all possible nonequivalent 1:2:1 distributions of B/C/N across all subgroups of this supercell were exhaustively explored. There are 465 possible configurations primarily concentrated in the 195, 198, 215, and 216 space groups, with 120, 142, 202, and 1 nonequivalent configurations, respectively. The ground state appears in space group 215 with 10 nonequivalent positions, consistent with previous work [Phys. Rev. B 107, 134101 (2023)]. However, in the previous study, only space group 215 was considered with 10 nonequivalent positions, and only 108 possible configurations were identified, while in our study, we reveal 131 in this case. Additionally, in our systematic and comprehensive work, we found that the systems prefer distributions with C and BN as separated as possible, and their energies decrease as the number of C–C or B–N bonds increases. Finally, we find that all these low-energy structures are superhard insulators, consistent with experimental results, and their XRD patterns are also in agreement with the experimental data, while their Raman spectra can serve as an effective criterion for distinguishing between different distributions.

The recent experimental syntheses of carbon nitrides ($\mathit{oP}\text{8-CN}, tI14\text{−}{\mathrm{C}}_3{\mathrm{N}}_4, tI24\text{-C}{\mathrm{N}}_2$, and $hP126\text{−}{\mathrm{C}}_3{\mathrm{N}}_4$) have created great scientific interest in the long-standing debate on their stability, ultra-incompressibility, and superhardness [D. Laniel et al., Adv. Mater. 36, 2308030 (2024)]. Herein, this study presents a systematic investigation of pressure-induced variations in thermodynamic and dynamic stability for these materials using high-throughput first-principles calculations. The results demonstrate that all structures transition from thermodynamic instability at ambient pressure to stability under high pressure, showing excellent agreement with experimental results. Mechanical characterization at ambient conditions reveals intrinsic ultra-incompressibility and superhard characteristics across the series, with exceptional bulk moduli (339–399 GPa) and ideal strength values (37.8–41.8 GPa). Within the maximum pressure range considered, up to 160 GPa, bulk moduli increase by 238–260% and ideal strength improves by 181–327% compared to ambient-pressure values. Analysis of bond deformation trajectories reveals that the mechanical anisotropy originates from the cooperative alignment of C-N tetrahedral units. Electronic structure analysis shows that pressure-induced charge accumulation enhances $sp$-orbital hybridization between C and N atoms while suppressing electronic reorganization of N lone pairs, governing structural strengthening and toughening mechanisms. These findings advance the understanding of the newly synthesized C-N superhard materials, and they provide theoretical guidance for strengthening mechanisms under extreme high pressures.

Spin waves, or quantized as magnons, are one of the basic excitations and fundamental spin carriers in magnetic systems. Understanding the propagation and scattering behaviors of spin waves upon inhomogeneous magnetic mediums is indispensable toward its full manipulation and exploitation. Here, we report a spin wave reconstruction scheme that retrieves phase information from magnon rays as an inverse procedure that decomposes the propagating spin wave into separate magnon rays. With the aid of magnon rays, the topological features of the spin wave profile upon a magnetic skyrmion is anatomized in a ray-by-ray fashion. The interplay between particle and wave aspects of spin waves offers another paradigm in designing functional magnetic devices.

We investigate the pairing symmetry in the novel superconductor ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ under pressure by the nonperturbative variational quantum Monte Carlo. Within the bilayer Hubbard model and extended $t\text{−}J$ model with two orbitals in the $E_g$ doublet, we find the local strong correlation triggers $s_{\pm }$-wave Cooper pairing, with sign change of the gap function among the various Fermi pockets, while the $d_{x^2-y^2}$-wave pairing is generically disfavored. This is in agreement with the results from functional renormalization group applied in the weak up to moderate correlation limit. We find the $3{\mathrm{d}}_{3z^2-r^2}$ orbital plays a leading role in the superconducting pairing. We also demonstrate the finite intraorbital double occupancy even in the strong correlation limit, shedding light on the itinerant versus local moment picture of the electrons in this material.