In anisotropic or bianisotropic waveguides, the standard coupled-mode theory fails due to the broken link between the forward- and backward-propagating modes, which together form the dual mode sets that are crucial in constructing coupled mode equations. We generalize the coupled-mode theory by treating the forward- and backward-propagating modes on the same footing via a generalized eigenvalue problem that is exactly equivalent to the waveguide Hamiltonian. The generalized eigenvalue problem is fully characterized by two operators, i.e., $(\overline{\mathit{L}},\overline{\mathit{B}})$, wherein $\overline{\mathit{L}}$ is a self-adjoint differential operator, while $\overline{\mathit{B}}$ is a constant antisymmetric operator. From the properties of $\overline{\mathit{L}}$ and $\overline{\mathit{B}}$, we establish the relation between the dual mode sets that are essential in constructing coupled-mode equations in terms of forward- and backward-propagating modes. By perturbation, the generalized coupled-mode equation can be derived in a natural way. Our generalized coupled-mode formalism (GCMF) can be used to study the mode coupling in waveguides that may contain gain, loss, anisotropy, or bianisotropy. We further illustrate how the generalized coupled theory can be used to study the modal coupling in anisotropy and bianisotropy waveguides through a few concrete examples.

We observed ultrafast charge transfer between distorted $1T\text{−}{\mathrm{ReS}}_2$ with anisotropic in-plane electronic and optical properties and $2H\text{−}{\mathrm{WS}}_2$ that is in-plane isotropic. Heterostructures of monolayer ${\mathrm{ReS}}_2$/monolayer ${\mathrm{WS}}_2$ and bilayer ${\mathrm{ReS}}_2$/monolayer ${\mathrm{WS}}_2$ were fabricated by mechanical exfoliation and dry transfer techniques. Significant photoluminescence quenching of ${\mathrm{WS}}_2$ in the heterostructures indicates efficient charge transfer. In femtosecond transient absorption measurements, it was found that holes injected in monolayer or bilayer ${\mathrm{ReS}}_2$ transfer to ${\mathrm{WS}}_2$ on a timescale that is shorter than the time resolution of the measurement. This observation provides evidence that the holes are delocalized in bilayer ${\mathrm{ReS}}_2$, revealing strong van der Waals interlayer couplings. These results also show that ${\mathrm{ReS}}_2$ and ${\mathrm{WS}}_2$ form type-II heterostructures with excellent charge transfer properties.

Using first-principles calculations based on density functional theory, we study the geometric, electronic, and magnetic properties of Pt-, Ni-, and Co-based half-Heusler alloys, namely, $\mathrm{Pt}BC, \mathrm{Ni}BC$, and $\mathrm{Co}BC$ ($B=\mathrm{Cr}$, Mn, and Fe; $C=\mathrm{Al}$ , Si, P, S, Ga, Ge, As, Se, In, Sn, Sb, and Te). We calculate the formation energy of these alloys in various crystal symmetries, which include the cubic $C{1}_b$ ($F\overline{4}3\mathrm{m}$), orthorhombic ($Pnma$), as well as hexagonal ($P\overline{6}2m$ and $P{6}_3/mmc$) structures. It has been observed that, out of the alloys studied, only 18 are energetically stable in the cubic lowest energy structure. These alloys primarily have either a $C$ atom or an $A$ atom (Pt, Ni, or Co) with a high atomic number. We also observe that, along with the alloys with $C$ atoms from groups IIIA, IVA, and VA, alloys with $C$ atoms from group VIA are also found to be, by and large, energetically stable. Furthermore, among the energetically stable cubic alloys, only CoMnSb, CoMnTe, and NiMnSb show the half-metallic property. Under volume-conserving tetragonal distortion, the half-metallic property is completely destroyed in CoMnSb, whereas CoMnTe and NiMnSb maintain half-metallicity for a $c/a$ value from 0.8 to 1.2 for CoMnTe and from 1.0 to 1.2 for NiMnSb, respectively. From the theoretical calculations, many of the half-Heusler alloys are reported to be half-metals in the cubic phase, but these are synthesized in noncubic structures. We analyze the magnetic moment, the electronic density of states, and the spin polarization at the Fermi level, in detail, to find whether a material in the noncubic lowest energy structure exhibits half-metallicity or not. Based on these analyses, the possibility of existence of any one-to-one relationship between the cubic symmetry and the half-metallicity in these half-Heusler alloys is explored. We predict about the existence of a new noncubic half-Heusler alloy with a substantially low density of states at one of the spin channels and subsequently a reasonably high spin polarization at the Fermi level. However, it is found that for alloys in the lowest energy structure, cubic symmetry is necessary for 100% spin polarization. Furthermore, for Pt-based alloys, the effects of spin-orbit coupling (SOC) have been explored. It is observed that inclusion of SOC in the Pt-based alloys does not play a crucial role in either the geometric or the electronic structure consideration.

In the presence of spin-orbit coupling two branches of the energy spectrum of two-dimensional electrons get shifted in the momentum space. Application of an in-plane magnetic field causes the splitting of the branches in energy. When both spin-orbit coupling and Zeeman splitting are present, the branches of the energy spectrum cross at a certain energy. Near this energy, the Landau quantization becomes peculiar since semiclassical trajectories, corresponding to individual branches, get coupled. We study this coupling as a function of the proximity to the topological transition. Remarkably, the dependence on the proximity is strongly asymmetric, reflecting the specifics of the behavior of the trajectories near the crossing. Equally remarkable, on one side of the transition, the magnitude of coupling is an oscillating function of this proximity. These oscillations can be interpreted in terms of the Stückelberg interference. Scaling of characteristic detuning with magnetic length is also unusual. This unusual behavior cannot be captured by simply linearizing the Fermi contours near the crossing point.

We demonstrate multifunctional acoustic metasurfaces that can simultaneously realize the same functionality or multiple different functionalities at multiple tunable frequencies. The fundamental physical mechanism is based on designing a supercell of Helmholtz resonators with multiple resonances operating at different frequencies. We theoretically, numerically, and experimentally demonstrate the achievement of multiple functionalities by the proposed designed metastructure, which produces extraordinary reflection at different angles and different acoustic focusing localizations under the same normal incidence. Our finding paves the way towards multifunctional compact acoustic devices and can lead to pragmatic contemporary applications such as multiple beam shaping, or functional devices with special dispersion properties.

Metallic transition metal dichalcogenides, such as tantalum diselenide $\left(\mathrm{TaS}{\mathrm{e}}_2\right)$, display quantum correlated phenomena of superconductivity and charge density waves (CDWs) at low temperatures. Here, the photophysics of 2H-$\mathrm{TaS}{\mathrm{e}}_2$ during CDW transitions is revealed by combining temperature-dependent, low-frequency Raman spectroscopy and density functional theory (DFT). The spectra contain amplitude, phase, and zone-folded modes that are assigned to specific phonons and lattice restructuring predicted by DFT calculations with superb agreement. The noninvasive and efficient optical methodology detailed here demonstrates an essential link between atomic-scale and microscopic quantum phenomena.

The distinctive character of water ice results from the partially disordered combination of covalent and hydrogen bonds in the network of hydrogen and oxygen atoms. The nontrivial hydrogen correlations we report in diffuse neutron scattering are analytically fit via a description of this state as a topological system exhibiting an emergent gauge field. This allows for the density of correlation-terminating point defects to be determined as one defect per 500 oxygen sites at 30 K. Application of an analytical model of ice paves the way towards a detailed understanding of this ubiquitous solid.

The propagation of light through a random medium is an important problem in photonics. When the random fluctuations of the orientation for individual rods were introduced to the ideal woodpile photonic structure, a crossover from Laue diffraction to randomly scattered fields, which is similar in appearance to speckle patterns, was observed and investigated. Unexpected interplay between order and disorder was discovered from anisotropic glassy samples when orientational disorder was added only in one direction of a square woodpile structure. It is found that the ordered sets of rods produced disordered patterns and the disordered sets of rods produced ordered patterns that continue to be bright and sharp with increasing disorder. To explain this effect, it was demonstrated theoretically and experimentally that the light scattering can be described purely in terms of the intersection points of the rods.

We obtain analytically close forms of benchmark quantum dynamics of the collapse and revival (CR), the reduced density matrix, Von Neumann entropy, and fidelity for the XXZ central spin problem. These quantities characterize the quantum decoherence and entanglement of the system with any number of bath spins, and for a short to infinitely long time evolution. For the homogeneous central spin problem, the effective magnetic field $B$, coupling constant $A$, and longitudinal interaction $\mathrm{\Delta }$ significantly influence the time scales of the quantum dynamics of the central spin and the bath, providing a tunable resource for quantum metrology. Under the resonance condition $B=\mathrm{\Delta }=A$, the location of the $m\mathrm{th}$ revival peak in time reaches a simple relation $t_r\simeq \frac{\pi N}{A}m$ for a large $N$. For $\mathrm{\Delta }=0$, $N\to \infty$, and a small polarization in the initial spin coherent state, our analytical result for the CR recovers the known expression found in the Jaynes-Cummings model, thus building up an exact dynamical connection between the central spin problems and the light-matter interacting systems in quantum nonlinear optics. In addition, the CR dynamics is robust to a moderate inhomogeneity of the coupling amplitudes while disappearing at strong inhomogeneity.

Two-dimensional topologically distinct Chern insulators are separated by gap closing points, which exist as Weyl points in three-dimensional momentum space. Slowly varying parameters in the two-dimensional Hamiltonian across two distinct phases therefore necessarily experience the gap closing process, which prevents the intrinsic physical observable, the Hall response, from equilibrating. Here we demonstrate a scheme to equilibrate the quantized Hall response from pure coherent dynamics as the Hamiltonian is slowly tuned from the topologically trivial to nontrivial regimes. We further apply our method to Weyl semimetals in three dimensions and find the equilibrated Hall response despite the underlying gapless band structure. Our finding not only lays the theoretical foundation for observing the Hall response in Chern insulators but also for observing and controlling Weyl semimetals in ultracold atomic gases.

The ground state of a molecular diamond lattice compound $(\mathrm{ET}){\mathrm{Ag}}_4{\left(\mathrm{CN}\right)}_5$ is investigated by magnetization and nuclear magnetic resonance spectroscopy. We found that the material exhibits a Mott-insulating ground state with antiferromagnetic long-range ordering at 102 K. The ordered moment shows weak ferromagnetism with a tiny canting angle. The spin susceptibility is well fitted into the diamond lattice Heisenberg model with a nearest-neighbor exchange coupling of 230 K, indicating the less frustrated interactions. The transition temperature elevates up to $\sim 195\mathrm{K}$ by applying pressure of 2 GPa, which records the highest temperature among organic molecular magnets. The first-principles band calculation without electron correlations suggests that the system is accessible to a three-dimensional topological semimetal with nodal Dirac lines, which has been anticipated on a half-filling diamond lattice.

Strongly interacting bosons that live in a lattice with degeneracy in its lowest-energy band experience frustration that can prevent the formation of a Bose-Einstein condensate. Such systems form an ideal playground to investigate spin-liquid behavior. We use the variational principle and the Chern-Simons technique of fermionization of hard-core bosons on the kagome lattice to find that below lattice filling fraction $\nu =\frac{1}{3}$ the system favors a topologically ordered chiral spin-liquid state that is gapped in bulk, spontaneously breaks time-reversal symmetry, and supports massless chiral bosonic edge mode. We construct the many-body variational wave function of the state and show that the corresponding energy coincides with the energy of the flat band. This result proves that the ground state of the system cannot stabilize a Bose condensate below $\nu =\frac{1}{3}$. The fermionization and variational scheme we outline apply to any non-Bravais lattice. We distinguish between the roles played by the Chern-Simons gauge field in lattices with a flat band and those exhibiting a moatlike dispersion (which is degenerate along a closed contour in the reciprocal space). We also suggest experimental probes to differentiate the proposed ground state from a condensate.

We report on high-pressure x-ray absorption near edge structure and x-ray magnetic circular dichroism (XMCD) measurements at the Yb $L_3$ edge on ${\mathrm{YbCu}}_2{\mathrm{Si}}_2$. This intermetallic is a well-known intermediate valence compound which shows a pressure-induced paramagnetic-ferromagnetic phase transition at about 8 GPa. The pressure dependence of the Yb magnetization has been determined by following the evolution with pressure of the maximum of the dichroic signal at the energy corresponding to the electric quadrupole ($2p_{3/2}-4f$) transitions. The observed XMCD deduced magnetization curves confirm the ferromagnetic nature of the high-pressure phase as well as the first-order nature of the transition. The Yb ordered moment deduced from XMCD which amounts to about $1.25{\mu }_B$ at 8.7 GPa and 2.7 K is in very good agreement with the one estimated by Mössbauer spectroscopy for the magnetically ordered component of the spectra. This observation indicates that the paramagnetic and ferromagnetic phases coexist only in a narrow pressure range in our XMCD experiment. This is not the case for the Mössbauer measurements, which show that the paramagnetic component vanishes only at 20 GPa. Our results clarify the existing discrepancy with dc magnetization measurements that reported values of the Yb moment more than two times smaller. We propose that these apparent contradictory results are due to different experimental conditions which influence the range of coexistence of the paramagnetic and ferromagnetic phases, as found in many similar situations and frequently addressed in the literature.

${\mathrm{SrMn}}_7{\mathrm{O}}_{12}$ is a recently synthesized homolog of multiferroic ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$. Upon cooling, ${\mathrm{SrMn}}_7{\mathrm{O}}_{12}$ undergoes a series of structural and magnetic phase transitions from cubic to rhombohedral symmetry, and to an incommensurately modulated crystal structure, which is connected with charge and orbital ordering of the Mn cations. We report infrared, terahertz, and Raman spectra of ${\mathrm{SrMn}}_7{\mathrm{O}}_{12}$ ceramics reflecting corresponding changes in phonon selection rules, including new phonons appearing in spin-order-induced ferroelectric phases. The observed phonon activities are compared with the predictions from the factor-group analysis. In the high-temperature phase, more phonons are observed than the number predicted for the cubic symmetry. This is explained by the presence of rhombohedral clusters in the cubic phase. The strongest variations occur in THz spectra near the two magnetic phase transitions, at $T_{\mathrm{N}1}=87\mathrm{K}$ and $T_{\mathrm{N}2}=63\mathrm{K}$. These activate new modes in the spectra, with resonance frequencies and intensities changing with temperature and magnetic field. Below $T_{\mathrm{N}2}$, we observed a transfer of oscillator strengths from low-frequency phonons to these excitations, which we assign to electromagnons.

The antiferromagnetic Weyl semimetal ${\mathrm{Mn}}_3\mathrm{Sn}$ has been shown to generate strong intrinsic anomalous Hall effect (AHE) at room temperature, due to large momentum-space Berry curvature from the time-reversal symmetry-breaking electronic bands of the Kagome planes. This prompts us to investigate intrinsic spin Hall effect, a transverse phenomenon with identical origin as the intrinsic AHE. We report inverse spin Hall effect experiments in nanocrystalline ${\mathrm{Mn}}_3\mathrm{Sn}$ nanowires at room temperature using spin absorption method, which enables us to quantitatively derive both the spin diffusion length and the spin Hall angle in the same device. We observed clear absorption of the spin current in the ${\mathrm{Mn}}_3\mathrm{Sn}$ nanowires when kept in contact with the spin transport channel of a lateral spin-valve device. We estimate spin diffusion length ${\lambda }_{s\left({\text{Mn}}_3\text{Sn}\right)}\sim 0.75$ $\pm$ 0.67 nm from the comparison of spin signal of an identical reference lateral spin valve without ${\mathrm{Mn}}_3\mathrm{Sn}$ nanowire. From inverse spin Hall measurements, we evaluate spin Hall angle ${\theta }_{\text{SH}}\sim 5.3$ $\pm$ 2.4 $\%$ and spin Hall conductivity ${\sigma }_{\text{SH}}\sim 46.99$ $\pm$ 20.63 $\left(\frac{\hslash }{e}\right){\left(\mathrm{\Omega }\mathrm{cm}\right)}^{-1}$. The estimated spin Hall conductivity agrees with both in sign and magnitude to the theoretically predicted intrinsic ${\sigma }_{\text{SH}}^{\text{int}}\sim 36$-96 ($\hslash /e$) (${\mathrm{\Omega }\mathrm{cm})}^{-1}$. We also observed anomalous Hall effect at room temperature in nano-Hall bars prepared at the same time as the spin Hall devices. Large anomalous Hall conductivity along with adequate spin Hall conductivity makes ${\mathrm{Mn}}_3\mathrm{Sn}$ a promising material for ultrafast and ultrahigh-density spintronics devices.

The magnetic structures of ${\mathrm{Er}}_2{\mathrm{Fe}}_2{\mathrm{Si}}_2\mathrm{C}$ and ${\mathrm{Tm}}_2{\mathrm{Fe}}_2{\mathrm{Si}}_2\mathrm{C}$ (monoclinic ${\mathrm{Dy}}_2{\mathrm{Fe}}_2{\mathrm{Si}}_2\mathrm{C}$-type structure, $C2/m$ space group) have been studied by neutron powder diffraction, complemented by magnetization, specific heat measurements, and ${}^{166}\mathrm{Er}$ Mössbauer spectroscopy, over the temperature range 0.5 to 300 K. Their magnetic structures are compared with those of other $R_2{\mathrm{Fe}}_2{\mathrm{Si}}_2\mathrm{C}$ compounds. Antiferromagnetic ordering of the rare-earth sublattice is observed below the Néel temperatures of $T_N=4.8\left(2\right)\mathrm{K}$ and $T_N=2.6\left(3\right)\mathrm{K}$ for ${\mathrm{Er}}_2{\mathrm{Fe}}_2{\mathrm{Si}}_2\mathrm{C}$ and ${\mathrm{Tm}}_2{\mathrm{Fe}}_2{\mathrm{Si}}_2\mathrm{C}$, respectively. While ${\mathrm{Er}}_2{\mathrm{Fe}}_2{\mathrm{Si}}_2\mathrm{C}$ and ${\mathrm{Tm}}_2{\mathrm{Fe}}_2{\mathrm{Si}}_2\mathrm{C}$ have the same crystal structure, they possess different magnetic structures compared with the other $R_2{\mathrm{Fe}}_2{\mathrm{Si}}_2\mathrm{C}$ ($R$ = Nd, Gd, Tb, Dy, and Ho) compounds. In particular, two different propagation vectors are observed below the Néel temperatures: $\mathbf{k}=[\frac{1}{2},\frac{1}{2},0]$ (for ${\mathrm{Er}}_2{\mathrm{Fe}}_2{\mathrm{Si}}_2\mathrm{C}$) and $\mathbf{k}=[0.403\left(1\right),\frac{1}{2},0]$ (for ${\mathrm{Tm}}_2{\mathrm{Fe}}_2{\mathrm{Si}}_2\mathrm{C}$). For both compounds, the difference in propagation vectors is also accompanied by different orientations of the Er and Tm magnetic moments. Although the magnetic structures of ${\mathrm{Er}}_2{\mathrm{Fe}}_2{\mathrm{Si}}_2\mathrm{C}$ and ${\mathrm{Tm}}_2{\mathrm{Fe}}_2{\mathrm{Si}}_2\mathrm{C}$ differ from those of the other $R_2{\mathrm{Fe}}_2{\mathrm{Si}}_2\mathrm{C}$ compounds, we have established that the two magnetic structures are closely related to each other. Our experimental and first-principles studies indicate that the evolution of the magnetic structures across the $R_2{\mathrm{Fe}}_2{\mathrm{Si}}_2\mathrm{C}$ series is a consequence of the complex interplay between the indirect exchange interaction and crystal field effects.