For diffusion of two-dimensional homoepitaxial clusters of $N$ atoms on metal (100) surfaces mediated by edge atom hopping, macroscale continuum theory suggests that the diffusion coefficient scales like $D_N\sim N^{-\beta }$ with $\beta =3/2$. However, we find quite different and diverse behavior in multiple size regimes. These include: (i) facile diffusion for small sizes $N<9$; (ii) slow nucleation-mediated diffusion with small $\beta <1$ for “perfect” sizes $N=N_p=L^2$ or $L(L+1)$, for $L=3,4, ...$ having unique ground-state shapes, for moderate sizes $9\le N\le \mathrm{O}\left({10}^2\right)$; the same also applies for $N=N_p+3, N_p+4, ...$ (iii) facile diffusion but with large $\beta >2$ for $N=N_p+1$ and $N_p+2$ also for moderate sizes $9\le N\le \mathrm{O}\left({10}^2\right)$; (iv) merging of the above distinct branches and subsequent anomalous scaling with $1\lesssim \beta <3/2$, reflecting the quasifacetted structure of clusters, for larger $N=\mathrm{O}\left({10}^2\right)$ to $N=\mathrm{O}\left({10}^3\right)$; (v) classic scaling with $\beta =3/2$ for very large $N=\mathrm{O}\left({10}^3\right)$ and above. The specified size ranges apply for typical model parameters. We focus on the moderate size regime where we show that diffusivity cycles quasiperiodically from the slowest branch for $N_p+3$ (not $N_p$) to the fastest branch for $N_p+1$. Behavior is quantified by kinetic Monte Carlo simulation of an appropriate stochastic lattice-gas model. However, precise analysis must account for a strong enhancement of diffusivity for short time increments due to back correlation in the cluster motion. Further understanding of this enhancement, of anomalous size scaling behavior, and of the merging of various branches, is facilitated by combinatorial analysis of the number of the ground-state and low-lying excited state cluster configurations, and also of kink populations.

In this study we present an analytical description of the ultrafast localized surface plasmon and magnetic resonance dynamics in a single nanoparticle (Ag or Si), driven by an ultrashort (fs time scale) Gaussian pulse. Three possible scenarios have been found depending on the incident field, i.e., pulse duration much shorter than, similar to, and much longer than the localized surface plasmon resonance (LSPR) lifetime. A rich physics arises for ${\tau }_{\mathrm{pulse}}<{\tau }_{\mathrm{LSPR}}$, even in the linear regime. The surface plasmon dynamics is manifested as (i) a temporal delay of the surface plasmon excitation with regard to the freely propagating pulse and as (ii) a negative exponential tail after the exciting pulse is over. In addition, for sub-fs pulses clear oscillations in the near-field decay have been observed. A similar scenario has been observed considering a nonabsorbing Si sphere. Nanoparticle resonance dynamics may lead to a wealth of new phenomena and applications in nanophotonics such as multipole order resonance interference, pulse-induced delay or temporal shaping on the fs scale, high harmonic generation, attosecond near-field pulse sources, and electron acceleration from metasurface or 3D engineered nanostructures.

The robustness of helical edge states in two-dimensional (2D) topological insulators (TIs) against strong interactions remains an intriguing issue. Here, by performing a sign-free quantum Monte Carlo (QMC) simulation of the Kane-Mele-Hubbard-Rashba model which describes an interacting 2D TI with two-particle backscattering on the edges, we verify that the gapless helical edge states are robust against a finite range of two-particle backscattering when the Coulomb repulsion is not strong. However, when the Coulomb repulsion is strong enough, the helical edge states can be gapped by infinitesimal two-particle backscattering, resulting in an edge magnetic order. We further reveal the universal properties of the magnetic edge quantum critical point (EQCP). At magnetic domain walls on edges, we find that a fractionalized charge of $e/2$ emerges. Implications of our results to recent transport experiments in an InAs/GaSb quantum well, which is a 2D TI with strong interactions, will also be discussed.

In this Rapid Communication, we address the chiral properties of valley exciton-polaritons in a monolayer of $\mathrm{W}{\mathrm{S}}_2$ in the regime of strong light-matter coupling with a Tamm-plasmon resonance. We observe that the effect of valley polarization, which manifests in the circular polarization of the emitted photoluminescence as the sample is driven by a circularly polarized laser, is strongly enhanced in comparison to bare $\mathrm{W}{\mathrm{S}}_2$ monolayers and can even be observed under strongly nonresonant excitation at ambient conditions. In order to explain this effect in more detail, we study the relaxation and decay dynamics of exciton-polaritons in our device, elaborate the role of the dark state, and present a microscopic model to explain the wave-vector-dependent valley depolarization by the linear polarization splitting inherent to the microcavity. We believe that our findings are crucial for designing novel polariton-valleytronic devices which can be operated at room temperature.

We give a self-contained derivation of the low-energy effective interactions of the $\mathrm{SU}\left(N\right)$ Hubbard model, a multiflavor generalization of the one-band Hubbard model, by using a generalized Schrieffer-Wolff transformation (SWT). The effective interaction of doublons and holons, which has been largely ignored in previous SWT studies (e.g., the $t\text{−}J$ model), leads to distinct peaks in the local density of states. As shown by Lee et al. [Phys. Rev. Lett. 119, 236402 (2017)], this underlying effective doublon-holon interaction explains the numerical observation of the subpeaks at the inner edges of the Hubbard bands in the metallic phase close to the Mott transition.

The fractional quantum Hall effect is the paradigmatic example of topologically ordered phases. One of its most fascinating aspects is the large variety of different topological orders that may be realized, in particular non-Abelian ones. Here we analyze a class of non-Abelian fractional quantum Hall model states which are generalizations of the Abelian Haldane-Halperin hierarchy. We derive their topological properties and show that the quasiparticles obey non-Abelian fusion rules of type $\mathrm{su}{\left(q\right)}_k$. For a subset of these states we are able to derive the conformal field theory description that makes the topological properties—in particular braiding—of the state manifest. The model states we study provide explicit wave functions for a large variety of interesting topological orders, which may be relevant for certain fractional quantum Hall states observed in the first excited Landau level.

In this paper we present a method to determine the occupation of Mn ions in epitaxial (In,Mn)As nanostructures by resonant x-ray diffraction near the Mn $K$-absorption edge, exploiting the dependency of the intensity of both (200) superstructure and the (400) fundamental reflections. The concentrations of Mn atoms on substitutional In sites, as well as on In- and As-interstitial sites, were unambiguously determined. A threshold concentration for the interstitial sites, which are occupied first for low nominal Mn deposition content, was found. Calculations using density-functional theory indicate that a higher occupancy of such sites can be favorable with respect to the occupation of substitutional sites, depending on surface potentials and growth kinetic effects.

All carbon materials, e.g., amorphous carbon (a-C) coatings and ${\mathrm{C}}_{60}$ fullerene thin films, play an important role in short-wavelength free-electron laser (FEL) research motivated by FEL optics development and prospective nanotechnology applications. Responses of a-C and ${\mathrm{C}}_{60}$ layers to the extreme ultraviolet (SPring-8 Compact SASE Source in Japan) and soft x-ray (free-electron laser in Hamburg) free-electron laser radiation are investigated by Raman spectroscopy, differential interference contrast, and atomic force microscopy. A remarkable difference in the behavior of covalent (a-C) and molecular (${\mathrm{C}}_{60}$) carbonaceous solids is demonstrated under these irradiation conditions. Low thresholds for ablation of a fullerene crystal (estimated to be around 0.15 eV/atom for ${\mathrm{C}}_{60}$ vs 0.9 eV/atom for a-C in terms of the absorbed dose) are caused by a low cohesive energy of fullerene crystals. An efficient mechanism of the removal of intact ${\mathrm{C}}_{60}$ molecules from the irradiated crystal due to Coulomb repulsion of fullerene-cage cation radicals formed by the ionizing radiation is revealed by a detailed modeling.

We study an antiferromagnetic order in the ground state of the half-filled Hubbard model on the Penrose lattice and investigate the effects of quasiperiodic lattice structure. In the limit of infinitesimal Coulomb repulsion $U\to +0$, the staggered magnetizations persist to be finite, and their values are determined by confined states, which are strictly localized with thermodynamics degeneracy. The magnetizations exhibit an exotic spatial pattern, and have the same sign in each of cluster regions, the size of which ranges from 31 sites to infinity. With increasing $U$, they continuously evolve to those of the corresponding spin model in the $U=\infty$ limit. In both limits of $U$, local magnetizations exhibit a fairly intricate spatial pattern that reflects the quasiperiodic structure, but the pattern differs between the two limits. We have analyzed this pattern change by a mode analysis by the singular value decomposition method for the fractal-like magnetization pattern projected into the perpendicular space.

We demonstrate that a weak external magnetic field can induce negative magnetothermal resistance for magnons in a disordered two-dimensional antiferromagnet. We study the main effect of a weak external magnetic field on the longitudinal thermal conductivity ${\kappa }_{xx}$ for a disordered antiferromagnet using the weak-localization theory for magnons. We show that the weak-localization correction term of ${\kappa }_{xx}$ positively increases with increasing the magnetic field parallel to the ordered spins. Since this increase corresponds to a decrease of the thermal resistivity, this phenomenon is negative magnetothermal resistance for magnons. This negative magnetothermal resistance and the weak localization of magnons will be used to control the magnon thermal current in antiferromagnetic spintronics devices. We also discuss several implications for further experimental and theoretical studies for disordered magnets.

Using element-resolved x-ray magnetic circular dichroism and x-ray magnetic linear dichroism measurements, we studied Ni/CoO/vicinal MgO(001) and Ni/CoO/Fe/vicinal MgO(001) systems at 350 and 78 K. Above the CoO Néel temperature, the Ni magnetization is fully in plane and parallel to the atomic steps in both systems due to step-induced magnetic anisotropy. Below the CoO Néel temperature, the CoO spins in Ni/CoO/vicinal MgO(001) are fully in plane and parallel to the atomic steps and the Ni magnetization is fully in plane and perpendicular to the atomic steps due to the 90° Ni/CoO magnetic coupling. The CoO spins in Ni/CoO/Fe/vicinal MgO(001), however, develop an out-of-plane canted spin component in addition to the in-plane component parallel to the atomic steps. Consequently, the Ni magnetization is canted towards the out-of-plane direction by an appreciable angle. Photoemission electron microscopy imaging shows a 90° interfacial magnetic coupling at both the Ni/CoO and the CoO/Fe interfaces and an absence of a direct interlayer coupling, showing that the Ni spin canting is due to its coupling to the canted CoO spin components which is caused by the underlying ferromagnetic Fe layer in Ni/CoO/Fe/vicinal MgO(001).

We predict a strong-field ultrafast optical Faraday effect in which a circularly polarized ultrashort optical pulse induces transient chirality in an achiral transparent dielectric. This effect is attractive for time-resolved measurements because it gives access to the noninstantaneity of the nonlinear medium response, and also because it represents a relaxation of time-reversal symmetry by all-optical means. We propose probing the induced transient chirality with a weak linearly polarized ultraviolet pulse that is shorter than the near-infrared pump pulse. The predicted effects are ultrafast: the induced chirality vanishes for probe delays exceeding the duration of the near-infrared pulse. This opens up possibilities for applications in ultrafast circular-polarization modulators and analyzers.

We study properties of magnetic nanoparticles adsorbed on the halloysite surface. For that a distinct magnetic Hamiltonian with a random distribution of spins on a cylindrical surface was solved by using a nonequilibrium Monte Carlo method. The parameters for our simulations, the anisotropy constant, nanoparticle size distribution, saturated magnetization, and geometrical characteristics of the halloysite template, were taken from recent experiments. We calculate the hysteresis loops and temperature dependence of the zero-field-cooling (ZFC) susceptibility, the maximum of which determines the blocking temperature. It is shown that the dipole-dipole interaction between nanoparticles moderately increases the blocking temperature and weakly increases the coercive force. The obtained hysteresis loops (e.g., the value of the coercive force) for Ni nanoparticles are in reasonable agreement with the experimental data. We also discuss the sensitivity of the hysteresis loops and ZFC susceptibilities to the change in anisotropy and dipole-dipole interaction, as well as the $3d$-shell occupation of the metallic nanoparticles; in particular we predict larger coercive force for Fe than for Ni nanoparticles.

Recently, orthorhombic CuMnAs has been proposed to be a magnetic material where topological fermions exist around the Fermi level. Here we report the magnetic structure of the orthorhombic ${\mathrm{Cu}}_{0.95}\mathrm{MnAs}$ and ${\mathrm{Cu}}_{0.98}{\mathrm{Mn}}_{0.96}\mathrm{As}$ single crystals. While ${\mathrm{Cu}}_{0.95}\mathrm{MnAs}$ is a commensurate antiferromagnet below 360 K with a propagation vector of $\mathbf{k}=0,{\mathrm{Cu}}_{0.98}{\mathrm{Mn}}_{0.96}\mathrm{As}$ undergoes a second-order paramagnetic to incommensurate antiferromagnetic phase transition at 320 K with $\mathbf{k}=(0.1,0,0)$, followed by a second-order incommensurate to commensurate antiferromagnetic phase transition at 230 K. In the commensurate antiferromagnetic state, the Mn spins order parallel to the crystallographic $b$ axis but antiparallel to their nearest neighbors, with the spin orientation along the $b$ axis. This magnetic order breaks ${\mathrm{S}}_{2z}$, the two-fold rotational symmetry around the $c$ axis, resulting in finite band gaps at the crossing point and the disappearance of the massless topological fermions. However, our first-principles calculations suggest that orthorhombic CuMnAs can still host spin-polarized surface states and signature induced by nontrivial topology, which makes it a promising candidate for antiferromagnetic spintronics.

We extend the standard effective model of $d$-wave superconductivity of a single band tight-binding Hamiltonian with a nearest-neighbor attraction to include finite range periodically modulated pair hopping. The pair hopping is characterized by a fixed wave number $\mathcal{Q}=\mathcal{Q}\widehat{x}$ breaking lattice rotational symmetry. Within self-consistent BCS theory we study the general variational state consisting of two incommensurate singlet pair amplitudes ${\mathrm{\Delta }}_{{\mathbf{Q}}_1}$ and ${\mathrm{\Delta }}_{{\mathbf{Q}}_2}$ and find two types of ground states; one of the Larkin-Ovchnnikov (LO) or pair-density wave (PDW) type with ${\mathrm{\Delta }}_{{\mathbf{Q}}_1}={\mathrm{\Delta }}_{{\mathbf{Q}}_2}$ and ${\mathbf{Q}}_1=-{\mathbf{Q}}_2\approx \mathcal{Q}$, and one of the Fulde-Ferrell (FF) type with ${\mathrm{\Delta }}_{{\mathbf{Q}}_2}=0$ and ${\mathbf{Q}}_1\approx \pm \mathcal{Q}$. An anomalous term in the static current operator arising from the pair hopping ensures that Bloch's theorem on ground state current is enforced also for the time-reversal and parity breaking FF state, despite no spin-population imbalance. We also consider a supercurrent by exploring the space of pair momenta ${\mathbf{Q}}_1$ and ${\mathbf{Q}}_2$ and identify characteristics of a state with multiple finite momentum order parameters. This includes the possibility of phase separation of current densities and spontaneous mirror-symmetry breaking manifested in the directional dependence of the depairing current.

A model based on the Dirac equation allows one to describe topological insulators. In this paper we extend this model by adding a Zeeman term to introduce magnetism. By this means we show that it can be used to describe the electronic properties of ferromagnetic Weyl and nodal line semimetals, which arise for distinct parameters of the model. We confirm the topological nontriviality of the nodal objects by calculating the topological invariants, as well as by demonstrating the existence of topological surface states in the spectral function of the semi-infinite systems. Furthermore, we calculate the anomalous and spin Hall conductivities for various model parameters, which allows us to identify typical signatures of Weyl points and nodal lines in electronic transport.

The quantum limit can be easily reached in Dirac semimetals under a magnetic field, which leads to some exotic many-body physics due to the high degeneracy of the topological zeroth Landau bands. By solving the effective Hamiltonian, which is derived by tracing out the high-energy degrees of freedom, at the self-consistent mean-field level, we have systematically studied the instability of Dirac semimetals under a strong magnetic field. A charge-density wave (CDW) phase and a polarized nematic phase formed by “exciton condensation” are predicted as the ground state for the tilted and untilted bands, respectively. Furthermore, we propose that, as distinguished from the CDW phase, the nematic phase can be identified in experiments by anisotropic transport and Raman scattering.

We report the physical properties of orthorhombic $o\text{−}\mathrm{CuMnAs}$ single crystal, which is predicted to be a topological Dirac semimetal with magnetic ground state and inversion symmetry broken. $o\text{−}\mathrm{CuMnAs}$ exhibits an antiferromagnetic (AFM) transition with $T_N\sim 312\mathrm{K}$. Further characterizations of magnetic properties suggest that the AFM order may be canted with the spin orientation in the $bc$ plane. Small isotropic magnetoresistance and linearly field-dependent Hall resistivity with positive slope indicate that single hole-type carries with high density and low mobility dominate the transport properties of $o\text{−}\mathrm{CuMnAs}$. Furthermore, the result of low-temperature heat capacity shows that the effective mass of carriers is much larger than those in typical topological semimetals. These results imply that the carriers in $o\text{−}\mathrm{CuMnAs}$ exhibit remarkably different features from those of Dirac fermions predicted in theory.

Rare-earth titanates ${\mathrm{RTiO}}_3$ are Mott insulators displaying a rich physical behavior, featuring most notably orbital and spin orders in their ground state. The origin of their ferromagnetic to antiferromagnetic transition as a function of the size of the rare earth however remains debated. Here we show on the basis of symmetry analysis and first-principles calculations that although rare-earth titanates are nominally Jahn-Teller active, the Jahn-Teller distortion is negligible and irrelevant for the description of the ground state properties. At the same time, we demonstrate that the combination of two antipolar motions produces an effective Jahn-Teller-like motion which is the key of the varying spin-orbital orders appearing in titanates. Thus, titanates are prototypical examples illustrating how a subtle interplay between several lattice distortions commonly appearing in perovskites can produce orbital orderings and insulating phases irrespective of proper Jahn-Teller motions.

We consider the design and modeling of metasurfaces that couple energy from guided waves to propagating wave fronts. To this purpose, we develop a comprehensive, multiscale dipolar interpretation for large arrays of complementary metamaterial elements embedded in a waveguide structure. Within this modeling technique, the detailed electromagnetic response of each metamaterial element is replaced by a polarizable dipole, described by means of an effective polarizability. In this paper, we present two methods to extract this effective polarizability. The first method invokes surface equivalence principles, averaging over the effective surface currents and charges induced in the element's surface in order to obtain the effective dipole moments, from which the effective polarizability can be inferred. The second method is based in the coupled-mode theory, from which a direct relationship between the effective polarizability and the amplitude coefficients of the scattered waves can be deduced. We demonstrate these methods on several variants of waveguide-fed metasurface elements (both one- and two-dimensional waveguides), finding excellent agreement between the two, as well as with the analytical expressions derived for circular and elliptical irises. With the effective polarizabilities of the metamaterial elements accurately determined, the radiated fields generated by a waveguide-fed metasurface can be found self-consistently by including the interactions between polarizable dipoles. The dipole description provides an effective perspective and computational framework for engineering metasurface structures such as holograms, lenses, and beam-forming arrays, among others.