In this work, we revisit the problem of superconductivity under the influence of boundary effects. By solving the Bogoliubov-de Gennes (BdG) equations for the tight-binding model, we demonstrate that the critical temperature of the nucleation of superconductivity near a sample surface can be considerably enhanced as compared to its bulk value. To bring to light this effect, we investigate different methods to solve numerically the BdG equations, including the continuous and Anderson approximations, and perform the calculations for a wide range of the system parameters. We obtain that all the self-consistent BdG eigenstates are delocalized and occupy the entire volume of the sample. Our results reveal that the enhancement of the surface critical temperature originates from the quantum interference of different BdG states contributing to the order parameter. We also find that the surface enhancement is the largest when the conduction band is symmetric with respect to the Fermi level, particularly, the half filling is an important proviso for the pronounced surface effect on the critical temperature. The approximate continuous model as well as the Anderson approximation do not capture the main feature of the surface effect. In addition, our study of this effect versus surface roughness reveals its fragile character.

We investigate the effect of enhancement of superconducting transition temperature $T_c$ by nonmagnetic atom disorder in the filled skutterudite-related tetragonal ${\mathrm{Y}}_5{\mathrm{Rh}}_6{\mathrm{Sn}}_{18}$ compound doped with Ca. We documented experimentally that ${\mathrm{Y}}_5{\mathrm{Rh}}_6{\mathrm{Sn}}_{18}$ and its Ca-doped alloys are electronically inhomogeneous at the nanoscale, when Ca content is smaller than $\sim 1.5$ in the ${\mathrm{Y}}_{5-x}{\mathrm{Ca}}_x{\mathrm{Rh}}_6{\mathrm{Sn}}_{18}$ system, while for $x\ge 1.5$ much stronger chemical phase inhomogeneity is observed with an about 20% volume fraction of the second 3:4:13 cubic phase, which we interpret as a fluctuation of stoichiometry within the bulk sample. Then the enhancement of $T_c$ vs $x$ could be modeled by a mechanism proposed in recent theoretical reports for increasing the mean-field transition temperature $T_c$ in the presence of nonmagnetic disorder. The increase in disorder with doping increases the sample inhomogeneity and causes a systematic increase in $T_c$, while for two-phase $x\ge 1.5$ samples the critical temperature $T_c^{★}\approx 2\times T_c$ rapidly increases. Based on band structure calculations performed under pressure, we demonstrate how the change in density of states would affect $T_c$ of ${\mathrm{Y}}_5{\mathrm{Rh}}_6{\mathrm{Sn}}_{18}$. We obtained the Grüneisen parameter ${\gamma }_G$ larger for the inhomogeneous phase with respect to ${\gamma }_G$ of the bulk $T_c$ phase and attribute the enhancement of $T_c$ to larger stiffening of the high-temperature $T_c^{★}$ phase.

The electronic spectrum of the Penrose rhombus quasicrystal exhibits a macroscopic fraction of exactly degenerate zero-energy states. In contrast to other bipartite quasicrystals, such as the kite-and-dart one, these zero-energy states cannot be attributed to a global mismatch $\mathrm{\Delta }n$ between the number of sites in the two sublattices that form the quasicrystal. Here, we argue that these zero-energy states are instead related to a local mismatch $\mathrm{\Delta }n\left(\mathbf{r}\right)$. Although $\mathrm{\Delta }n\left(\mathbf{r}\right)$ averages to 0, its staggered average over self-organized domains gives the correct number of zero-energy states. Physically, the local mismatch is related to a hidden structure of nested self-similar domains that support the zero-energy states. This allows us to develop a real-space renormalization-group scheme, which yields the scaling law for the fraction of zero-energy states, $Z$, versus the size of their support domain, $N$, as $Z\propto N^{-\eta }$ with $\eta =1-ln2/2ln\tau \approx 0.2798$ (where $\tau$ is the golden ratio). It also reproduces the known total fraction of zero-energy states, $81-50\tau \approx 0.0983$. We also show that the exact degeneracy of these states is protected against a wide variety of local perturbations, such as irregular or random hopping amplitudes, magnetic field, and random dilution of the lattice. We attribute this robustness to the hidden domain structure.

Coherent conversion from microwave to optical wave opens new research avenues towards a long distance quantum network covering quantum communication, computing, and sensing out of the laboratory. Especially a multimode enabled system is essential for practical applications. Here we experimentally demonstrate coherent multimode conversion from the microwave to optical wave via collective spin excitation in a single crystal yttrium iron garnet (YIG, ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$) which is strongly coupled to a microwave cavity mode in a three-dimensional rectangular cavity. Expanding a collective spin excitation mode of our magnon-cavity hybrid system from Kittel to multimagnetostatic modes, we verify that the size of the YIG sphere predominantly plays a crucial role for the microwave-to-optical multimode conversion efficiency at resonant conditions. We also find that the coupling strength between multimagnetostatic modes and a cavity mode is manipulated by the position of a YIG inside the cavity. It is expected to be valuable for designing a magnon-hybrid system that can be used for coherent conversion between microwave and optical photons.

In this paper, we introduce Berry curvature, topological Chern number, and topological chiral edge mode that emerge from a hybridization between magnon and electromagnetic wave in a ferromagnet insulator. By focusing on the energy conservation, we first reformulate the Landau-Lifshitz-Maxwell equation into a Hermitian eigenvalue equation. From the eigenvalue equation, we define the Berry curvature of the magnon-photon coupled waves. We show that the Berry curvature thus introduced shows a prominent peak around a hybridization point between magnon mode and photon mode, and a massive hybrid mode takes a nonzero Chern number ($\pm 1$) due to the magnon-photon coupling. In accordance with the nonzero Chern number, the topological edge modes emerge inside the hybridization gap at a domain wall between two ferromagnetic insulators with opposite magnetizations.

Building on a recent investigation of the Shastry-Sutherland model [S. Wessel et al., Phys. Rev. B 98, 174432 (2018)], we develop a general strategy to eliminate the Monte Carlo sign problem near the zero-temperature limit in frustrated quantum spin models. If the Hamiltonian of interest and the sign-problem-free Hamiltonian, obtained by making all off-diagonal elements negative in a given basis, have the same ground state and this state is a member of the computational basis, then the average sign returns to one as the temperature goes to zero. We illustrate this technique by studying the triangular and kagome lattice Heisenberg antiferrromagnet in a magnetic field above saturation, as well as the Heisenberg antiferromagnet on a modified Husimi cactus in the dimer basis. We also provide detailed Appendices on using linear programming techniques to automatically generate efficient directed loop updates in quantum Monte Carlo simulations.

We develop a phenomenological mean-field theory describing the hidden-order phase in $\mathrm{U}{\mathrm{Ru}}_2{\mathrm{Si}}_2$ as a nematic of the $B_{1g}$ representation staggered along the $c$ axis. Several experimental features are reproduced by this theory: the topology of the temperature-pressure phase diagram, the response of the elastic modulus $(C_{11}-C_{12})/2$ above the transition at ambient pressure, and orthorhombic symmetry breaking in the high-pressure antiferromagnetic phase. In this scenario, hidden order is characterized by broken rotational symmetry that is modulated along the $c$ axis, the primary order of the high-pressure phase is an unmodulated nematic, and the triple point joining those two phases with the high-temperature paramagnetic phase is a Lifshitz point.

The multiferroic nature of the honeycomb-lattice $\mathrm{M}{\mathrm{n}}_2{\mathrm{V}}_2{\mathrm{O}}_7$ was investigated through detailed temperature, high-pressure, and magnetic-field-dependent measurements. A first-order martensiticlike structural phase transition with the thermal hysteresis associated with magnetic, heat-capacity, and dielectric anomalies was observed between $T_{Mh}$ (303 K) and $T_{Mc}$ (291 K). External pressure up to 15.41 kbar suppresses the thermal hysteresis in the magnetization data, indicating that the high-temperature β-phase persists down to the lower temperature under 15.41 kbar. Furthermore, isothermal capacitance-stress hysteresis loops along with crystallographic Aizu notation of $2/mF\overline{1}$ supports a martensitic phase transition driving ferroelastic ordering near or below room temperature. At low temperature, a long-range antiferromagnetic ordering was observed at $T_N\sim 17\mathrm{K}$. With increasing the external pressure up to 15.41 kbar, 100% enhancement of $T_N$ was observed and a metamagnetic transition at 5 K was enhanced near 3 T. High-field magnetization study up to 60 T induces multiple metamagnetic transitions below $T_N$. Below $T_N$, a magnetostriction induced magnetoelectric coupling was observed and further supported by the temperature-dependent x-ray studies. Taking these comprehensive research findings into account, we established that $\mathrm{M}{\mathrm{n}}_2{\mathrm{V}}_2{\mathrm{O}}_7$ is a unique multifunctional material with the coexistence of ferroelastic and antiferromagnetic orderings and with weak magnetoelectric coupling.

We develop a field theory of quantum magnets and magnetic (semi)metals, which is suitable for the analysis of their universal and topological properties. The systems of interest include collinear, coplanar, and general noncoplanar magnets. At the basic level, we describe the dynamics of magnetic moments using smooth vector fields in the continuum limit. Dzyaloshinskii-Moriya interaction is captured by a non-Abelian vector gauge field, and chiral spin couplings related to topological defects appear as higher-rank antisymmetric tensor gauge fields. We distinguish type-I and type-II magnets by their equilibrium response to the non-Abelian gauge flux, and characterize the resulting lattices of skyrmions and hedgehogs, the spectra of spin waves, and the chiral response to external perturbations. The general spin-orbit coupling of electrons is similarly described by non-Abelian gauge fields, including higher-rank tensors related to the electronic Berry flux. Itinerant electrons and local moments exchange their gauge fluxes through Kondo and Hund interactions. Hence, by utilizing gauge fields, this theory provides a unifying physical picture of “intrinsic” and “topological” anomalous Hall effects, spin-Hall effects, and other correlations between the topological properties of electrons and moments. We predict “topological” magnetoelectric effect in materials prone to hosting hedgehogs. Links to experiments and model calculations are provided by deriving the couplings and gauge fields from generic microscopic models, including the Hubbard model with spin-orbit interactions. Much of the formal analysis is generalized to $d$ spatial dimensions in order to access the ${\pi }_{d-1}\left(S^{d-1}\right)$ homotopy classification of the magnetic hedgehog topological defects, and establish the possibility of novel quantum spin liquids that exhibit a fractional magnetoelectric effect. However, we emphasize the form of all results in the physically relevant $d=3$ dimensions, and discuss a few applications to topological magnetic conductors like ${\mathrm{Mn}}_3\mathrm{Sn}$ and ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$.

We study optical coefficients that characterize wave propagation through layered structures called plasmonic crystals. These consist of a finite number of stacked metallic sheets embedded in dielectric hosts with a subwavelength spacing. By adjustment of the frequency, spacing, number as well as geometry of the layers, these structures may exhibit appealing transmission properties in a range of frequencies from the terahertz to the mid-infrared regime. Our approach uses a blend of analytical and numerical methods for the distinct geometries with infinite, translation-invariant, flat sheets and nanoribbons. We describe the transmission of plane waves through a plasmonic crystal in comparison to an effective dielectric slab of equal total thickness that emerges from homogenization, in the limit of zero interlayer spacing. We demonstrate numerically that the replacement of the discrete plasmonic crystal by its homogenized counterpart can accurately capture a transmission coefficient akin to the extinction spectrum, even for a relatively small number of layers. We point out the role of a geometry-dependent corrector field, which expresses the effect of subwavelength surface plasmons. In particular, by use of the corrector we describe lateral resonances inherent to the nanoribbon geometry.

The exchange splitting and resulting electromagnetic response of graphene in a monolayer chromium triiodide ($\mathrm{Cr}{\mathrm{I}}_3$)–graphene van der Waals heterostructure are considered using a combination of density-functional theory and electromagnetic calculations. Although the effective exchange fields are in the hundreds of Tesla, for the equilibrium separation nonreciprocal effects are found to be weak compared to those for a comparable external magnetic bias. For nonequilibrium separations, nonreciprocal effects can be substantial.

We revisit the $\eta$-pairing states in Hubbard models and explore their connections to quantum many-body scars to discover a universal scars mechanism. $\eta$-pairing occurs due to an algebraic structure known as a spectrum generating algebra (SGA), giving rise to equally spaced towers of eigenstates in the spectrum. We generalize the original $\eta$-pairing construction and show that several Hubbard-like models on arbitrary graphs exhibit SGAs, including ones with disorder and spin-orbit coupling. We further define a restricted spectrum generating algebra (RSGA) and give examples of perturbations to the Hubbard-like models that preserve an equally spaced tower of the original model as eigenstates. The states of the surviving tower exhibit a subthermal entanglement entropy, and we analytically obtain parameter regimes for which they lie in the bulk of the spectrum, showing that they are exact quantum many-body scars. The RSGA framework also explains the equally spaced towers of eigenstates in several well-known models of quantum scars, including the Affleck-Kennedy-Lieb-Tasaki model.

Radial anisotropy in small objects has been linked to exotic optical properties. It can be implemented with a spherical inclusion that manifests self-similarity. We show that, when a self-similar, onion-like structure with alternating layers is homogenized by using an effective material approximation, the homogenized material becomes uniaxially anisotropic with the axis of anisotropy pointed radially outward from the center of the inclusion. This radial anisotropy becomes exact in the limit of a dense set of layers. The exact equivalence of the layered self-similar inclusion and the radially anisotropic inclusion manifests itself both in the effective permittivities of the two inclusions—when homogenized over the entire volumes—and in the internal potentials. Because the layered sphere and the radially anisotropic sphere are analogous, it is possible to study some of the interesting scattering features of radially anisotropic spheres in a realistic configuration. In particular, we show that the outcome of homogenizing the self-similar inclusion, and consequently the electric response, depends on what the core material at the center of the inclusion is and that a continuous transition between the two homogenization models is possible. The findings suggest intriguing applications in nanophotonics.

We study the behavior of the out-of-time-ordered correlator (OTOC) in a non-Hermitian quantum Ising system. We show that the OTOC can diagnose not only the exceptional point in the states with lowest real parts of Hamiltonian spectra (LRHS), which host the Yang-Lee edge singularity, but also the exceptional point in states with higher real parts of Hamiltonian spectra (HRHS). We find that the evolution of the OTOC in the parity-time symmetric phase can be divided into two stages: In the short-time stage, the OTOC oscillates periodically, and when the parameter is near the exceptional point of the LRHS, this oscillation behavior can be described by both the scaling theory of the zero-dimensional ($0\mathrm{D}$) quantum Yang-Lee edge singularity and the scaling theory of the $1\mathrm{D}$ quantum Ising model, while in the long-time stage the OTOC increases exponentially, controlled by the exceptional point of the HRHS. Possible experimental realizations are then discussed.

We present a systematic ${}^{57}\mathrm{Fe}$ Mössbauer study on highly diluted Fe centers in ${\mathrm{Li}}_2\left({\mathrm{Li}}_{1-x}{\mathrm{Fe}}_x\right)\mathrm{N}$ single crystals as a function of temperature and magnetic field applied transverse and longitudinal with respect to the single-ion anisotropy axis. Below 30 K, the Fe centers exhibit a giant magnetic hyperfine field of ${\overline{B}}_A=70.25\left(2\right)\mathrm{T}$ parallel to the axis of strongest electric field gradient ${\overline{V}}_{zz}=-154.0\left(1\right)\mathrm{V}/{\AA }^2$. Fluctuations of the magnetic hyperfine field are observed between 50 and 300 K and described by the Blume two-level relaxation model. From the temperature dependence of the fluctuation rate, an Orbach spin-lattice relaxation process is deduced. An Arrhenius analysis yields a single thermal activation barrier of ${\overline{E}}_A=570\left(6\right)\mathrm{K}$ and an attempt frequency ${\overline{\nu }}_0=309\left(10\right)\mathrm{GHz}$. Mössbauer spectroscopy studies with applied transverse magnetic fields up to 5 T reveal a large increase of the fluctuation rate by more than one order of magnitude. In longitudinal magnetic fields, a splitting of the fluctuation rate into two branches is observed consistent with a Zeeman induced modification of the energy levels. The experimental observations are qualitatively reproduced by a single-ion effective spin Hamiltonian analysis assuming a ${\mathrm{Fe}}^{1+}{d}^7$ charge state with the unquenched orbital moment and a $J=7/2$ ground state. It is demonstrated that a weak axial single-ion anisotropy $D$ of the order of a few Kelvin can cause a two orders of magnitude larger energy barrier for longitudinal spin fluctuations.

In this study, Gd ion implantation and annealing were performed at ${900}^{\circ }\mathrm{C}$ for nominally undoped wurtzite GaN grown by metal-organic chemical vapor deposition. Spin-polarized positron annihilation measurements showed that vacancy clusters including at least 12 vacancies per cluster were the major positron-trapping centers and that the electrons in the vacancy clusters were spin-polarized. These observations could be explained by first-principles calculations. The previous speculation about the defect-assisted ferromagnetism of Gd-implanted GaN may be supported if vacancy clusters are considered.

Dzyaloshinskii-Moriya interaction (DMI) is an antisymmetric fundamental magnetic exchange interaction, which is responsible for the formation of exotic topological spin textures in chiral magnets. Here by investigating the DMI-induced energy asymmetry of the magnon dispersion relation, we quantify the atomistic DMI vectors in two atomic layers made of Fe and Co epitaxially grown on W(110). We provide direct experimental evidence that in layered ferromagnets this fundamental interaction can be tailored via quantum engineering of the lattice symmetry, direct intra- and interlayer DMI coupling. We report on a giant DMI in epitaxial Co/Fe bilayers grown on W(110), exhibiting $C_{2v}$ symmetry. Our results pave the way for tailoring DMI on the atomic length scales with the perspective of designing desired topological spin textures.

A stochastic model for the field-driven polarization reversal in rhombohedral ferroelectrics is developed, providing a description of their temporal electromechanical response. Application of the model to simultaneous measurements of polarization and strain kinetics in a rhombohedral $\mathrm{Pb}\left(\mathrm{Zr},\mathrm{Ti}\right){\mathrm{O}}_3$ ceramic over a wide time window allows the identification of preferable switching paths, fractions of individual switching processes, and their activation fields. In conjunction, the phenomenological Landau-Ginzburg-Devonshire theory is used to analyze the impact of an external field and stress on switching barriers, showing that residual mechanical stress may promote the fast switching.

Two-dimensional (2D) van der Waals (vdW) magnets have recently attracted increasing attention, as they provide a novel system for exploring 2D magnetism. However, intrinsic ferromagnetism in 2D systems has almost exclusively been observed at low temperatures, limiting their technological relevance. ${\mathrm{Fe}}_{\mathrm{N}}{\mathrm{Ge}\mathrm{Te}}_2$ ($N=3$, 4, and 5) systems are currently becoming the most attractive 2D vdW materials due to their relatively high Curie temperatures and large saturation magnetization. However, the nature of their complex yet intriguing magnetic behaviors is still unclear, in part due to the multiple inequivalent iron sites and iron vacancies. Here, we show evolution of magnetic ordering transitions in ${\mathrm{Fe}}_{5-x}{\mathrm{Ge}\mathrm{Te}}_2$ with high Curie temperature and a strong saturation magnetization using photoemission electron microscopy and transport measurements. At 275 K, the ferromagnet transitions to a ferrimagnet, and below 110 K transitions to a state with glassy clusters. These are evidenced from temperature-dependent magnetic stripe domain evolution and anisotropic magnetoresistance measurements. Our findings show a clear magnetic ground state of ${\mathrm{Fe}}_{5-x}{\mathrm{Ge}\mathrm{Te}}_2$ at room temperature which signals that ${\mathrm{Fe}}_{5-x}{\mathrm{Ge}\mathrm{Te}}_2$ system is a very promising candidate for spintronic devices and provides a material design pathway to further increase the Curie temperature and saturation moments in vdW ferromagnets.