The subtle interaction of low dimensionality and spin correlations in two-dimensional quantum magnets results in novel states of matter. Herein, we investigate the structural, magnetic, heat capacity, ${}^{31}\mathrm{P}$ nuclear magnetic resonance (NMR) measurements, and density functional theory $+$ Hubbard $U$ (DFT $+U$) electronic structure calculations on the ${\mathrm{Cu}}^{2+}$ ($\mathit{S}=\frac{1}{2}$)-based compound ${\mathrm{BaCu}}_2{\left({\mathrm{PO}}_4\right)}_2\left({\mathrm{H}}_2\mathrm{O}\right)$. Based on the hopping parameters obtained from DFT, the titled compound comprises the 2D layer of 1/3-depleted anisotropic kagome lattice with the magnetic couplings $J_1,J_2, J_3$, and $J_4$. At high temperatures, magnetic susceptibility ($\chi$) exhibits paramagnetic behavior, with a Curie-Weiss temperature of ${\theta }_{CW}\approx -67$ K, indicating the presence of dominant antiferromagnetic interactions. The appearance of a broad maximum in the magnetic susceptibility and heat capacity reveals the low-dimensional nature of the compound. While the sharp magnetic anomaly features are not seen clearly in the bulk measurements, the ${}^{31}\mathrm{P}$ NMR local probe measurements unambiguously show the presence of magnetic transition at $T_N=10.5$ K. The temperature ($T$) dependence of nuclear spin-lattice relaxation rate ($1/T_1$) exhibits a sharp peak at $T_{\mathrm{N}}$. While $1/T_1$ falls very steeply below $T_{\mathrm{N}}$, it follows a sublinear power-law behavior above $T_{\mathrm{N}}$, indicating the presence of dynamic short-range correlations, which could be attributed to the complex 2D spin network of the compound.

We present an approach to compute the Floquet quasienergy spectrum of time-periodic systems. The method allows to characterize the light-matter interaction in finite and extended structures by carefully addressing the resolution of the position operator. In periodic systems we discuss the role of the quantum-geometric gauge freedom of Bloch states and employ a Wannier-based scheme to compute the required matrix elements. As a consequence, the method is accurate and applicable to a broad range of systems, from atoms and molecules to cold atomic gases and materials described by density functional theory, as well as model systems. We demonstrate the applicability of the approach by studying two cases: a particle trapped in a one-dimensional box and the semiconducting material ${\mathrm{BC}}_2\mathrm{N}$. We employ the first example to provide a numerical proof of the invariance of the Floquet quasienergy spectrum with respect to the choice of electromagnetic gauge. The analysis of ${\mathrm{BC}}_2\mathrm{N}$ then serves to illustrate the physical effects described by the quasienergies, such as multiphoton resonances, and their expected range of occurrence in real materials in terms of external electric field and frequency of the drive pulse.

In sufficiently clean materials where electron-electron interactions are strong compared to momentum-relaxing scattering processes, electron transport resembles the flow of a viscous fluid. We study hydrodynamic electron transport across density interfaces (n-n junctions) in a 2DEG in the Corbino geometry. From numerical simulations in comsol using realistic parameters, we show that we can produce tunable viscous layers at the density interface by varying the density ratio of charge carriers. We quantitatively explain this observation with simple analytic expressions together with boundary conditions at the interface. We also show signatures of these viscous layers in the magnetoresistance. Breaking down viscous and Ohmic contributions, we find that when the outer radial region of the Corbino has higher charge density compared to the inner region, the viscous layers at the interface serve to suppress the magnetoresistance produced by momentum-relaxing scattering. Conversely, the magnetoresistance is enhanced when the inner region has higher density than the outer. Our results add to the repertoire of techniques for engineering viscous electron flows, which hold a promise for applications in future electronic devices.

Spin parity effects refer to those special situations where a dichotomy in the physical behavior of a system arises, solely depending on whether the relevant spin quantum number is integral or half-odd integral. As is the case with the Haldane conjecture in antiferromagnetic spin chains, their pursuit often derives deep insights and invokes new developments in quantum condensed matter physics. Here, we put forth a simple and general scheme for generating such effects in any spatial dimension through the use of anisotropic interactions, and a setup within reasonable reach of state-of-the-art cold-atom implementations. We demonstrate its utility through a detailed analysis of the magnetization behavior of a specific one-dimensional spin chain model, an anisotropic antiferromagnet in a transverse magnetic field, unraveling along the way the quantum origin of finite-size effects observed in the magnetization curve that had previously been noted but not clearly understood.

We report on the anisotropic electronic properties of the metallic kagome ferromagnet ${\mathrm{Fe}}_3\mathrm{Sn}$, as revealed by magnetotransport studies on single-crystalline samples and material-specific ab initio calculations. The longitudinal resistivity shows a remarkable anisotropy, where surprisingly the resistivity perpendicular to the kagome planes $\left({\rho }_{zz}\right)$ is about three times lower than the in-plane resistivity $\left({\rho }_{xx}\right)$. The ordinary Hall constants are negative for the magnetic field applied parallel to the $\mathbf{H}\left|\right|\mathbf{c}$ and positive for $\mathbf{H}\left|\right|\mathbf{a}$, indicating the coexistence of electron- and hole-like carriers at the Fermi surface. The anomalous Hall resistivity $\left({\rho }_{ij}^A\right)$ shows large values over a wide temperature range and exhibits a significant anisotropy ratio $({\rho }_{xy}/{\rho }_{zy})$, with ${\rho }_{xy}=8 \mu \mathrm{\Omega }\mathrm{cm} \text{and} {\rho }_{zy}=3.2 \mu \mathrm{\Omega }\mathrm{cm}$ at room temperature. Our study reveals that the anisotropy ratio scales almost linearly with the magnetocrystalline anisotropy constant $\left(K_u\right)$ over a broad temperature range $(2 \mathrm{K} \le \mathrm{T} \le 300 \mathrm{K})$, indicating that spin-orbit coupling is the underlying mechanism driving both the anisotropic transport properties and the magnetocrystalline anisotropy energy. Material-specific ab initio calculations further demonstrate that the magnetic reconstruction of bands near the Fermi level, induced by the spin-orbit coupling, is predominantly responsible for the anisotropic behavior of the Berry curvature and, consequently, the large anomalous Hall effect observed in ${\mathrm{Fe}}_3\mathrm{Sn}$. These results provide valuable insight into the complex interplay between charge transport and magnetism in kagome magnets, emphasizing the strong manifestation of spin-orbit coupling on kagome lattices.

The pursuit of multiferroic magnetoelectrics, combining simultaneous ferroelectric and magnetic orders, remains a central focus in condensed matter physics. Here we report that centrosymmetric, one-dimensional (1D) antiferromagnetic $\mathrm{WO}{\mathrm{I}}_3$ undergoes a strain-induced ferroelectric distortion. The paraelectric-ferroelectric transition is originated from the unconventional anisotropic $d^1$ mechanism, where an unpaired $d$ electron of each ${\mathrm{W}}^{5+}$ ion contributes to magnetic orders. Employing a Heisenberg model with Dzyaloshinskii-Moriya interaction, we predict an antiferromagnetic spin configuration as the paraelectric ground state, transitioning to a ferroelectric phase with noncollinear spin arrangement under uniaxial strain. The ferroelectric polarization and noncollinear spin arrangement can be manipulated by varying the applied strain. While the energy barriers for switching ferroelectric polarizations with magnetic orders are on the order of a few dozen $\mathrm{meV}$, the shift current bulk photovoltaic effect exhibits remarkable differences, providing a precise and valuable tool for experimentally probing the interplay of ferroelectric and magnetic orders in 1D $\mathrm{WO}{\mathrm{I}}_3$.

Antiferromagnets have aroused widespread interest in spintronics due to negligible stray field and ultrafast spin dynamics. However, antiferromagnets are usually difficult to exhibit the versatile functional properties featured by ferromagnetic materials, particularly the multiple coupling effect among spin, charge, and orbital. Here, based on first-principles calculations, we propose that by exploiting magnetic-field-induced spin canting, the triple coupling of spin, electric, and valley polarization in antiferromagnetic semiconductors can be easily achieved. Taking the two-dimensional (2D) antiferromagnetic semiconductors ${\mathrm{MnPS}}_3$ and ${\mathrm{MnPSe}}_3$ as examples, we demonstrate the occurrence of ferroelectricity and magnetization driven by different canted-antiferromagnetic orders, and their controllability by both electric and magnetic fields. Remarkably, spin canting further results in bipolar magnetic semiconductor properties with reversible spin polarization and valley polarization in valence and conduction bands. Moreover, we illustrate that such spin-driven multiferroics is derived from the subtle interaction of lattice and spin order. This work paves the way to explore magnetoelectric coupling and valley polarization in 2D antiferromagnetic semiconductors.

We discuss the topology of the parameter space of invertible phases with an onsite symmetry $G$, i.e., quantum many-body ground states that have neither fractionalization nor spontaneous breaking of the symmetry. The classification of invertible phases is known to be obtained by counting the connected components in the parameter space of the invertible phases. We consider its generalization — the deformation classes of the mappings from $n$-dimensional spheres $S^n$ to this parameter space for arbitrary integer $n$. We argue a direct one-to-one correspondence in the framework of lattice models between the noncontractibility of $S^n$ and (i) the classification of invertible phases in $d$ dimensions when $d\ge n$; or (ii) zero-dimensional invertible Hamiltonians parametrized by $S^{n-d}$ when $d<n$, using an isotropic modulating Hamiltonian approach. Explicitly, we construct the noncontractible spheres of two-dimensional invertible phases, i.e., $n=2$ and $d=2$. We also propose a large class of crystalline topological phases protected by a generalized magnetic translations.

The evolution of the magnetic moment as a function of the applied magnetic field for a superconducting material is usually described by the so-called Bean model. We show here that this model fails to explain the magnetic response of conventional type-II superconductor films to a field applied perpendicular to the film plane when their thickness is below 100 nm. More precisely, after zero-field cooling below the critical temperature, a positive moment forms in ascending field and an increasing negative moment develops when sweeping the field back to zero. We infer that such an inverted loop behavior in the case of low-thickness films originates from a combination of low pinning, large penetration depth, and large edge demagnetization field. From relaxation experiments, we demonstrate that the magnetic states along the inverted moment versus field loop are stable equilibrium states. Our findings provide some hints to further understand the high-field paramagnetic Meissner effect reported in thin films and prove that field cooling is not required to produce a paramagnetic-like response.

The $C_n$-symmetric topological crystalline insulator (TCI) emerges as a well-established platform known for exhibiting confined edge and corner states protected by spatial rotational symmetry in Hermitian systems. However, the exploration of non-Hermitian photonic TCIs remains relatively underdeveloped. In this study, we introduce a topological hierarchy (TH) within an alternating gain-loss photonic crystal, encompassing non-Hermitian two-dimensional surface, one-dimensional (1D) hinge, and zero-dimensional corner modes. Our methodology demonstrates a complete TH by manipulating vertical and in-plane couplings. Our analysis shows that both the real and imaginary parts of the energy bands maintain symmetry along the zero-energy line, illustrating a TH similar to that observed in Hermitian systems. Study reveals that in the non-Hermitian case, 1D hinge modes are split into two distinct directions with different real and imaginary component wave intensities. Further investigation shows that our design supports a TH and non-Hermitian higher-order topological modes in higher-orbital band gaps. This work expands the study of three-dimensional non-Hermitian photonic systems and offers a promising route to manipulate wave transmission in disentangled higher-orbital bands.

We study the dynamics of quantum skyrmions under a magnetic field gradient using neural network quantum states. First, we obtain a quantum skyrmion lattice ground state using variational Monte Carlo with a restricted Boltzmann machine as the variational ansatz for a quantum Heisenberg model with a Dzyaloshinskii-Moriya interaction. Then, using the time-dependent variational principle, we study the real-time evolution of quantum skyrmions after a Hamiltonian quench with an inhomogeneous external magnetic field. We show that field gradients are an effective way of manipulating and moving quantum skyrmions. Furthermore, we demonstrate that quantum skyrmions can decay when interacting with each other. This work shows that neural network quantum states offer a promising way of studying the real-time evolution of quantum magnetic systems that are outside the realm of exact diagonalization.

Many intriguing quantum states of matter, such as unconventional superconductivity, magnetic phases, and fractional quantum Hall physics, emerge from the spatially correlated localized electrons in the flat bands of solid materials. By using scanning tunneling microscopy and spectroscopy (STM/STS), we report on the real-space investigation of correlated electrons in the flat band of superlattice $4H_b\text{−}\mathrm{TaS}{\mathrm{e}}_x{\mathrm{S}}_{2-x}$. In contrast with the pristine $4H_b\text{−}\mathrm{Ta}{\mathrm{S}}_2$, the selenium (Se) substitutions significantly affect the interfacial transfer of correlated electrons between the charge density wave (CDW) states of $1T$- and $1H\text{−}\mathrm{Ta}{\mathrm{S}}_2$ layers and contribute the real-space fractional electron-filling configurations with the distributed electron-filled and void Star of David (SoD) clusters of the $1T$ layer. The site-specific STS spectra directly reveal their respective prominent spectra weight above $E_{\mathrm{F}}$ and symmetric Mott-like spectra. In addition, the spatial distributions of these electron-filled SoDs in the $1T$ layer of $4H_b\text{−}\mathrm{TaS}{\mathrm{e}}_{0.7}{\mathrm{S}}_{1.3}$ demonstrate different local short-range order, clearly indicating the complex neighboring interactions among the localized electrons in the flat band of the $1T$ layer. Our results not only provide in-depth insight into correlated electrons in the flat CDW band but also provide a simple platform to manipulate the electron-correlation-related quantum states.

Molybdenum disulfide (${\mathrm{MoS}}_2$) is a next-generation semiconductor and is frequently integrated into emergent optoelectronic technologies based on two-dimensional materials. Here, we present a method that provides direct optical feedback on the thickness and crystallinity of sputter-deposited ${\mathrm{MoS}}_2$ down to the few-layer regime. This colorimetric sensing enables tracking the material's functional properties, such as excitonic response, sheet resistance, and hardness across the amorphous-crystalline transition. To illustrate the potential of such feedback-controlled fabrication, we realized ${\mathrm{MoS}}_2$-based hyperbolic metamaterials (HMMs) with controllable optical topological transitions and hardness.

The existence of a toroidal-like eigenmode and its electromagnetic coupling in a system of dielectric particles are studied. A constituent structure (metamolecule) is made of a ring consisting of the radial arrangement of several vertically standing dielectric disks (meta-atoms). In the eigenstate of the given metamolecule, the second-order term related to the exact electric dipole in the multipole decomposition is much greater than the first-order term. This eigenstate is defined as a toroidal-like mode. Then, the characteristics of a system (metamacromolecule) composed of two identical rings are studied in both eigen- and excited states to reveal the peculiarities of the toroidal-like mode coupling. Similar to the well-known electric dipole-dipole and magnetic dipole-dipole interactions, the interaction of toroidal-like modes also appears in symmetric (bonding) and antisymmetric (antibonding) forms. Their excitation in the metamacromolecule depends on the propagation direction and polarization of the irradiating wave. The manifestation of toroidal-like mode coupling is confirmed by checking the extinction cross section and near-field distributions obtained from the full-wave numerical simulation and microwave experiment. A clear understanding of the nature of toroidicity is important from the fundamental physics perspective and practical implementation of metamaterials operated in such exotic states.

Recently, a novel class of 2D carbon material, covalent-bond-linked monolayer ${\mathrm{C}}_{60}$ networks with quasihexagonal phase (qHP-${\mathrm{C}}_{60}$) was experimentally fabricated [Hou et al., Nature (London) 606, 507 (2022)]. Here, using first-principles calculations, we predict that such a two-dimensional network serves as an ideal platform in stabilizing transition metals (TM: Mn, Fe, Co, and Ni) into dispersive single atoms, exhibiting remarkable efficiency for spin-triplet ${\mathrm{O}}_2$ activation and CO oxidation with low reaction barriers $(0.3\sim 0.5\mathrm{eV})$. First, the two-dimensional qHP-${\mathrm{C}}_{60}$ network acts as an electronic reservoir responsible for charge transfer to the antibonding orbital of ${\mathrm{O}}_2$. Second, and important, it functions as a spin sponge in accommodation of the reduced spin magnetic moment from ${\mathrm{O}}_2$ molecule, facilitating its spin triplet-to-singlet transition in the framework of Wigner's spin conservation rule. Delicate quantitative calculations demonstrate that the spin component contributes approximately twice as significantly as that of pure charge transfer in reducing the activation barrier for CO oxidation.

The symmetry-assisted anomalous valley Hall effect offers exciting prospects in valleytronics and spintronics. Here, using density functional theory and symmetry analysis, we propose an underlying mechanism for the fundamental origin of enhanced anomalous Hall conductivity ${\sigma }_{xy}$ in the ${\mathrm{CrS}}_2$ layer in the ${\mathrm{CrS}}_2/{\mathrm{CrBr}}_3$ heterostructure. Notably, we find that the magnetic proximity effect (MPE) induces an identical nature of spin magnetic moments from the magnetic ${\mathrm{CrBr}}_3$ to nonmagnetic ${\mathrm{CrS}}_2$ layer. For out-of-plane spin components $\left(0^{\circ }\le \theta <{90}^{\circ }\right)$, in addition to orbital magnetic moments, induced magnetization and correction from Berry curvatures $\left[{\mathrm{\Omega }}_z\left(\mathbf{k}\right)\right]$ leads to an additional contribution to ${\sigma }_{xy}$ in the ${\mathrm{CrS}}_2$ layer. Under in-plane magnetization directions, both time-reversal symmetry $\left(\mathcal{T}\right)$ and out-of-plane mirror symmetry $\left({\mathcal{M}}_{\mathcal{Z}}\right)$ are broken; however, their joint operation is preserved. This joint symmetry operation guarantees Kramers spin degeneracy at the K and ${\mathrm{K}}^{\prime }$ valleys, resulting in vanishing ${\sigma }_{xy}$. The exchange coupling between spins at valleys and magnetization directions induces an angular profile of ${\sigma }_{xy}$ identical to the magnetic moment nature in the ${\mathrm{CrBr}}_3$ layer. Our study reveals a potential approach to predict the variation of ${\sigma }_{xy}$ in valley-polarized heterostructures through symmetry-assisted MPE and sheds light on understanding recent experimental findings in valleytronics.

Based on first-principles calculations and quantum transport simulations, we systematically study the transport properties of $n$-type Dirac-source transistors based on lateral graphene/$\mathrm{Mo}{\mathrm{S}}_2$ heterostructures. Through manipulation of the graphene source doping concentration, we achieve a steep subthreshold swing (SS) of 48 mV/decade in the graphene/$\mathrm{Mo}{\mathrm{S}}_2$ lateral heterostructure Dirac-source transistor, while maintaining an on-state current of 456.718 $\mu \mathrm{A}/\mu \mathrm{m}$, meeting the [International Technology Roadmap for Semiconductors 2013 ed., https://www.semiconductors.org/resources/2013] requirements for low-power devices. Our analysis reveals that too high or too low source doping concentrations are detrimental to both SS and on-state currents due to unfavorable band alignments at the graphene/$\mathrm{Mo}{\mathrm{S}}_2$ interface. Additionally, we observe a dual effect of interface states on device performance. The interface Schottky barrier (SB) is slightly decreased from the off state to the on state due to the pinning of the interface states, and the increase of the current is attributed to the thinning of the SB. On the other hand, interface states shorten the tunneling path through the triangular SB at the on state, thereby enhancing the on-state currents. Finally we summarize the working mechanism of lateral heterostructure Dirac-source transistors. Our calculations can serve as a theoretical guide for designing Dirac-source transistors with both steep SS and large on-state currents based on two-dimensional lateral heterostructures.