Low-temperature magnetization curves and thermodynamics of a frustrated spin-$\frac{1}{2}$ Heisenberg triangular bilayer with the antiferromagnetic intradimer interaction and either ferromagnetic or antiferromagnetic interdimer interaction are investigated in a highly frustrated parameter region, where localized many-magnon eigenstates provide the most dominant contribution to magnetothermodynamics. Low-energy states of the highly frustrated spin-$\frac{1}{2}$ Heisenberg triangular bilayer can be accordingly found from a mapping correspondence with an effective triangular-lattice spin-$\frac{1}{2}$ Ising model in a field. A description based on the effective Ising model implies that the frustrated Heisenberg triangular bilayer with the ferromagnetic interdimer coupling displays in a zero-temperature magnetization curve discontinuous magnetization jump, which is reduced upon increasing of temperature until a continuous field-driven phase transition from the Ising universality class is reached at a certain critical temperature. The frustrated Heisenberg triangular bilayer with the antiferromagnetic interdimer coupling contrarily exhibits multistep magnetization curve with intermediate plateaus at $\frac{1}{3}$ and $\frac{2}{3}$ of the saturation magnetization, whereas discontinuous magnetization jumps observable at zero temperature change to continuous field-driven phase transitions from the universality class of three-state Potts model at sufficiently low temperatures. Exact results and Monte Carlo simulations of the effective Ising model are confronted with full exact diagonalization data for the Heisenberg triangular bilayer in order to corroborate these findings.

Magnetic skyrmions are topologically protected noncollinear spin textures. Their condensed state, called skyrmion crystal phase (SkX), is usually presumed to be hexagonally symmetric as observed in most helimagnets. However, careful study of the experimental results indicates the existence of intrinsic anisotropy of SkX, reflected by breaking of SkX hexagonal symmetry, direction-dependent properties of SkX, and even the appearance of novel emergent crystalline states. Here, we systematically study the effects of exchange anisotropy on Bloch-type SkX in cubic helimagnets and provide a possible explanation to the phenomena mentioned above. By energy minimization, we find that exchange anisotropy causes intrinsic distortion of SkX. As the magnitude of exchange anisotropy changes, a triangular-square transition occurs, with two possible transition paths for different choices of anisotropy parameters. We also reproduce the ${30}^{\circ }$ rotational transition of SkX.

Resonant soft x-ray scattering was used to study the magnetic ordering of the multiferroic materials ${\mathrm{SmMn}}_2{\mathrm{O}}_5$ and ${\mathrm{GdMn}}_2{\mathrm{O}}_5$. In the case of ${\mathrm{SmMn}}_2{\mathrm{O}}_5$, the results confirm that antiferromagnetic ordering of Mn magnetic moments occurs with magnetic propagation vector ${\mathbf{q}}_{\mathrm{M}}=(1/2,0,1/3+{\delta }^{\prime })$ in the incommensurate magnetic phase, followed by the appearance of the commensurate magnetic phase with ${\mathbf{q}}_{\mathrm{M}}=(1/2,0,0)$ as the temperature is decreased. The energy spectrum around Mn $L_{\mathrm{II},\mathrm{III}}$ edges suggests that the Mn ions adopt unique electronic states in the CM phase of ${\mathrm{SmMn}}_2{\mathrm{O}}_5$. No evidence was found for spin polarization of oxygen ions through $2p\text{−}3d$ orbital hybridization between oxygen and Mn ions in this compound, although this phenomenon is clearly evident in ${\mathrm{GdMn}}_2{\mathrm{O}}_5$ and other $R{\mathrm{Mn}}_2{\mathrm{O}}_5$ ($R$ = Y, Er, Tb) compounds. The energy spectra around O $K$ edge strongly suggest that electronic polarization resulting from charge transfer between oxygen and Mn ions has little contribution to the ferroelectricity while lattice distortion likely plays a key role in promoting ferroelectricity in ${\mathrm{SmMn}}_2{\mathrm{O}}_5$.

In order to theoretically identify the factors governing superconductivity in multilayer cuprates, a three-layer Hubbard model is studied with the two-particle self-consistent (TPSC) approach so as to incorporate electron correlations. The linearized Eliashberg equation is then solved for the gap function in a matrix form to resolve the role of outer ${\mathrm{CuO}}_2$ planes (OPs) and inner plane (IP). We show that OPs dominate IP in the $d_{x^2-y^2}$-wave superconductivity, while IP dominates in the antiferromagnetism. This comes from an electron correlation effect in that the correlation makes the doping rates different between OPs and IP (i.e., a self-doping effect), which occurs in intermediate and strong correlation regimes. Namely, the antiferromagnetic fluctuations in IP are stronger due to a stronger electron correlation, which simultaneously reduces the quasiparticle density of states in IP with a suppressed $d_{x^2-y^2}$-wave superconductivity. Intriguingly, while the off-diagonal (interlayer) elements in the gap function matrix are tiny, interlayer pair scattering processes are in fact at work in enhancing the superconducting transition temperature $T_{\text{c}}$ through the interlayer Green's functions. This actually causes the trilayer system to have higher $T_{\text{c}}$ than the single-layer in a weak- and intermediate-coupling regimes. This picture holds for a range of values of the on-site Hubbard repulsion $U$ that contains those estimated for the cuprates. The present result is qualitatively consistent with nuclear magnetic resonance experiments in multilayer cuprate superconductors.

We study the collective dynamics of a two-dimensional honeycomb lattice of magnetic skyrmions. By performing large-scale micromagnetic simulations, we find multiple chiral and nonchiral edge modes of skyrmion oscillations in the lattice. The nonchiral edge states are due to the Tamm-Shockley mechanism, while the chiral ones are topologically protected against structure defects and hold different handedness depending on the mode frequency. To interpret the emerging multiband nature of the chiral edge states, we generalize the massless Thiele's equation by including a second-order inertial term of skyrmion mass as well as a third-order non-Newtonian gyroscopic term, which allows us to model the band structure of skyrmion oscillations. Theoretical results compare well with numerical simulations. Our findings uncover the importance of high-order effects in strongly coupled skyrmions and are helpful for designing novel skyrmionic topological devices.

We present a theoretical study of two-dimensional spatially and temporally varying magnetic textures in the presence of spin-orbit coupling (SOC) of both the Rashba and Dresselhaus types. We show that the effective gauge field due to these SOCs, contributes to the dissipative and reactive spin torques in exactly the same way as in electromagnetism. Our calculations reveal that Rashba (Dresselhaus) SOC induces a chiral dissipation in interfacial (bulk) inversion asymmetric magnetic materials. Furthermore, we show that in addition to chiral dissipation ${\alpha }_c$, these SOCs also produce a chiral renormalization of the gyromagnetic ratio ${\tilde{\gamma }}_c$, and show that the latter is intrinsically linked to the former via a simple relation ${\alpha }_c=(\tau /{\tau }_{\mathrm{ex}}){\tilde{\gamma }}_c$, where ${\tau }_{\mathrm{ex}}$ and $\tau$ are the exchange time and the electron relaxation time, respectively. Finally, we propose a theoretical scheme based on the Scattering theory to calculate and investigate the properties of damping in chiral magnets. Our findings should in principle provide a guide for material engineering of effects related to chiral dynamics in magnetic textures with SOC.

Materials with $sp$ magnetism demonstrate strongly nonlocal Coulomb interactions, which opens a way to probe correlations in the regimes not achievable in transition metal compounds. By the example of Sn monolayer on a SiC(0001) surface, we show that such systems exhibit unusual but intriguing magnetic properties at the nanoscale. Physically, this is attributed to the presence of a significant ferromagnetic coupling, the so-called direct exchange, which fully compensates ubiquitous antiferromagnetic interactions of the superexchange origin. Having a nonlocal nature, the direct exchange was previously ignored because it cannot be captured within the conventional density functional methods and significantly challenges ground state models earlier proposed for Sn/SiC(0001). Furthermore, heavy adatoms induce strong spin-orbit coupling, which leads to a highly anisotropic form of the spin Hamiltonian, in which the Dzyaloshinskii-Moriya interaction (DMI) is dominant. The latter is suggested to be responsible for the formation of a nanoskyrmion state at realistic magnetic fields and temperatures.

We study quantum oscillations for a system of fermionic and bosonic dimers and compare the results to those experimentally observed in the cuprate superconductors in their underdoped regime. We argue that the charge carriers obey the Onsager quantization condition and quantum oscillations take on a Lifshitz-Kosevich form. We obtain the effective mass and find good qualitative agreement with experiments if we tune the model to the point where the observed mass divergence at optimum doping is associated to a van Hove singularity at which four free-dimer Fermi pockets touch pairwise in the interior of the Brillouin zone. The same van Hove singularity leads to a maximum in the $d$-wave superconducting pairing amplitude when antiferromagnetic interactions are included. Our combined results therefore suggest that a quantum critical point separating the underdoped and overdoped regimes is marked by the location of the van Hove saddle point in the fermionic dimer dispersion.

Transition-metal dichalcogenides open novel opportunities for the exploration of exciting new physics and devices. As a representative system, $2H\text{-Mo}{\mathrm{S}}_2$ has been extensively investigated owing to its unique band structure with a large band gap, degenerate valleys, and nonzero Berry curvature. However, experimental studies of metastable $1T$ polytypes have been a challenge for a long time, and electronic properties are obscure due to the inaccessibility of single phase without the coexistence of $1T^{\prime }$, $1T^{″}$, and $1T^{\prime ″}$ lattice structures, which hinder the broad applications of $\mathrm{Mo}{\mathrm{S}}_2$ in future nanodevices and optoelectronic devices. Using ${\mathrm{K}}_x{\left({\mathrm{H}}_2\mathrm{O}\right)}_y\mathrm{Mo}{\mathrm{S}}_2$ as the precursor, we have successfully obtained high-quality layered crystals of the metastable $1T^{\prime ″}\text{-Mo}{\mathrm{S}}_2$ with $\sqrt{3}a\times \sqrt{3}a$ superstructure and metastable $1T^{\prime }\text{-Mo}{\mathrm{S}}_2$ with $a\times 2a$ superstructure, as evidenced by structural characterizations through scanning tunneling microscopy, Raman spectroscopy, and x-ray diffraction. It is found that the metastable $1T^{\prime }\text{-Mo}{\mathrm{S}}_2$ is a superconductor with onset transition temperature $\left(T_{\mathrm{c}}\right)$ of 4.2 K, while the metastable $1T^{\prime ″}\text{-Mo}{\mathrm{S}}_2$ shows either superconductivity with $T_{\mathrm{c}}$ of 5.3 K or insulating behavior, which strongly depends on the synthesis procedure. Both of the metastable polytypes of $\mathrm{Mo}{\mathrm{S}}_2$ crystals can be transformed to the stable $2H$ phase with mild annealing at about 70 °C in He atmosphere. These findings provide pivotal information on the atomic configurations and physical properties of $1T$ polytypes of $\mathrm{Mo}{\mathrm{S}}_2$.

Topological nodal superconductors possess gapless low energy excitations that are characterized by point or line nodal Fermi surfaces. In this work, using a coupled wire construction, we study topological nodal superconductors that have protected Dirac nodal points. In this construction, the low-energy electronic degrees of freedom are confined in a three-dimensional array of wires, which emerge as pairing vortices of a microscopic superconducting system. The vortex array harbors an antiferromagnetic time-reversal and a mirror glide symmetry that protect the massless Dirac fermion in the single-body noninteracting limit. Within this model, we demonstrate exact-solvable many-body interactions that preserve the underlying symmetries and introduce a finite excitation energy gap. These gapping interactions support fractionalization and generically lead to nontrivial topological order. We also construct a special case of $N=16$ Dirac fermions where the corresponding gapping interaction leads to a trivial $E_8$ topological order that is closely related to the cancellation of the large gravitational anomaly.

Recent studies on fully dielectric multilayered metamaterials have shown that the negligibly small nonlocal effects (spatial dispersion) typically observed in the limit of deeply subwavelength layers may be significantly enhanced by peculiar boundary effects occurring in certain critical parameter regimes. These phenomena, observed so far in periodic and randomly disordered geometries, are manifested as strong differences between the exact optical response of finite-size metamaterial samples and the prediction from conventional effective-theory-medium models based on mixing formulas. Here, with specific focus on the Thue-Morse geometry, we make a first step toward extending the studies above to the middle ground of aperiodically ordered multilayers, lying in between perfect periodicity and disorder. We show that, also for these geometries, there exist critical parameter ranges that favor the buildup of boundary effects leading to strong enhancement of the (otherwise negligibly weak) nonlocality. However, the underlying mechanisms are fundamentally different from those observed in the periodic case and exhibit typical footprints (e.g., fractal gaps, quasilocalized states) that are distinctive of aperiodic order. The outcomes of our study indicate that aperiodic order plays a key role in the buildup of the aforementioned boundary effects and may also find potential applications to optical sensors, absorbers, and lasers.

We investigated the photoluminescence spectra of ${\mathrm{Cu}}_2\mathrm{O}$ under photoexcitation at 3.05 eV across the violet band gap. The following three features were found: photoluminescence from blue and violet excitons; photoluminescence from yellow excitons of $s,d$, and $f$ states in addition to $p$ states with a quantum number up to ten; and emissions associated with the inelastic collision of the $1s$ yellow excitons. The first process is relevant for the separation of radiative and nonradiative decay rates. The second process likely indicates radiative enhancement of high Rydberg yellow excitons. The last process verifies up-conversion of $1s$ yellow paraexcitons into higher Rydberg states, which is a critical factor impeding the realization of a high-density paraexciton gas towards transition to the Bose-Einstein condensation.

Silicene is a two-dimensional atomic layer material with buckled honeycomb arrangements of Si atoms. The diversity of those arrangements, which expands its potential applications, makes it difficult to determine its structure in any particular case. In this paper, we show that atomic force microscopy (AFM) has the capability of structural determination of unknown phases of silicene. We carried out an AFM observation of $(\sqrt{13}\times \sqrt{13})R13.9^{\circ }$ silicene of unknown structures on Ag(111). Remarkably, it was shown that all constituent Si atoms forming a honeycomb lattice can be resolved by AFM whereas scanning tunneling microscopy (STM) can image only the topmost Si atoms. High-resolution AFM imaging allowed us to identify two types of buckled structure of $(\sqrt{13}\times \sqrt{13})R13.9^{\circ }$ silicene on Ag(111), which had not been previously discriminated. The structure models obtained by theoretical simulation reproduced AFM images as well as previous STM images. In addition, the mechanism of high-resolution AFM imaging was elucidated by force spectroscopy combined with first-principles calculations. Namely, attractive interaction with the tip pulls up buckled down Si atoms, causing local flips of the buckled structures.

The formation of a superstructure—with a related moiré pattern—plays a crucial role in the extraordinary optical and electronic properties of twisted bilayer graphene, including the recently observed unconventional superconductivity. Here we present an interdisciplinary approach to determine the moiré angle in twisted bilayer graphene based on the photonic spin Hall effect. We show that the photonic spin Hall effect exhibits clear fingerprints of the underlying moiré pattern, and the associated light beam shifts are well beyond current experimental sensitivities in the near-infrared and visible ranges. By discovering the dependence of the frequency position of the maximal photonic spin Hall effect shift on the moiré angle, we argue that the latter could be unequivocally accessed via all-optical far-field measurements. We also disclose that, when combined with the Goos-Hänchen effect, the spin Hall effect of light enables the complete determination of the electronic conductivity of the bilayer. Altogether our findings demonstrate that subwavelength spin-orbit interactions of light provide an unprecedented toolset for investigating optoelectronic properties of multilayer two-dimensional van der Waals materials.

In twisted bilayer graphene (TBLG), extremely small deviations from the magic twist angle ${\theta }_m\approx 1.{08}^{\circ }$ change its electronic structure near the Fermi level drastically, causing a meV-wide flat band to appear or disappear. In view of such sensitivity to minute structural deformations, we investigate the combined effect of shear and atomic relaxation on the electronic structure. Using precise experimental data for monolayer and bilayer graphene as input in a simplified formalism for the electronic structure and elastic energy, we find TBLG near ${\theta }_m$ to be unstable with respect to global shear by the angle $\alpha \approx 0.{08}^{\circ }$. In TBLG, the effect of shear on the electronic structure is as important as that of atomic relaxation. Under optimum global shear, calculated ${\theta }_m$ is reduced by $0.{04}^{\circ }$ and agrees with the observed value.

A periodically driven quantum system with avoided level crossing experiences both nonadiabatic transitions and wave-function phase changes. These result in coherent interference fringes in the system's occupation probabilities. For qubits, with repelling energy levels, such interference, named after Landau-Zener-Stückelberg-Majorana, displays arc-shaped resonance lines. In the case of a multilevel system with an avoided level crossing of the two lower levels, we demonstrate that the shape of the resonances can change from convex arcs to concave heart-shaped and harp-shaped resonance lines. Indeed, the whole energy spectrum determines the shape of such resonance fringes and this also provides insight into the slow-frequency system spectroscopy. As a particular example, we consider this for valley-orbit silicon quantum dots, which are important for the emerging field of valleytronics.

To verify the effect of geometrical frustration, we artificially distort the triangular lattice of the quasi-two-dimensional organic conductor $\kappa -{(\mathrm{BEDT}-\mathrm{TTF})}_2{\mathrm{Cu}}_2{\left(\mathrm{CN}\right)}_3$ [BEDT-TTF: bis(ethylenedithio)tetrathiafulvalene] by analogous-molecular substitution and apply ${}^{13}\mathrm{C}$ NMR of bulk and substituted sites, electric conductivity, and static magnetic susceptibility measurements. The results indicate that the magnetic characteristics of the substituted sample are quantitatively similar to those of the pure sample. Moreover, the magnetic characteristics at the substituted sites are also the same as in the bulk. These results suggest that the observed magnetic properties may not be due to the geometrical frustration but the importance of disorder.

We report on orbital-dependent quasiparticle dynamics in ${\mathrm{EuFe}}_2{\mathrm{As}}_2$, a parent compound of Fe-based superconductors, and a way to experimentally identify this behavior using time- and angle-resolved photoelectron spectroscopy across the spin density wave transition. We observe two different relaxation timescales for photoexcited $d_{xz}/d_{yz}$ and $d_{xy}$ electrons. While the itinerant $d_{xz}/d_{yz}$ electrons relax faster through the electron-electron scattering channel, $d_{xy}$ electrons form a quasiequilibrium state with the lattice due to their localized character, and the state decays slowly. Our findings suggest that electron correlation in Fe pnictides is an important property, which should carefully be taken into account when describing the electronic properties of both parent and carrier-doped compounds, and therefore establish a strong connection with cuprates.