Recently, higher-order topology has been expanded to encompass aperiodic quasicrystals, including those with eightfold or twelvefold rotational symmetry. The underlying mechanism for these high-order topological phases is generally protected by $C_n{\mathcal{M}}_z$ symmetry, resulting in the presence of $n$ corner states. However, this mechanism is not applicable to other $C_{2N}$ quasicrystals when $N$ is an odd number. In this work, we propose the realization of a second-order topological superconductor (SOTSC) within a sixfold symmetric bronze-mean hexagonal quasicrystal with six Majorana zero-energy modes. This SOTSC emerges from the combination of vertical and horizontal mirror symmetries, which flips the mass-term sign along the horizontal mirror-invariant line and produces Majorana zero-energy modes at each corner of the quasicrystal sample. Moreover, this mechanism can extend to quasicrystals with $C_{4N+2}$ and $C_{4N}$ rotational symmetries, namely encompassing systems with $C_{2N}$ symmetry. Our findings provide useful guidance for achieving SOTSC in quasicrystals featuring $C_{2N}$ rotational symmetry and introduce bronze-mean hexagonal quasicrystals as a promising platform for exploring quasicrystal SOTSC.

The quest for advancing the development of next-generation nanospintronic devices has propelled extensive research into the realization and control of half-metallicity in 2D materials. Here, the multiferroic ${\mathrm{VSe}}_2/{\mathrm{Sc}}_2{\mathrm{CO}}_2$ vdW heterostructures are theoretically investigated by using density functional theory to search for half-metallicity. Our theoretical exploration reveals that the ${\mathrm{VSe}}_2$ layer showcases a unique capability to transit between semiconducting and half-metallic behavior by precisely manipulating the ferroelectric polarization states of the ${\mathrm{Sc}}_2{\mathrm{CO}}_2$ layer. We further delve into the diverse electronic properties of the ${\mathrm{VSe}}_2$ layer within the heterostructure, employing uniaxial tensile strain engineering to investigate its behavior in both the semiconductor and half-metallic states. In the semiconductor state, this electronic property of the ${\mathrm{VSe}}_2$ layer remains unchanged with strain. In contrast, in the half-metallic state, the ${\mathrm{VSe}}_2$ layer undergoes a fascinating modulation, transiting from the spin-down half-metal to the metal and then to the spin-up half-metal as the strain increases from $0\%$ to $6\%$. This intriguing phenomenon is elucidated by the intricate rearrangement of the inner V atomic orbitals in response to strain.

We study localization and many-body localization transition in one-dimensional systems in the presence of deterministic quasiperiodic potential. We use single-particle excitations obtained through single-particle Green's function in real space to characterize the localization to delocalization transition. A single parameter scaling analysis of the ratio of the typical to average value of the local density of states (LDOS) of single-particle excitations shows that the critical exponent with which the correlation length $\xi$ diverges at the transition point $\xi \sim |h-h_c{|}^{-\nu }$, coming from the localized side, satisfies the inequality $\nu \ge 1$ for the noninteracting Aubry-Andre (AA) model. For the interacting system with AA potential, we study single-particle excitations produced in highly excited many-body eigenstates across the MBL transition and found that the critical exponent obtained from finite-size scaling of the ratio of the typical to average value of the LDOS satisfies $\nu \ge 1$ here as well. This analysis of the local density of states shows that the localization and MBL transition in systems with quasiperiodic potential belong to a different universality class than the localization and MBL transition in systems with random disorder where $\nu \ge 2$. In complete contrast to this, finite-size scaling of the level spacing ratio is known to support the same universality class for MBL transitions in systems with quasiperiodic as well as random disorder potentials. For the interacting systems with quasiperiodic potentials, though finite-size scaling of the level spacing ratio shows a transition at $h_c^{\mathrm{lsr}}$ which is close to the transition point obtained from LDOS within numerical precision, the critical exponent obtained from finite-size scaling of level spacing ratio is $\nu \sim 0.54$ in close similarity to the MBL systems with random disorder.

We report the results of high-field magnetization measurements on a powdered sample of ${\mathrm{Sr}}_2{\mathrm{CoTeO}}_6$, which approximates the spin-1/2 fcc lattice Heisenberg antiferromagnet. This compound undergoes a magnetic ordering into a type-I antiferromagnetic state at $T_{\mathrm{N}}=13.4\mathrm{K}$. The magnetization exhibits a plateau at one-half of the saturation magnetization. This indicates antiferromagnetic nearest-neighbor and ferromagnetic next-nearest-neighbor exchange interactions, consistent with the type-I antiferromagnetic state. However, the one-half magnetization plateau is indistinct. This can be ascribed to the small exchange anisotropy or the significant finite-temperature effect due to the energy structure characteristic of the spin-1/2 fcc lattice Heisenberg antiferromagnet. The observed transition sequence is consistent with the theory, although the magnetization anomalies are not sharp.

$\mathrm{Cr}{\mathrm{I}}_3$ is a prototypical van der Waals ferromagnet with a magnetic honeycomb lattice. Previous inelastic neutron scattering studies have suggested topological nature of its magnetic excitations with a magnon gap at the Dirac points, which are anticipated to give rise to magnon thermal Hall effect. Here we report thermal transport properties of $\mathrm{Cr}{\mathrm{I}}_3$ and show that the long-sought thermal Hall signal anticipated for topological magnons is fairly small. In contrast, we find that $\mathrm{Cr}{\mathrm{I}}_3$ exhibits an appreciable anomalous thermal Hall signal at lower temperature that may arise from magnon-phonon hybridization or magnon-phonon scattering. These findings are anticipated to stimulate further neutron scattering studies on $\mathrm{Cr}{\mathrm{I}}_3$ single crystal, which can shed light not only on the intrinsic nature of magnetic excitations but also on the magnon-phonon interaction.

The Li-Haldane conjecture is one of the most famous conjectures in physics and opens a new research area in the quantum entanglement and topological phase. Although a lot of theoretical and numerical works have confirmed the conjecture in topological states with bulk-boundary correspondence, the cases with gapped boundary and the systems in high dimension are widely unknown. What is the valid scope of the Li-Haldane conjecture? Via the newly developed quantum Monte Carlo scheme, we are now able to extract the large-scale entanglement spectrum (ES) and study its relation with the edge energy spectrum generally. Taking the two-dimensional Affleck-Kennedy-Lieb-Tasaki model with a tunable boundary on the square-octagon lattice as an example, we find several counterexamples which cannot be explained by the Li-Haldane conjecture; e.g., the low-lying entanglement spectrum does not always show similar behaviors as the energy spectrum on the virtual boundary, and sometimes the ES resembles the energy spectrum of the edge even if it is gapped. Finally, we demonstrate that the newly proposed “wormhole mechanism” on the path integral of a reduced density matrix is the formation principle of the general ES. We find that the Li-Haldane conjecture is a particular case in some limit of the wormhole picture while all the examples of the conjecture we have studied can totally be explained within the wormhole mechanism framework. Our results provide important evidence for demonstrating that the wormhole mechanism is the fundamental principle to explain the ES.

In this paper we present an ab initio scheme based on linear response theory of exchange torque correlation, implemented into the real-space Korringa-Kohn-Rostoker (RS-KKR) framework to calculate diagonal elements of the atomic-site-dependent intrinsic Gilbert damping tensor. The method is first applied to bcc iron and fcc cobalt bulk systems. Besides reproducing earlier results from the literature for those bulk magnets, the effect of the lattice compression is also studied for Fe bulk, and significant changes for the Gilbert damping are found. Furthermore, (001)-oriented surfaces of Fe and Co are also investigated. It is found that the on-site Gilbert damping increases in the surface atomic layer and decreases in the subsurface layer, and approaches the bulk value moving further inside the magnets. Realistic atomic relaxation of the surface layers enhances the identified effects. The first-neighbor damping parameters are extremely sensitive to the surface relaxation. Despite their inhomogeneity caused by the surface, the transverse Gilbert damping tensor components remain largely insensitive to the magnetization direction.

We performed metadynamics Monte Carlo simulations to obtain the free energy as a function of the topological charge in the skyrmion-hosting magnetic model systems $\left({\mathrm{Pt}}_{0.95}{\mathrm{Ir}}_{0.05}\right)/\text{Fe}/\text{Pd}\left(111\right)$ and Pd/Fe/Ir(111), using a spin model containing parameters based on ab initio calculations. Using the topological charge as collective variable, this method allows for evaluating the temperature dependence of the number of skyrmionic quasiparticles. In addition, from the free-energy cost of increasing and decreasing the topological charge of the system we determined chemical potentials as a function of the temperature. At lower temperature, the chemical potential for creating skyrmions and antiskyrmions from the topologically trivial state is different. This splitting of the chemical potential is particularly pronounced for large external magnetic fields when the system is in a field-polarized phase. We observed a change in the shape of the free-energy curves when skyrmion-skyrmion interactions become more pronounced.

The magnetization and electric polarization of a polar antiferromagnet ${\mathrm{Fe}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$ are studied up to 66 T for spin-saturation magnetic fields applied along the polar axis. The magnetization process at 1.4 K exhibited an unusual six-step structure below the saturation field of 65 T, which has scarcely been observed in frustrated magnets. The electric polarization along the polar axis exhibits a similar multistep behavior with a total change of 1.2 $\text{µ}\mathrm{C}/{\mathrm{cm}}^2$. A combined triangular-lattice antiferromagnetic model with strong Ising-type spin anisotropy reproduces this multistep magnetoelectric (ME) effect. The exchange striction mechanism explains the remarkable ME response in the two sublattice type-I multiferroic materials. These results and their interpretation demonstrate a method for realizing multistage magnetoelectric effects in hybrid spin systems.

We propose that geometric curvature and torsion may be used to probe the quality of an uncompensated antiferromagnetic interface, using the proximity effect. We study a helix of antiferromagnetic wire coupled to a conventional superconductor, and show that a density of states measurement can give information about the quality of an uncompensated interface, crucial for many recently predicted antiferromagnetic proximity effects. Furthermore, we show that geometric curvature alone can result in long-ranged superconducting triplet correlations in the antiferromagnet, and we discuss the impact curvature and torsion can have on the future development of superconducting spintronic devices.

As an emerging antiferroelectric material, ${\mathrm{AgNbO}}_3$ holds promise in various applications like sensors, high-density data storage, and energy conversion. Understanding its structural behavior under high pressure is vital for establishing a phase diagram, which is of importance for properties design of antiferroelectric materials. However, the detailed phase structures of representative ${\mathrm{AgNbO}}_3$ under high pressures were still under debate. Hence, we investigated high-pressure structural evolution of ${\mathrm{AgNbO}}_3$ using Raman spectroscopy, in situ high-pressure synchrotron x-ray diffraction, and ab initio density-functional theory. The results revealed a transition path of $Pbcm\to Cmcm\to Pm\overline{3}m$ with the increases of pressures. The ${\mathrm{AgNbO}}_3$ initially exhibited an orthorhombic structure with the Pbcm space group at ambient pressure, transitioning to Cmcm at 5.83 GPa. With further pressure increasing to 9.89 GPa, a second cubic phase with the $Pm\overline{3}m$ space group could be observed. The coexistence of Cmcm and $Pm\overline{3}m$ phases transformed into a pure $Pm\overline{3}m$ structure at around 16.71 GPa. Ab initio density-functional theory validated the phase transition path with high pressures. The structural transformations were mainly driven by the pressure-induced movement of Ag ions and oxygen octahedron rotations. These findings carry significant implications for the design and optimization of devices operating under high pressures.

We propose two strategies to construct a family of nonintegrable spin chains with exactly solvable subspaces based on the idea of quasiparticle excitations from the matrix product vacuum state [Haegeman et al., Phys. Rev. B 88, 075133 (2013)]. The first one allows the boundary generalization, while the second one makes it possible to construct the solvable subspace with interacting quasiparticles. Each generalization is realized by removing the assumption made in the conventional method [Moudgalya et al., Phys. Rev. B 102, 085120 (2020)], which is the frustration-free condition or the local orthogonality, respectively. We found that the structure of the embedded equally spaced energy spectrum is not violated by the diagonal boundaries, as long as quasiparticles are identical and noninteracting in the invariant subspace. On the other hand, we show that there exists a one-parameter family of nonintegrable Hamiltonians, which shows the perfectly embedded energy spectrum of the integrable spin chain. Surprisingly, the embedded energy spectrum does not change by varying the free parameter of the Hamiltonian. The constructed models weakly break ergodicity, in which strong ETH is expected to be violated.

Magnetism in two-dimensional (2D) materials has attracted considerable attention recently for both fundamental understanding of magnetism and its tunability towards device applications. The isostructural ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ and ${\mathrm{Fe}}_3{\mathrm{GaTe}}_2$ are two members of the Fe-based van der Waals (vdW) ferromagnet family, but exhibit very different Curie temperatures ($T_C$) of 210 and 360 K, respectively. Here, by using angle-resolved photoemission spectroscopy and density functional theory, we systematically compare the electronic structures of the two compounds. Qualitative similarities in the Fermi surface can be found between the two compounds, with expanded hole pockets in ${\mathrm{Fe}}_3{\mathrm{GaTe}}_2$ suggesting additional hole carriers compared to ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$. Interestingly, we observe almost no band shift in ${\mathrm{Fe}}_3{\mathrm{GaTe}}_2$ across its $T_C$ of 360 K, compared to a small shift in ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ across its $T_C$ of 210 K. The weak temperature-dependent evolution strongly deviates from the expectations of an itinerant Stoner mechanism. Our results suggest that itinerant electrons have minimal contributions to the enhancement of $T_C$ in ${\mathrm{Fe}}_3{\mathrm{GaTe}}_2$ compared to ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$, and that the nature of ferromagnetism in these Fe-based vdW ferromagnets must be understood with considerations of the electron correlations.

We report a comprehensive investigation into the magnetic and magnetoelectric characteristics of green phase compounds $R_2\mathrm{BaCu}{\mathrm{O}}_5$ ($R=\mathrm{Er}$, Eu, Y, Tm, and Lu) through an array of experimental techniques, including dc magnetization, specific heat, dielectric, pyrocurrent, and neutron diffraction measurements. Our study reveals that all these compounds exhibit antiferromagnetic ordering of $\mathrm{C}{\mathrm{u}}^{2+}$ ions in the range $T_{\mathrm{N}}^{\mathrm{Cu}}$ = 15–20 K. Specifically, magnetic ordering of $\mathrm{E}{\mathrm{r}}^{3+}$ ions is observed at $T_{\mathrm{N}}^{\mathrm{Er}}$ = 5.1 K. Intriguingly, independent ordering of $\mathrm{T}{\mathrm{m}}^{3+}$ ions is not observed. Furthermore, the isothermal magnetization curves for the Er compound confirm the metamagnetic transition at a critical magnetic field of ${\mathrm{H}}_{\mathrm{c}}=0.9\mathrm{T}$, reaching a saturation magnetization value of $9{\mu }_{\mathrm{B}}/\mathrm{f}.\mathrm{u}.$ Notably, above ${\mathrm{H}}_{\mathrm{c}}$, this compound exhibits field-induced magnetoelectric states at $T_{\mathrm{N}}^{\mathrm{Er}}$, underscoring a pronounced magnetoelectric coupling. Conversely, the compounds with $R=\mathrm{Eu}$, Y, Tm, and Lu do not display magnetoelectric coupling. The presence or absence of such coupling aligns with the magnetic symmetry derived from neutron diffraction. Our findings conclusively establish that $4f\text{−}3d$ exchange coupling is pivotal in enabling the magnetoelectric or multiferroic properties in these well-established green phase compounds. Consequently, our study underscores the rich and diverse magnetism and magnetoelectric properties exhibited by the green phase family, positioning them as equally intriguing as manganites in condensed matter physics.

We theoretically investigate a voltage-biased normal metal–superconductor–normal metal (NSN) junction. Using the nonequilibrium Green's function technique, we derive a quantum kinetic equation to determine the superconducting order parameter self-consistently. The derived equation is an integral-differential equation with memory effects. We solve this equation by converting it into a system of ordinary differential equations with the use of a pole expansion of the Fermi-Dirac function. When the applied voltage exceeds the critical value, the superconductor switches to the normal state. We find that when the voltage is decreased from the normal phase, the system relaxes to a Larkin-Ovchinnikov-type (LO) inhomogeneous superconducting state, even in the absence of a magnetic Zeeman field. We point out that the emergence of the LO-type state can be attributed to the nonequilibrium energy distribution of electrons due to the bias voltage. We also point out that the system exhibits bistability, which leads to hysteresis in the voltage-current characteristic of the NSN junction.

Recently, we realized the formation of a single quantized vortex in nonresonantly optically stirred exciton-polariton condensates [I. Gnusov et al., Sci. Adv. 9, eadd1299 (2023)]. In this work, we demonstrate that the number of emerging vortices depends on the characteristic size of the rotating potential induced by the nonresonant laser excitation. For smaller sizes, we observe only a single vortex with a topological charge of $\pm 1$ defined by the stirring direction. For larger trap sizes, clusters of up to four corotating vortices are observed, also following the stirring direction. We find that the interplay of stirring speed and confining potential size dictates the number of vortices in a cluster. This is confirmed by observed energy distribution of condensed polaritons as a function of rotation frequency. Our findings offer an insight into the behavior of stirred condensates, complementing previous works on optically trapped polariton condensates in static traps.

Realizing topological semimetal states with novel emergent fermions in magnetic materials is a focus of current research. Based on first-principles calculations and symmetry analysis, we reveal interesting magnetic emergent fermions in an existing material ${\mathrm{MnB}}_2$. In the temperature range from 157 K to 760 K, ${\mathrm{MnB}}_2$ is a collinear antiferromagnet. We find the coexistence of eightfold nodal points and nodal network close to the Fermi level, which are protected by the spin group in the absence of spin-orbit coupling. Depending on the Néel vector orientation, consideration of spin-orbit coupling will either open small gaps at these nodal features, or transform them into magnetic linear and quadratic Dirac points and nodal rings. Below 157 K, ${\mathrm{MnB}}_2$ acquires weak ferromagnetism due to spin tilting. We predict that this transition is accompanied by a drastic change in anomalous Hall response, from zero above 157 K to $\sim 200\mathrm{\Omega }{\text{cm}}^{-1}$ below 157 K.

We study transport in an interacting tilted (Stark) chain. We show that the crossover between diffusive and subdiffusive relaxation is governed by $F\sqrt{L}$, where $F$ is the strength of the field, and $L$ is the wavelength of the excitation. While the subdiffusive behavior persists for large fields, the corresponding transport coefficient is exponentially suppressed with $F$ so that the finite-time dynamics appears almost frozen. We (i) explain the crossover scale between the diffusive and subdiffusive transport by bounding the dynamics of the dipole moment for arbitrary initial state, (ii) prove its emergent conservation at infinite temperature for $F\gg 1/L$, and (iii) argue that the numerical data for the tilted chain are consistent with the hydrodynamics of fractons.

Quantum metric and Berry curvature are the real part and imaginary part of the quantum geometric tensor, respectively. The $\mathcal{T}$-odd ($\mathcal{T}$, time-reversal) nonlinear Hall effect driven by the quantum metric dipole, recently confirmed in [Science 381, 181 (2023)] and [Nature (London) 621, 487 (2023)], established the geometric duality to the $\mathcal{T}$-even nonlinear Hall effect that driven by the Berry curvature dipole. Interestingly, a similar geometric duality between the quantum metric and the Berry curvature, particularly for the linear response of Bloch electrons, has not been established, although the $\mathcal{T}$-odd linear intrinsic anomalous Hall effect (IAHE) solely driven by the Berry curvature has been known for a long time. Herein, we develop the quantum theory for displacement current under an AC electric field. Particularly, we show that the $\mathcal{T}$-even component of the linear displacement current conductivity (LDCC) is solely determined by the quantum metric, by both the response theory and the semiclassical theory. Notably, with symmetry analysis we find that the $\mathcal{T}$-even LDCC can contribute a Hall current in $\mathcal{T}$-invariant systems but with low symmetry, while its longitudinal component is immune to symmetry. Furthermore, employing the model Hamiltonians, we arrive at a $1/\mu$ ($\mu$, chemical potential) experimental observable enhancement of the displacement current owing to the divergent behavior of quantum metric near Dirac point, similar to the IAHE at Weyl point. Our study reveals the band geometric origin of the linear displacement current and establishes, together with the IAHE, the geometric duality for the linear response of Bloch electrons. Additionally, our paper offers the intrinsic Hall effect in $\mathcal{T}$-invariant materials, which cannot be envisioned in DC transport in both linear and nonlinear regimes.