The anomalous Hall effect (AHE) has been extended into the nonlinear regime, where the Hall voltage shows higher-order response to the applied current. Nevertheless, the microscopic mechanism of the nonlinear AHE remains unclear. Here we report the orbital polarization and its induced third-order AHE in few-layer $\mathrm{W}{\mathrm{Te}}_2$ flakes. Through angle-dependent electric measurements, it is found that the third-order AHE is quite consistent with the electric field induced polarization of orbital magnetic moment caused by the Berry connection polarizability tensor, which is further directly detected by polar reflective magnetic circular dichroism spectroscopy. The microscopic mechanisms of third-order AHE are analyzed through the scaling law, that is, the opposite orbital magnetic moments (up or down) deflect to opposite directions driven by electric field induced Berry curvature, forming the intrinsic contribution; driven by the Magnus effect of the self-rotating Bloch electrons, the opposite orbital magnetic moments are scattered towards opposite transverse directions, resulting in the skew scattering.

Plasmonic waveguides provide an integrated platform to develop efficient nanoscale ultrafast photonic devices. Although metals display a rich variety of nonlocal optical effects and surface nonlinearities, the study of plasmonic waveguides has been limited to considering conventional bulk nonlinearities. Such analytical tools, however, do not allow us to incorporate the nonlocal optical effects on the studied phenomenon or the nonlinearities arising from it. In this work, we present a method based on the numerical calculation of the inhomogeneous solution that enables the study of nonlinear optical effects, such as second-harmonic generation, in waveguides displaying nonlocal response effects as well as surface nonlinearities. We use the proposed method to study the nonlinear response arising from the hydrodynamic description of free electrons in the metallic constituents of the waveguides, comparing local and nonlocal approximations. As a more general application of our method, we also consider nonlinearities arising from the quantum hydrodynamic theory with electron spill-out. Our results may find applicability in the design and analysis of integrated photonic platforms for nonlinear optics incorporating a wide variety of nonlinear materials such as heavily doped semiconductors for midinfrared applications.

Actively tunable nanodevices play an important role in modern photonics systems. Metasurfaces based on phase-change materials (PCMs) provide a new way for the realization of such devices. At present, the PCM is usually integrated with the resonant metasurfaces with low $Q$ factor or as a resonator to achieve the optical switches. Note that less work has focused on the switching characteristics of strong light trapping of in high-$Q$-factor metasurfaces. The main reason is that PCM has a significant intrinsic loss. Recently, the PCM ${\text{Ge}}_2{\text{Sb}}_2{\text{Se}}_4{\text{Te}}_1$ (GSST) with ultralow loss has been proved by in experiment ($k\approx 0$), which makes it is possible to achieve the active metasurfaces with high $Q$ factor. Moreover, the symmetry-protected bound states in the continuum (BICs) provides an effective method to achieve the high-$Q$-factor metasurface. The perturbation that breaks the in-plane inversion symmetry of a structure can transform such a BIC mode into a leaky quasi-BIC with high $Q$ factor. In this work, the BIC and the light trapping characteristics of quasi-BIC in PCM GSST metasurfaces are studied numerically. Through moving the relative position of nanobars, the structure symmetry of the amorphous GSST metasurface is disturbed, which makes an ideal BIC convert to a quasi-BIC with high $Q$ factor. The average field-enhancement factor (EF) of quasi-BIC is evaluated, which is proportional to the $Q$ factor of resonance mode. Meanwhile, the effects of structure parameters, polarization angle and incident angle of light on EF are also discussed. In addition, by calculating the EF values under different disturbance parameters $d$ and crystallization degrees $m$. The switching characteristic of light trapping of quasi-BICs is discussed. It is worth noting that the asymmetric parameters can be precisely controlled in the process of the excitation of BICs in this way, which provides a way for the realization of ultrahigh $Q$ factors and makes it possible to strongly trap light and manipulate it dynamically. Our work provides a route for actively tunable and reconfigurable micro or nano optical devices.

Crystallographic structure and long-range magnetic order of iron have been measured in pressure-temperature domains of 2–18 GPa and 300–800 K, using x-ray absorption spectroscopy and x-ray magnetic circular dichroism (XMCD) in resistively heated diamond anvil cells under hydrostatic pressurizing conditions. A fine coverage of pressure-temperature space allowed monitoring $\alpha \leftrightarrow \epsilon , \alpha \to \gamma$, and $\gamma \to \epsilon$ transformations, evidencing large metastability phenomena. $\alpha$-Fe remains ferromagnetic under high pressure and temperature in its whole stability domain, and no magnetic response could be measured with XMCD in pure $\gamma$-Fe and $\epsilon$-Fe. Structural and magnetic transformations are observed concomitantly within experimental uncertainties.

Laser ablation of dielectrics by ultrashort pulsed laser radiation is induced by nonlinear photoexcitation, such as multiphoton and tunneling processes, and the subsequent impact excitation, due to electron-electron collisions. Previous theoretical and experimental studies demonstrate that these two phenomena strongly depend on the transient optical properties of the dielectric and the electron-electron collision times. To estimate these transient optical properties and the collision time, the excited electrons are usually considered as a nearly free-electron gas, being described by the Drude theory. All previous experimental studies support using the Drude theory by time-resolved measurements of the transient reflectance during and after irradiation. However, a comprehensive characterization of the transient complex refractive index, and, thus, a more complex view of the optical properties upon irradiation above the ablation threshold fluence was still missing. Therefore, this paper presents the time-, spectral-, and fluence-resolved complex refractive index of fused silica during the interaction with ultrashort pulsed laser radiation (800 nm, 40 fs, and 4.4 J/${\mathrm{cm}}^2$) measured by spectroscopic imaging pump-probe ellipsometry. Comparing the state-of-the-art Drude model to the experimental data reveals that, although the Drude model replicates the transient reflectance of the material, it deviates significantly from the transient refractive index in the considered temporal range up to 200 fs after irradiation. Thus, the Drude model cannot correctly describe the transient optical properties, which leads to the assumption that the electrons cannot be considered as a nearly free-electron gas at this time. Alternatively, a Lorentz model, considering the excited electrons as bound, can replicate the measured data much better, which indicates that the electrons might be excited into localized states.

We report the magneto-optic Kerr effect (MOKE) angle of Au magnetically excited by spin accumulation. We perform time-resolved polar MOKE measurements on Au/Co heterostructures. In our experiment, the ultrafast optical excitation of the Co drives spin accumulation into an adjacent Au layer. The spin accumulation, together with spin-orbit coupling, leads to nonzero terms in the off-diagonal conductivity tensor of Au, which we measure by recording the polarization and ellipticity of light reflected from the Au surface for photon energies between 1.3 and 3.1 eV. In a narrow energy range near the interband transition threshold of Au, the sensitivity to magnetization measured exceeds $1\mu \mathrm{rad}\mathrm{per}\mathrm{A}/\mathrm{m}$. In the photon energy interval of 0.6–4.4 eV, the maximum value for transition ferromagnetic metals like Ni are $<10\mathrm{nrad}\mathrm{per}\mathrm{A}/\mathrm{m}$, while predicted values for heavy metals like Pt or W are $<13\mathrm{nrad}\mathrm{per}\mathrm{A}/\mathrm{m}$. The exceptional sensitivity of the optical properties of Au to spin magnetic moments make Au an exceptionally sensitive optical magnetometer, with potential applications in the development of optospintronic technologies.

We study higher-spin ($S\ge 1$) generalization of the one-dimensional Kondo-Heisenberg model, in which the local spin-$S$ moments of the Kondo-lattice model interact with each other via the antiferromagnetic Heisenberg interaction ($J_{\text{H}}$), by analytical and numerical methods. The strong-coupling (i.e., large Kondo coupling) expansion maps out an insulating phase at half-filling whose magnetic correlation depends on the parity of $2S$ as well as a ferromagnetic metallic phase which dominates the strong-coupling region at generic fillings. Then, we carried out the density-matrix renormalization-group simulations for $S=1$ to closely investigate the phase structure at large but finite Kondo coupling. At half-filling, the Kondo coupling and $J_{\text{H}}$ do not compete and the insulating spin-gapless phase is stable, while the competition of the two leads to a stepwise collapse of the strong-coupling ferromagnetism via an intervening dimerized insulating phase with power-law spin correlation at quarter-filling.

The Kitaev model exhibits a canonical quantum spin liquid as a ground state and hosts two fractional quasiparticles, i.e., itinerant Majorana fermion and localized flux excitation. The former can carry heat and spin modulations in the quantum spin liquid, but the role of the latter remains unknown for the transport phenomena. Here, we focus on spin transport in the presence of excited fluxes and report that they yield strong interference in the propagation of the Majorana fermions, which have a gaugelike potential emergent around the fluxes. We examine the transient spin dynamics triggered by a pulsed magnetic field at an edge. In the absence of excited fluxes, the magnetic-field pulse creates the plane wave of the Majorana fermions, which flows in the quantum spin liquid. Although this wave does not accompany the change of local spin moments in bulk, it induces local moments at the side opposite to the edge under the magnetic-field pulse. We observe the spatial modulation of induced spin moments when fluxes are excited in the bulk region. This behavior is more striking than the case of lattice defects. Moreover, we find that although the amplitude of the spatial change is almost independent of the distance between lattice defects, it is strongly enhanced by increasing the distance for the case of excited fluxes. The difference is understood from the influence on the itinerant Majorana fermions; the lattice defects change the system locally, but flux excitations alter all the transfer integrals on the string connecting them. The present results will provide another route to observing intrinsic flux excitations distinguished from extrinsic effects such as lattice defects.

In this paper, we report the results of magnetic resonance spectroscopy of ${\mathrm{EuFe}}_2{\mathrm{As}}_2$ single crystals. We observe magnetic resonance responses, which are attributed to antiferromagnetic resonances of the Eu sublattice with orthorhombic crystal structure and with different orientations of twin domains relative to the external field. We confirm the validity of the recently proposed spin Hamiltonian with anisotropic Eu-Eu exchange interaction and biquadratic Eu-Fe exchange interaction.

Motivated by the giant phonon anomalies in $\alpha -\mathrm{Ru}{\mathrm{Cl}}_3$ reported by H. Li et al. [Nat. Commun. 12, 3513 (2021)], we investigate the thermal Hall effect in a Kitaev-Heisenberg system in the presence of the coupling between spins and phonons arising from chlorine atoms' vibration. We observe that the coupling modifies the relative stability between different magnetic states under a magnetic field, especially stabilizing a canted zigzag antiferromagnetic state. Remarkably, the spin-phonon interaction has distinct effects on the thermal Hall conductivity in different magnetically ordered states. For a canted zigzag state, which is relevant to $\alpha {\text{-RuCl}}_3$, the spin-phonon interaction enhances the magnon excitation gap induced by a magnetic field and suppresses the thermal Hall conductivity at low temperatures. For the Kitaev spin liquid state, we find that the spin-phonon interaction reduces the excitation gap of Majorana fermions and destabilizes the quantized thermal Hall effect. Our results demonstrate a crucial role of phonon degrees of freedom in the thermal Hall effect in Kitaev materials.

We report inelastic neutron scattering study of the antiferromagnetic spin stripe fluctuations above the spin stripe melting temperature ${\mathrm{T}}_{so}\approx 190\mathrm{K}$ in the hole doped ${\mathrm{Pr}}_{2-x}{\mathrm{Sr}}_x{\mathrm{NiO}}_{4+\delta }$ with stripe incommensurability $\epsilon =0.33$. The fluctuations are nondispersive and detected upto 10 meV at the incommensurate wave vector indicating a persisting instantaneous spin and charge stripe correlation above ${\mathrm{T}}_{so}$, while they are strongly diminished already below the charge stripe melting temperature ${\mathrm{T}}_{co}\approx 255\mathrm{K}$, which indicates that static charge stripe order is essential for the dynamical spin stripe correlation to exist. Furthermore, it also suggests that the presence of spin stripe fluctuations is not a prerequisite for the formation of static charge stripes.

An effective spin model for Mott insulators is determined by the symmetries involved among magnetic sites, electron fillings, and their interactions. Such a spin Hamiltonian offers insight to mechanisms of magnetic orders and magnetic anisotropy beyond the Heisenberg model. For a spin moment S bigger than 1/2, single-ion anisotropy is in principle allowed. However, for $d^3$ Mott insulators with large cubic crystal field splitting, the single-ion anisotropy is absent within the LS coupling, despite S = 3/2 local moment. On the other hand, preferred magnetic moment directions in $d^3$ materials have been reported, which calls for a further theoretical investigation. Here we derive the single-ion anisotropy interaction using the strong-coupling perturbation theory. The cubic crystal field splitting including $e_g$ orbitals, trigonal distortions, Hund's coupling, and spin-orbit coupling beyond the LS scheme are taken into account. For compressed distortion, the spin-orbit coupling at magnetic sites can favor either the easy-axis or the easy-plane while that of anions leads to easy-axis anisotropy. We apply the theory on ${\mathrm{CrX}}_3$ with X = Cl and I, and show the dependence of the single-ion anisotropy on the strength of the spin-orbit couplings of both magnetic and anion sites. Significance of the single-ion anisotropy in ideal two-dimensional magnets is also discussed.

Multiphonon physics is an emerging field that serves as a test bed for fundamental quantum physics and several applications in metrology and on-chip communication, among others. Quantum acoustic cavities or resonators are devices that are being used to study multiphonon phenomena both theoretically and experimentally. In particular, we study a system consisting of a semiconductor quantum dot pumped by a driving laser and coupled to an acoustic cavity. This kind of system has proven to yield interesting multiphonon phenomena, but the description of the quantum dot has been limited to a two-level system. This limitation restrains the complexity that a true semiconductor quantum dot can offer. Instead, in this work we consider a model where the quantum dot can have both bright and dark excitons, the latter being particularly useful due to their lower decoherence rates, because they do not present spontaneous photon emission. In this setup, we demonstrate that by fine-tuning the driving laser frequency, one is able to realize giant Rabi oscillations between the vacuum state and a dark-exciton state with $N$-phonon bundles. From this, we highlight two outstanding features: first, we are able to create dark-state excitations in the quantum dot without the usual external magnetic field needed to do so; and second, in a dissipative scenario where the acoustic cavity and the quantum dot suffer from losses, the system acts as a phonon gun able to emit $N$-phonon bundles.

Resonant optical responses of anisotropic molybdenum disulfide (${\mathrm{MoS}}_2$) nanoparticles (NPs) and their two-dimensional arrays (metasurfaces) are investigated. The nanoparticles in the form of disks with holes and with ${\mathrm{MoS}}_2$ layers oriented perpendicular to the disk's basis (in-plane material anisotropy) are considered. Using numerical calculations with analytical multipole analysis, we show that the material anisotropy of NPs provides an additional degree of freedom for manipulation of their resonant magnetic and electric dipole responses and affect the effective dipole polarizabilities. Based on this possibility and applying a special tuning procedure, we construct the ${\mathrm{MoS}}_2$ metasurfaces supporting the quasitrapped mode (QTM) resonance around the telecom wavelength of 1550 nm with high quality factor and high sensitivity to the environment. It is shown that regardless of extremely weak absorption of the single nanoparticles, the excitation of the QTM leads to effective narrowband absorption in the telecom wavelength range depending on the polarization direction of normally incident waves. It is demonstrated that a metasurface, composed of the ${\mathrm{MoS}}_2$ disks with the in-plane material anisotropy, has the properties of a continuous birefringent medium. Due to these properties, a normally incident linearly polarized wave can be transformed into transmitted and reflected waves with changed polarizations.

The combination of two-dimensional Dirac surface states with $s$-wave superconductivity is expected to generate localized topological Majorana zero modes in vortex cores. Putative experimental signatures of these modes have been reported for heterostructures of proximitized topological insulators, iron-based superconductors or certain transition metal dichalcogenides. Despite these efforts, the Majorana nature of the observed excitation is still under debate. We propose to identify the presence of Majorana vortex modes using a nonlocal transport measurement protocol originally employed for one-dimensional settings. In the case of an isolated subgap state, the protocol provides a spatial map of the ratio of local charge- and probability-density which offers a clear distinction between Majorana and ordinary fermionic modes. We show that these distinctive features survive in the experimentally relevant case of hybridizing vortex core modes.

We investigate Majorana modes in a quantum spin chain with bond-dependent exchange interactions by studying its dynamics. Specifically, we consider two-time correlations for the anisotropic Kitaev-Heisenberg (KH) Hamiltonian close to the so-called Kitaev critical point. Here the model coincides with a phase boundary of two uncoupled instances of Kitaev's model for $p$-wave superconductors, together supporting a degenerate ground state characterized by multiple Majorana modes. In this regime, the real-time dynamics of local spins reveal a set of strong zero modes, corresponding to a set of protruding frequencies in the two-time correlation function. We derive perturbative interactions that map the KH spin chain onto the topological regime of Kitaev's fermionic model, thus opening up a bulk gap while retaining almost degenerate modes in the mesoscopic regime, i.e., for finite system sizes. This showcases the emergence of Majorana modes in a chain of effective dimers. Here, the binding energy within each unit cell competes with the interdimer coupling to generate a finite-size energy gap, in analogy with local energy terms in the transverse-field Ising model. These modes give rise to long coherence times of local spins located at the system edges. By breaking the local symmetry in each dimer, one can also observe a second class of Majorana modes in terms of a beating frequency in the two-time correlations function of the edge spin. Furthermore, we develop a scenario for realizing these model predictions in ion-trap quantum simulators with collective addressing of the ions.

Stacked graphene multilayers with a small relative twist angle between each of the layers have been found to host flat bands at a series of “magic” angles. We consider the effect that Dirac point asymmetry between the layers, and in particular different Fermi velocities in each layer, may have on this phenomenon. Such asymmetry may be introduced by unequal Fermi velocity renormalizations through Coulomb interactions with a dielectric substrate. It also arises in an approximate way in tetralayer systems, in which the outer twist angles are large enough that there is a dominant moiré periodicity from the stacking of the inner two layers. We find in such models that the flat band phenomenon persists in spite of this asymmetry, and that the magic angles acquire a degree of tunability through either controlling the screening in the bilayer system or the twist angles of the outer layers in the tetralayer system. Notably, we find in our models that the quantitative values of the magic angles are increased.

While the optical band gap of pristine hexagonal boron nitride (hBN) is about 6 eV, emissions from defects in the visible regime with single-photon characteristics have been observed in experiment for a long time. To tackle the question which kind of defects are responsible for these emissions, many ab initio studies have been conducted. Most of them are on the level of density-functional theory (DFT). While DFT provides an efficient method to obtain band dispersion and optimal structure, it lacks the ability to calculate the quasiparticle energy levels correctly. In this work, we employ an efficient approximation of the $GW$ theory to calculate quasiparticle energy levels of small atomic defects: Two carbon substitutions ${\mathrm{C}}_{\mathrm{N}}$ and ${\mathrm{C}}_{\mathrm{B}}$, the nitrogen vacancy ${\mathrm{V}}_{\mathrm{N}}$, and the divacancy ${\mathrm{V}}_{\text{NB}}$. Optical spectra are calculated by solving the Bethe-Salpeter equation. The defect systems which are examined in this work allow for transitions between intrinsic states of hBN and deep defect states which lie inside the band gap, resulting in bright excitons at $\sim 2\mathrm{eV}$.

The spin Nernst effect is a phenomenon in which the spin current flows perpendicular to a temperature gradient. Similar to the spin Hall effect, this phenomenon also causes spin accumulation at the boundaries. Here, we study the spin response to the gradient of the temperature gradient with the use of Green's functions. Our formalism predicts physically observable spin accumulation without the ambiguity regarding the definition of the spin current or the magnetization correction. We prove the generalized Mott relation between the electric and thermal responses assuming the presence of time-reversal symmetry and the absence of inelastic scattering. We also find that thermal spin accumulation vanishes for the three-dimensional Luttinger model but is nonzero for the two-dimensional Rashba model with $\delta$-function nonmagnetic disorder in the first Born approximation.

We study the low-energy single-electron transport across a junction of two magnetic Weyl semimetals, in which the anisotropy axes are tilted one respect to the other. Using a two-band model with a potential step, we compute the transmission factor for normal and Klein tunneling and the refraction properties of the interface as a function of the tilt angle. We show that the interface acts as a beam splitter, separating electrons with different chiralities. We also characterize interface states, only appearing for finite tilt angle, which connect the projection of the Fermi surfaces on the two sides of the junction, and we discuss transport effects due to their interplay with Fermi arcs.