${\mathrm{Me}}_{3+\delta }\mathrm{Ge}$, being a Weyl semimetal, shows a large anomalous Hall effect (AHE), which decreases slowly with an increase in $\delta$ from 0.1 to 0.4. However, AHE in this compound remains significantly large in the whole range of $\delta$ because of the robust nature of the topology of bands. To explore the possibility of tuning the anomalous transport effects in Weyl semimetals, we have studied the single-crystal hexagonal-($\mathrm{Mn}_{0.78}\mathrm{Fe}_{0.22}){}_3\mathrm{Ge}$ compound. Magnetization of this compound shows two magnetic transitions at 242 K ($T_{\text{N1}}$) and 120 K ($T_{\text{N2}}$). We observed that the AHE persists between $T_{\text{N2}}\text{−}{T}_{\text{N1}}$ and vanishes below $T_{\text{N2}}$. Further, we performed single-crystal neutron diffraction experiments (using spherical neutron polarimetry and unpolarized neutron diffraction) to determine the magnetic structures of ($\mathrm{Mn}_{0.78}\mathrm{Fe}_{0.22}){}_3\mathrm{Ge}$ at different temperatures. Our neutron diffraction results show that the sample possesses a collinear antiferromagnetic structure below $T_{\text{N2}}$. However, the magnetic structure of the sample remains noncollinear antiferromagnetic, the same as ${\mathrm{Mn}}_3\mathrm{Ge}$, between $T_{\text{N1}}$ to $T_{\text{N2}}$. The presence of AHE, and noncollinear magnetic structure in ($\mathrm{Mn}_{0.78}\mathrm{Fe}_{0.22}){}_3\mathrm{Ge}$, between $T_{\text{N1}}$ and $T_{\text{N2}}$, suggest the existence of Weyl points in this temperature regime. Below $T_{\text{N2}}$, AHE is absent, and the magnetic structure also changes to a collinear antiferromagnetic structure. These observations signify a strong link between the magnetic structure of the sample and AHE.

The lifetime of a magnetic skyrmion in a two-dimensional lattice is calculated as a function of size, from nanometer scale to microns, while the shape of the skyrmion remains the same. Values of the parameters in the extended Heisenberg Hamiltonian that includes exchange, anisotropy, Dzyaloshinskii-Moriya interaction, and the effect of an external field, are scaled in accordance with a continuous micromagnetic description. The lifetime increases dramatically with increased skyrmion size both because of a decrease in the entropy of the transition state with respect to that of the skyrmion state, resulting in an increase in the pre-exponential factor by four orders of magnitude, and because the activation energy increases towards an upper bound consistent with the energy of the Belavin-Polyakov soliton. While the calculated lifetime of the skyrmion for the Hamiltonian parameter values chosen here is less than a microsecond when the radius is 5 lattice constants, it reaches years when the radius is 100 lattice constants at a temperature of 200 K and an hour at room temperature. The calculations of the largest skyrmion studied here explicitly include over 20 000 000 spins.

${\mathrm{EuMnSb}}_2$ is an intriguing magnetic topological semimetal containing two antiferromagnetic sublattices, and the interplay of magnetism between Eu and Mn sublattices leads to rich interesting transport phenomena. Here we report a comprehensive experimental study of the magnetic properties in ${\mathrm{EuMn}}_{1-x}{\mathrm{Zn}}_x{\mathrm{Sb}}_2$ (0 $\le x\le$ 1) by using structural, resistivity, magnetization, and specific heat measurements. The magnetic phase diagrams of ${\mathrm{EuMn}}_{1-x}{\mathrm{Zn}}_x{\mathrm{Sb}}_2$ along two magnetic field orientations are established based on magnetization and specific heat measurements, constituted by the antiferromagnetic ordering of Mn at high temperature, and successive magnetic transitions of Eu at low temperatures. The antiferromagnetic transition temperature of Mn is suppressed by Zn doping and cannot be detected by specific heat measurements when $x>$ 0.3. The antiferromagnetic transition temperature of Eu exhibits a weak nonmonotonic doping dependence with a significant anisotropy in the doping range of 0 $\le x\le$ 0.4. The spin orientation of Eu is gradually reoriented from the out-of-plane direction to the in-plane direction. It closely correlates with the Mn antiferromagnetic ordering, indicating a strong coupling between the Eu and Mn magnetism. Our study will be helpful for understanding the magnetic properties of compounds with two antiferromagnetic lattices and open an avenue for tuning the spin orientation through the interaction between the different magnetic lattices.

Magnetic skyrmions are fascinating topological particle-like textures which are promoted by a trade-off among interfacial properties (perpendicular anisotropy and Dzyaloshinskii-Moriya interaction) and dipolar interactions. Depending on the dominant interaction, complex spin textures, including pure Néel and hybrid skyrmions, have been observed in magnetic multilayers. A quantification of these different spin textures typically requires a depth-reoslved magnetic imaging or scattering techniques. In the present work, we will show qualitatively different collapsing dynamics for pure Néel and hybrid skyrmions induced by a perpendicular magnetic field in two representative systems, ${[\mathrm{Pt}/\mathrm{Co}/\mathrm{Ir}]}_{15}$ and ${\left[\mathrm{Ta}/\mathrm{CoFeB}/\mathrm{MgO}\right]}_{15}$ multilayers. Skyrmions in the former stack undergo a first morphological transition at zero field to labyrinth domains, and followed by a second morphological transition to skyrmions with opposite chirality and polarity, upon reversing the direction of perpendicular fields. On the other hand, skyrmions in ${\left[\mathrm{Ta}/\mathrm{CoFeB}/\mathrm{MgO}\right]}_{15}$ multilayers exhibit a continuous transition as a function of the field, which is mainly linked to a reversible change of the skyrmion size. A full micromagnetic phase diagram is presented to identify these two collapsing mechanisms as a function of material parameters. Since the two distinct collapsing dynamics rely on the detailed layer-dependent spin structures of skyrmions, we propose to use them as potential fingerprints for identifying the type of skyrmions in magnetic multilayers. Our work could be important for employing pure and hybrid skyrmions for specific applications, due to the strong correlation between the skyrmion dynamics and three-dimensional spin profiles.

The paper demonstrates the existence of modulational instability (MI) in nonlinear exciton-polariton condensates (EPCs). A set of coupled two-dimensional (2D) driven-dissipative Gross-Pitaevskii equations describing the spin-up and spin-down polaritons, containing the photonic spin-orbit (SO) coupling and the rate equations describing the density of incoherent excitonic reservoir density, is reduced to a system of two coupled 2D complex Ginzburg-Landau (2DCGL) equations, with saturable nonlinearities for complex polariton order parameters, thanks to the adiabatic approximation and small density fluctuations approximation. The analytical approach relies on the linear stability analysis of continuous waves (CWs) to derive an expression for the growth rate and conduct a parametric study of MI. The effect of different parameters on the growth rate spectrum is discussed with an emphasis on the photonic SO coupling and the pumping power. The predictions are verified against a direct simulation of the 2DCGL equations, and excellent agreement is found. The emergence of solitonic clusters manifests the evolution of MI. Phase diagrams on a MI spectrum for the CWs are presented against the magnetic field ($B$) and SO coupling strength ($\sigma$), based on which the dynamical behaviors of the emerging structures are debated, along with their response to changing $\sigma$ and $B$. The results suggest that the photonic SO coupling and the magnetic field constitute efficient tools for nonlinear mode selection and characterization via the MI process and are equally important in any eventual experimental realization of such a process in the studied EPC system.

Kagome materials exhibit fascinating properties and hold important research significance. Inspired by the extensive studies on the $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ family of materials, here, we investigate the topological and superconducting properties of the bilayer kagome metal materials $\mathrm{Y}{T}_6{\mathrm{Sn}}_6$ ($T$=V, Nb, Ta) using first-principles calculations. These kagome materials exhibit the ${\mathrm{MgFe}}_6{\mathrm{Ge}}_6$-prototype structure and have no magnetism. The calculated results for formation energy and the phonon dispersion spectrum demonstrate their stability. Based on the calculation of topologically invariant and surface states, they can be categorized as ${\mathbb{Z}}_2$ topological metals. The Van Hove singularity and Dirac points are also observed near the Fermi level. According to electron-phonon coupling (EPC) calculations, $\mathrm{Y}{T}_6{\mathrm{Sn}}_6$ systems are all predicted to be weak superconductors. Using the Allen-Dynes modified McMillan formula, the superconducting critical temperatures $T_c$ of ${\mathrm{YV}}_6{\mathrm{Sn}}_6, {\mathrm{YNb}}_6{\mathrm{Sn}}_6$, and ${\mathrm{YTa}}_6{\mathrm{Sn}}_6$ are predicted to be 0.65, 1.17, and 0.89 K, respectively. The EPC is mainly contributed by the vibrations of V atoms and partially by the out-of-plane vibrational modes of Sn atoms. The coexistence of nontrivial topological properties and superconducting properties in these bilayer kagome systems is helpful to study the relationship between different physical properties and to design new topological superconductors.

The superconducting phase of topological semimetals has become a promising route for the implementation of topological superconductivity and non-Abelian Majorana fermions. Here, we investigate quantum transport in the junctions composed of a nodal-line superconductor, i.e., a topological nodal-line semimetal with superconducting pairing. It is shown that two topologically nontrivial regions exist in the surface Brillouin zone of the nodal-line superconductor labeled by the transverse momentum. Specifically, topological regions with topological invariants $\mathcal{N}=1$ and $\mathcal{N}=2$ host a single and a pair of Majorana zero modes at the surface, respectively. We show that the single Majorana zero mode in the $\mathcal{N}=1$ region can induce resonant equal-spin Andreev reflection, while the Majorana pair in the $\mathcal{N}=2$ region can lead to resonant spin-flipped normal reflection. Both reflection processes can give rise to spin currents but with different polarization directions, whose proportions can be adjusted by a Zeeman field. We also study the transport properties of the device with a sandwich structure and predict that strong crossed Andreev reflection can be implemented with a finite bias. Detection schemes for all these novel transport properties, which can be revealed by spin-resolved transport signatures, are proposed. Our work paves the way for the implementation and detection of Majorana fermions in nodal-line superconductors.

We study the scattering theory of delicate topological insulators (TIs), which are novel topological phases beyond the paradigm of the tenfold way, topological quantum chemistry, and the symmetry indicator method. We demonstrate that the phase of the reflection amplitude can probe the delicate topology by capturing a characteristic feature of a delicate TI. This feature is the returning Thouless pump, where an integer number of charges are pumped forward and backward in the first and second half of the adiabatic cycle, respectively. As a by-product of our analysis we show that requiring additional symmetries can stable the boundary states of a delicate TI beyond the conventional requirement of a sharply defined surface. Furthermore, we propose a waveguide array experiment to implement a delicate TI and measure its reflection phase which reveals the delicate topology.

We study the valence crossover and strong electron-phonon coupling of ${\mathrm{EuPd}}_2{\mathrm{Si}}_2$ by polarization-resolved Raman spectroscopy. The fully symmetric phonon mode shows strongly asymmetric line shape at low temperature, indicating Fano-type interaction between this mode and a continuum of electron-hole excitations. Moreover, the frequency and linewidth of the phonon modes exhibit anomalies across the valence-crossover temperature, suggesting the coupling between valence fluctuations and lattice vibration. In particular, two phonon modes show a significantly enhanced Grüneisen parameter, possibly related to a nearby critical elastic regime. The relative contribution of the structural change and valence change to the phonon anomalies is evaluated by density-functional-theory calculations.

The non-Bloch band theory can describe energy bands in a one-dimensional (1D) non-Hermitian system. On the other hand, whether the non-Bloch band theory can be extended to higher-dimensional non-Hermitian systems is nontrivial. In this work, we construct the non-Bloch band theory in two classes of two-dimensional non-Hermitian systems by reducing the problem to that for a 1D non-Hermitian model. In these classes of systems, we get the generalized Brillouin zone for a complex wave vector and investigate topological properties. In the model of the non-Hermitian Chern insulator, as an example, we show the bulk-edge correspondence between the Chern number defined from the generalized Brillouin zone and the appearance of the edge states.

The Nielsen-Ninomiya theorem, dubbed “fermion doubling,” poses a problem for the naive discretization of a single (massless) Dirac cone on a two-dimensional surface. The inevitable appearance of an additional, unphysical fermionic mode can, for example, be circumvented by introducing an extra dimension to spatially separate Dirac cones. In this work, we propose a geometry-independent protocol based on a tight-binding model for a three-dimensional topological insulator on a cubic lattice. The low-energy theory, below the bulk gap, corresponds to a Dirac cone on its two-dimensional surface which can have an arbitrary geometry. We introduce a method where only a thin shell of the topological insulator needs to be simulated. Depending on the setup, we propose to gap out the states on the undesired surfaces either by breaking the time-reversal symmetry or by introducing a superconducting pairing. We show that it is enough to have a thickness of the topological-insulator shell of three to nine lattice constants. This leads to an effective two-dimensional scaling with minimal and fixed shell thickness. We test the idea by comparing the spectrum and probability distribution to analytical results for both a proximitized Dirac mode and a Dirac mode on a sphere, which exhibits a nontrivial spin connection. The protocol yields a tight-binding model on a cubic lattice simulating Dirac cones on arbitrary surfaces with only a small overhead due to the finite thickness of the shell.

Two-dimensional (2D) materials with high in-plane anisotropy offer promising candidates for hosting highly directional surface plasmons, but few of them have been demonstrated to reach this goal thus far. In this paper, we propose a design principle of 2D hyperbolic materials (2D-HMs) based on orbital anisotropy and predict from first-principles calculations a family of 2D-HMs: aluminum disulfide monolayer and its analogues $X{Y}_2$ $(X=\mathrm{Al},\mathrm{Ga},\mathrm{In};Y=\mathrm{S},\mathrm{Se},\mathrm{Te})$. These natural 2D-HMs exhibit broadband hyperbolic regimes across the near-infrared to ultraviolet spectrum, enabling the propagation of highly directional hyperbolic surface plasmons. Undamped plasmons emerge along the $x$ direction with the maximum wave vector of $\sim 0.16{\AA }^{-1}$ and frequency of 4.6 eV, whereas the plasmons along the $y$ direction have low frequency $\left(<0.6\mathrm{eV}\right)$ and decay rapidly to electron-hole pairs for the $\mathrm{Al}{\mathrm{S}}_2$ monolayer. By solving Maxwell's equation, we simulate the directional propagation of the surface waves with hyperbolic dispersion relations. We correlate the fascinating plasmonic properties with the unique electronic structures of these highly anisotropic 2D materials, which offers a promising strategy for the design of 2D-HMs.

Over the last two decades, the hierarchical equations of motion (HEOM) of Tanimura and Kubo have become the equation of motion-based tool for numerically exact calculations of system-bath problems. The HEOM is today generalized to many cases of dissipation and transfer processes through an external bath. In spatially extended photonic systems, the propagation of photons through the bath leads to retardation/delays in the coupling of quantum emitters. Here, the idea behind the HEOM derivation is generalized to the case of photon retardation and applied to the simple example of two dielectric slabs. The derived equations provide a simple reliable framework for describing retardation and may provide an alternative to path-integral treatments.

As a class of promising structural material, recently synthesized face centered cubic phased high-entropy alloys (HEAs) exhibit excellent room-temperature (RT) fracture toughness as well as an abnormally increasing one at cryogenic temperatures (CTs). The intrinsic toughening mechanisms are not yet well understood. Attention here is focused on the atomistic crack initiation and propagation in a model HEA CoCrFeMnNi under RT and CTs, by means of atomistic simulations integrated with theoretical analysis. Hierarchical deformation mechanisms of the incipient plasticity; the local amorphization; and the formation, growth, and coalescence of voids are found, based on which the strain energy stored in the material is continually dissipated, resulting in the outstanding fracture toughness of the HEA at both RT and CTs. The origin for low-temperature toughening may be attributed to fewer immobile dislocations at CTs, delaying the occurrence of amorphization and microvoids. The differences in mechanisms for low-temperature toughening of the HEA and low-temperature embrittlement of traditional metals are further comparatively revealed. This study provides mechanistic insights into the fundamental understanding of intrinsic toughening mechanisms in the HEA.

We consider manifolds of tunable all-bands-flat (ABF) lattices in dimensions $d=1,2$, parameterized by a manifold angle parameter $\theta$. We study localization properties of eigenstates in the presence of weak magnetic flux disorder and weak spin-orbit disorder. We demonstrate that weakly disordered ABF lattices are described by effective scale-free models, where the disorder strength is scaled out. For weak magnetic flux disorder, we observe subexponential localization at flatband energies in $d=1$, which differs from the usual Anderson localization. We also find diverging localization length at flatband energies for weak flux values in $d=2$; however, the character of the eigenstates at these energies is less clear. For weak spin-orbit coupling disorder in $d=2$ we identify a tunable metal-insulator transition with mobility edges. We also consider the case of mixed spin-orbit and diagonal disorder and obtain the metal-insulator transition driven by the manifold parameter $\theta$.

A major challenge in condensed matter physics is to manipulate collective quantum phases by all-optical methods, which can open enormous new possibilities for materials and device engineering. Here we report an anomalous optical modulation of charge density waves (CDWs) in recently discovered kagome metal $\mathrm{Cs}{\mathrm{V}}_3{\mathrm{Sb}}_5$ using femtosecond-resolved coherent phonon spectroscopy. This optically suppressed CDW phase surprisingly persists for nanoseconds, exhibits a monotonically lowering of transition temperature with increasing fluence, and does not require a critical absorbed photon density, which is intriguingly distinct from those found in the “optically suppressed potential energy” scenario. Pump-pump-probe experiments conclusively rule out the laser-induced thermal effect and time-dependent density functional theory simulations confirm that this nonthermal modulation stems from an optical tuning of the energy resonance between the band fermiology and the Van Hove singularity in kagome lattices. These findings open exciting prospects for all-optical engineering of the Van Hove scenario to tune correlated quantum phases in topology networks.

Topological quantum magnets FeSn and ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$ were studied using neutron scattering and first-principles calculations. Both materials are metallic but host dispersionless flat bands with Dirac nodes at the $K$ point in reciprocal space. The local structure determined from the pair density function analysis of the neutron-diffraction data provided no evidence for electron localization in both compounds, consistent with their metallic nature. At the same time, in FeSn, an anomalous suppression in the $c$-axis lattice constant coupled with changes in the phonon spectra were observed across $T_N$ indicating the presence of magnetoelastic coupling and spin-phonon interactions. In addition, it was observed that spin waves persisted well above $T_N$, suggesting that the in-plane ferromagnetic spin correlations survive at high temperatures. In contrast, no lattice anomaly was observed in ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$. The inelastic signal could be mostly accounted for by phonons, determined from density-functional theory, showing typical softening on warming.

Using a hybrid density functional, we study the electronic, magnetic, and neutral excitations of the paradigmatic Cr-doped GaN solid. Our results indicate that the $\approx 1$% doped wurtzite GaN crystal retains the semiconducting nature of the host, associated with a magnetic moment of 3 ${\mu }_B$. As a consequence of Cr doping, additional hybridized bands are formed within the intrinsic band gap of GaN, leading to a considerable band gap narrowing by 1.4 eV and low-energy optical transitions. Our results indicate dark Cr $d\text{−}d$ transitions at very low energy (0.5–0.7 eV), followed by bright transitions in the visible energy range (1.8–2.2 eV). Characterization of the electron-hole pairs suggests that the latter originates from the internal transitions among hybridized ${\mathrm{Cr}}_d\text{–}{\mathrm{N}}_p$ states. With the existence of these additional optical features within the visible energy window, one can expect an enhancement to the photoelectric conversion efficiency of GaN upon Cr doping, in addition to applications in spintronics.

We propose a generalization of the crystalline order: the ground-state fractal crystal. We demonstrate that by deriving a simple continuous-space-discrete-field model whose ground state is a crystal where each unit cell is a fractal.