Electron spin dynamics was studied down to 80 mK in the triangular-lattice quantum spin-liquid candidate ${\mathrm{YbZnGaO}}_4$ using muon spin relaxation, finding no evidence for freezing or ordering of the Yb spins. The muon spin relaxation rate can be represented by the sum of two contributions, one dependent on longitudinal magnetic field and the other independent of field. The field-dependent term follows the form expected for two-dimensional diffusion of mobile spin excitations. The spin-diffusion rate obtained for these excitations in the high temperature paramagnetic regime is comparable with the exchange coupling frequency $J/h$, reducing significantly in the low temperature quantum regime. This slowdown is assigned to the effect of quantum entanglement. The exchange coupling $J$ is estimated to be 2.0(2) K from the crossover between the two regimes. The field-independent term is only weakly dependent on temperature, and at 15 K its absolute value is consistent with dipolar coupling of the muon to the three Yb moments closest to the muon site, where the spin dynamics of these moments is determined by exchange fluctuations. The temperature-dependent properties in the quantum regime are compared against the three possible U(1) spin-liquid models that have been obtained for the strongly spin-orbit coupled triangular lattice by Y.-D. Li, Y.-M. Lu, and G. Chen [Phys. Rev. B 96, 054445 (2017)]. The comparison with theory takes published specific heat and thermal conductivity data into account, along with the spin-diffusion rate obtained from the muons. It is found that the nodal spin-liquid model U1A11 containing both linear and quadratic nodes provides better agreement with experiment than either the U1A00 spinon Fermi surface (FS) model or the U1A01 model that contains only linear nodes.

Mismatched lattice constants at a van der Waals epitaxy interface often introduce in-plane strains to the lattice of the epitaxial layer, termed epitaxy strain, wherein the strains do not follow the intralayer Poisson's relation. In this study, we obtained the magnetic phase diagrams of ${\mathrm{CrSe}}_2$ and ${\mathrm{CrTe}}_2$ mono- and bilayers under epitaxy strain up to 8%, as predicted using density functional theory calculations. The magnetic phase diagrams indicate that the in-plane epitaxy strain manipulates either the intra- or interlayer magnetism. The in-plane strain varies the interlayer distance, defined using an interlayer Poisson's ratio, which determines whether the interlayer magnetism follows a Bethe–Slater curve-like (BSC-like) or a reversed BSC-like behavior, depending on the in-plane magnetism. The tunability of the intralayer magnetism is a result of competing intralayer Cr–Cr superexchange interactions. A graphene substrate was introduced to examine the validity of our diagrams in practice. This study also afforded a tentative explanation on the previously reported magnetizations in ${\mathrm{CrSe}}_2$ and ${\mathrm{CrTe}}_2$ epitaxial mono- or bilayers under epitaxy strains, which had given rise to some controversy.

In order to determine the role of nonthermal transport of hot carriers, which is decisive for the dissipation of energy in condensed matter, we performed time-resolved broadband femtosecond transient reflectivity measurements on 7–197-$\mathrm{nm}$-thick Bi(111) films epitaxially grown on Si(111). We monitored the behavior of the Fourier amplitude and the central frequency of the coherent $A_{1g}$ phonon mode as a function of the incident fluence, film thickness, and probe wavelength in the range 580–$700\mathrm{nm}$. The frequency redshift that follows photoexcitation was used as a robust quantity to determine the effective distribution of excited carriers that governs the displacive excitation mechanism of coherent $A_{1g}$ phonons in Bi. For Bi films up to $50\mathrm{nm}$ thickness a homogeneous excitation due to the ultrafast transport of hot charge carriers is observed, limited by a carrier penetration depth of $60\mathrm{nm}$ independent of the totally deposited laser energy.

Using finite-temperature strong-coupling expansions for the SU($N$) Hubbard model, we calculate the thermodynamic properties of the model in the infinite-$U$ limit for arbitrary density $0\le \rho \le 1$ and all $N$. We express the ferromagnetic susceptibility of the model as a Curie term plus $\mathrm{\Delta }\chi$, an excess susceptibility above the Curie behavior. We show that, on a bipartite lattice, graph by graph the contributions to $\mathrm{\Delta }\chi$ are non-negative in the limit that the hole density $\delta =1-\rho$ goes to zero. By summing the contributions from all graphs consisting of closed loops we find that the low-hole-density ferromagnetic susceptibility diverges exponentially as $exp\mathrm{\Delta }/T$ as $T\to 0$ in two and higher dimensions. This demonstrates that the Nagaoka-Thouless ferromagnetic state exists as a thermodynamic state of matter at low enough density of holes and sufficiently low temperatures. The constant $\mathrm{\Delta }$ scales with the SU($N$) parameter $N$ as $1/N$ implying that ferromagnetism is gradually weakened with increasing $N$ as the characteristic temperature scale for ferromagnetic order goes down.

MnBi is remarkable for having a magnetocrystalline anisotropy (MCA) that increases with temperature. This unusual behavior has been attributed to the thermal expansion of the lattice and, more recently, to an anisotropic vibrational free energy. However, the effect of magnetic fluctuations on the MCA has not yet been quantified. Here, first-principles density-functional theory calculations based on the disordered local moment picture (DFT-DLM) are used to calculate the MCA of MnBi in the presence of magnetic disorder. The MCA is obtained from the magnetic torque, calculated as a function of magnetization angle and temperature $T$. At fixed ionic positions, the MCA decays monotonically with increasing $T$. The DFT-DLM torques provide access to the individual anisotropy constants ${\kappa }_l$ (which parametrize the relation between magnetic energy and magnetization angle), and their dependence on order parameter $m$. The lowest order constant ${\kappa }_2$ follows single-ion-like behavior at low $T$ but decays as $m^4$ as $T$ increases, while the higher-order constants deviate strongly from single-ion predictions. Zero-$T$ calculations show that a spin reorientation transition can be triggered by removing 0.1 electrons, resulting in $c$-axis magnetization once 0.25 electrons have been removed. The zero-temperature calculations are cross-validated using an alternative implementation of DFT based on wave functions, plane waves, and pseudopotentials.

Frequency multiplication is an essential part of electronics and optics which led to numerous indispensable applications. In this paper, we utilize a combination of scanning transmission x-ray microscopy and micromagnetic simulations to directly image magnonic frequency multiplication by means of dynamic real-space magnetization measurements. We experimentally demonstrate frequency multiplication up to the seventh order, which enables the generation of nanoscale spin waves at $6\mathrm{G}\mathrm{Hz}$ with excitation frequencies of less than $1\mathrm{G}\mathrm{Hz}$. Good agreement between the experiment and micromagnetic simulations allows us to build a micromagnetic model capable of predicting conversion efficiencies and multiplexing capabilities of the system. Furthermore, simulations reveal that more than two rows of antidots do not increase the conversion efficiency substantially. By enabling magnonic multiplexing with low input frequencies while not exceeding the size of a few microns, the device will lead to numerous applications, further advancing the capabilities of magnonic data transmission.

The optical properties of $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ (K12442, $T_c=33.5$ K) and $\mathrm{K}{\mathrm{Ca}}_2{\left({\mathrm{Fe}}_{0.95}{\mathrm{Ni}}_{0.05}\right)}_4{\mathrm{As}}_4{\mathrm{F}}_2$ (Ni-K12442, $T_c=29$ K) have been examined at a large number of temperatures. For both samples, a nodeless superconducting gap is clearly observed in the optical conductivity at 5 K. The superconducting gap $\mathrm{\Delta }\simeq 8.7$ meV ($2\mathrm{\Delta }/k_{\text{B}}{T}_c\simeq 6.03$) in K12442, pointing towards strong-coupling Cooper pairs, but in sharp contrast, $\mathrm{\Delta }\simeq 4.6$ meV ($2\mathrm{\Delta }/k_{\text{B}}{T}_c\simeq 3.68$) in Ni-K12442, which agrees with the BCS weak-coupling pairing state. More intriguingly, below $T^{*}\simeq 75$ K, the optical conductivity of K12442 reveals a pseudogap that smoothly evolves into the superconducting gap below $T_c$, while no such behavior is detected in the electron-doped Ni-K12442. The comparison between the two samples suggests that the pseudogap and strong-coupling Cooper pairs in K12442 may be intimately related to the shallow and incipient bands. We provide arguments supporting a preformed pairing mechanism of the pseudogap, but at the moment a magnetic scenario cannot yet be excluded.

In the present work, the effect of elevated pressure and lowered temperature on the structural and vibrational stability of dysprosium scandate (${\mathrm{DyScO}}_3$) is studied via high-pressure synchrotron x-ray diffraction (HPXRD) and high-pressure (HP) and low-temperature Raman spectroscopy. A solid-state reaction route is employed to synthesize the material with a crystallite size of 92 nm, which at ambient conditions exhibits an orthorhombic phase with the space group $Pbnm$ (62). HPXRD results reveal excellent phase stability of the material, with the ratio of the polyhedral volumes and the compressibility for the ${\mathrm{DyO}}_{12}$ and ${\mathrm{ScO}}_6$ polyhedra to be around 4.26 and 1 for the entire applied pressure range of up to 40 GPa. Interestingly, the combination of HPXRD and HP Raman measurements signals a change in the preferred orientations in the crystalline structure with the increased pressure, while keeping the structure stable. The bulk modulus of the material is estimated to be 189.4 GPa from the HPXRD data and is further used to estimate the mode Grüneisen parameter (γ) for various Raman modes. The behavior of phonon frequency with varying temperature is explained by considering the anharmonic effects, i.e., lattice expansion and perturbation in the Hamiltonian, with an increase in temperature. Furthermore, the implicit and explicit anharmonicity contributions were calculated to elucidate the phonon decay mechanisms. Our results offer valuable insights relating to the behavior of this intriguing class of materials under extreme conditions and lays the foundation for further exploration.

The elastic response of monolayer silicon-germanium alloys (${\mathrm{Si}}_{1\text{−}x}{\mathrm{Ge}}_x, 0\le x\le 1$) is investigated using first-principles calculations. It is found that the atomic arrangement of monolayer ${\mathrm{Si}}_{1\text{−}x}{\mathrm{Ge}}_x$ alloys has a significant impact on their elastic anisotropy, which can be categorized by their crystal systems. The hexagonal ${\mathrm{Si}}_{1\text{−}x}{\mathrm{Ge}}_x$ is elastically isotropic because of high symmetry, while some rectangular and oblique ${\mathrm{Si}}_{1\text{−}x}{\mathrm{Ge}}_x$ are elastically anisotropic because of the presence of the zigzag interface. The degree of anisotropy is related to the width and ratio of silicene/germanene strips in the ${\mathrm{Si}}_{1\text{−}x}{\mathrm{Ge}}_x$ superlattice structure. This work provides a guideline for experimentally realizing this series of materials that may find applications in ${\mathrm{Si}}_{1\text{−}x}{\mathrm{Ge}}_x$-based optoelectronics and flexible electronics.

We theoretically study the terahertz-induced high-order harmonic generation (HHG) and nonlinear electric transport in graphene based on the quantum master equation with the relaxation time approximation. To obtain microscopic insight into the phenomena, we compare the results of the fully dynamical calculations with those under a quasistatic approximation, where the electronic system is approximated as a nonequilibrium steady state. As a result, we find that the THz-induced electron dynamics in graphene can be accurately modeled with the nonequilibrium steady state at each instance. The population distribution analysis further clarifies that the THz-induced HHG in graphene originates from the reduction of effective conductivity due to a large displacement of electrons in the Brillouin zone. By comparing the present nonequilibrium picture with a thermodynamic picture, we explore the role of the nonequilibrium nature of electron dynamics on the extremely nonlinear optical and transport phenomena in graphene.

The study of higher-order and real topological states as well as the material realization have become a research forefront of topological condensed matter physics in recent years. Twisted bilayer graphene (tbG) is proved to have higher-order and real topology. However, whether this conclusion can be extended to other two-dimensional twisted bilayer carbon materials and the mechanism behind it lack explorations. In this paper, we identify the twisted bilayer $\alpha$-graphyne (tbGPY) at large twisting angle as a real Chern insulator (also known as Stiefel-Whitney insulator) and a second-order topological insulator. Our first-principles calculations suggest that the tbGPY at $21.{78}^{\circ }$ is stable at 100 K with a larger bulk gap than the tbG. The nontrivial topological indicators, including the real Chern number and a fractional charge, and the localized in-gap corner states are demonstrated from first-principles and tight-binding calculations. Moreover, with ${\mathcal{C}}_{6z}$ symmetry, we prove the equivalence between the two indicators, and explain the existence of the corner states. To decipher the real and higher-order topology inherited from the moiré heterostructure, we construct an effective four-band tight-binding model capturing the topology and dispersion of the tbGPY at large twisting angle. A topological phase transition to a trivial insulator is demonstrated by breaking the ${\mathcal{C}}_{2y}$ symmetry of the effective model, which gives insights on the trivialization of the tbGPY as reducing the twisting angle to $9.{43}^{\circ }$ suggested by our first-principles calculations.

We study the effect of acoustic phonons on the quantum phase transition in the $\mathrm{O}(N$) model. We develop a renormalization group (RG) analysis near $(3+1)$ space-time dimensions and derive the RG equations using an $\epsilon$ expansion. Our results indicate that when the number of flavors of the underlying $\mathrm{O}(N$) model exceeds a critical number $N_c=4$, the quantum transition remains second-order of the Wilson-Fisher type while, for $N\le 4$, it is a weakly first-order transition. We characterize this weakly first-order transition by a length scale ${\xi }^{*}$, below which the behavior appears to be critical. At finite temperatures for $N\le 4$, a tricritical point separates the weakly first-order and second-order transitions.

A method to produce synthetic dimensions in an optical cavity is presented. The system is obtained by coupling two one-dimensional optical cavities by means of a moving mirror. Its translation generates a new synthetic dimension resulting in a transmittance pattern that corresponds to the energy dispersion of electrons in a two-dimensional lattice: in this case a strained triangular lattice. We elucidate the analogy between these two systems by relating the distribution of transmittances of the optical cavity to the density of states of the two-dimensional lattice and the Bragg diffraction modes to the Van Hove singularities. Our mapping makes the coupled optical cavity a simulator for lattice Hamiltonians found in solid-state physics, providing an easier alternative platform to access some of their properties, as for example, the electronic conductivity, which is found here using the Boltzmann formula. Moreover, it is proved that the truly synthetic behavior appears only when the two cavities have an irrational length ratio as modes resonant on one cavity are never resonant in the other. Mathematically, wave phase differences act independently as they are given by a function that behaves as a pseudorandom number generator. This provides an elegant way to study synthetic dimensions without the need to move the central mirror, i.e., in a single, fixed geometry device. Thus, our work establishes a bridge between the fields of optical cavities, synthetic dimensions, and two-dimensional materials.

Motivated by the recent wealth of exotic magnetic phases emerging in two-dimensional frustrated lattices, we investigate the origin of possible magnetism in the monolayer family of triangular lattice materials $M{X}_2$ ($M$=V, Mn, Ni and $X$=Cl, Br, I). We first show that consideration of general properties such as filling and hybridization enables to formulate the trends for the most relevant magnetic interaction parameters. In particular, we observe that the effects of spin-orbit coupling (SOC) can be effectively tuned through the ligand elements as the considered $3d$ transition metal ions do not strongly contribute to the anisotropic component of the intersite exchange interaction. Consequently, we find that the corresponding SOC matrix elements differ significantly from the atomic limit. In the next step and by using two ab initio based complementary approaches, we extract realistic effective spin models and find that in the case of heavy ligand elements, SOC effects manifest in anisotropic exchange and single-ion anisotropy only for specific fillings.

Quasi-two-dimensional objects appear to be promising for the development of new optical devices since their electronic properties are expected to be governed by their size. The understanding of these properties can be achieved by means of theoretical spectroscopy based on the state-of-the-art ab initio formalisms. Time-dependent density functional theory is well suited since it accounts for the local field effects, which are expected to be large at the interfaces with vacuum. This framework allows the calculation of the response function to the external potential. For bulk materials, this quantity is related to the macroscopic dielectric function following the Adler and Wiser formula. This expression contains dimensionless quantities, while for the two-dimensional object, the physical observables should be proportional to the thickness. In this paper, we propose a mixed-space approach which allows us to calculate in a direct way the out-of-plane component and to evidence how the ambiguity on the thickness of the slab affects the calculation of the macroscopic dielectric function. The classical Lorentz model adapted to a thin slab reveals how the huge change of the induced electric field, and the arising of a transverse polarization, lead to modify the expression of the macroscopic dielectric function to get the absorption spectrum. Despite the influence of the thickness of the slab on the macroscopic dielectric function, the optical response resulting from the classical electromagnetism can be unambiguously calculated from the mixed-space simulations.

We theoretically investigate the mapping of the supercurrent distribution in a planar superconductor-normal-superconductor junction in the presence of a perpendicular magnetic field via the scanning gate microscopy technique. We find that the distribution of counterpropagating supercurrents aligned in Josephson vortices can be mapped by the change in the critical current induced by the tip of the scanning probe if the flux in the junction is set close to the maxima of the Fraunhofer pattern. Instead, when the magnetic field drives the junction to a supercurrent minimum in the Fraunhofer pattern, the superconducting phase adapts, and the tip always increases the supercurrent. The perpendicular magnetic field leads to the formation of Josephson vortices, whose extension for highly transparent junctions depends on the current circulation direction. We show that this leads to an asymmetric supercurrent distribution in the junction and that this can be revealed by scanning gate microscopy. We explain our findings on the basis of numerical calculations for both short- and long-junction limits and provide a phenomenological model for the observed phenomena.

The unoccupied part of the band structure in the magnetic topological insulator ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ is studied by first-principles calculations. We propose a possible second, unoccupied topological surface state with a similar electronic structure to the celebrated occupied topological surface state. The conventional density functional theory method employed here may not describe excited state properties precisely, and therefore the calculations for the current study can be considered as model simulations. This unoccupied topological surface state is energetically located approximate 1.5 eV above the occupied massive Dirac surface state around the $\mathrm{\Gamma }$ point, which permits it to be directly observed by two-photon angle-resolved photoemission spectroscopy. We propose a unified effective model for the occupied and unoccupied surface states. Due to the direct optical coupling between these two surface states, we further propose two optical effects to detect the unoccupied surface state if it exists. One is the polar Kerr effect in odd layers from nonvanishing ac Hall conductance ${\sigma }_{xy}\left(\omega \right)$, and the other is higher-order terahertz-sideband generation in even layers, where the nonvanishing Berry curvature of the unoccupied surface state is directly observed from the giant Faraday rotation of optical emission.

We study the dynamics of the spin system that consists of a positively charged II-VI semiconductor quantum dot doped with a single ${\mathrm{Cr}}^{+}$ ion. The resonant photoluminescence (PL) of the positively charged exciton coupled with the ${\mathrm{Cr}}^{+}$ spin is used to analyze the main spin relaxation channels. The intensity of the resonant PL is reduced by an optical pumping of the spin of the resident hole-${\mathrm{Cr}}^{+}$ complex that can be seen as a nanomagnet. The spin memory can be partially erased by a nonresonant optical excitation. This leads to an increase of the resonant PL signal. The resonant PL is cocircularly polarized and corresponds to relaxation channels that conserve the ${\mathrm{Cr}}^{+}$ spin $|S_z|$. The observation in the resonant-PL excitation spectra of optical transitions with a change of the ${\mathrm{Cr}}^{+}$ spin permits to determine the magnetic anisotropy of the magnetic atom. Optical pumping, autocorrelation measurements, and the power dependence of the PL intensity distribution show that the effective temperature of the hole-${\mathrm{Cr}}^{+}$ spin system is affected by the optical excitation through the local generation of phonons.

Second-order photon correlation measurements [$g^{\left(2\right)}\left(\tau \right)$ functions] are widely used to classify single-photon emission purity in quantum emitters or to measure the multiexciton quantum yield of emitters that can simultaneously host multiple excitations – such as quantum dots – by evaluating the value of $g^{\left(2\right)}\left(\tau =0\right)$. Accumulating enough photons to accurately calculate this value is time consuming and could be accelerated by fitting of few-shot photon correlations. Here, we develop an uncertainty-aware, deep adversarial autoencoder ensemble (AAE) that reconstructs noise-free $g^{\left(2\right)}\left(\tau \right)$ functions from noise-dominated, few-shot inputs. The model is trained with simulated $g^{\left(2\right)}\left(\tau \right)$ functions that are facilely generated by Poisson sampling time bins. The AAE reconstructions are performed orders-of-magnitude faster, with reconstruction errors and estimates of $g^{\left(2\right)}\left(\tau =0\right)$ that are lower in variance and similar in accuracy compared to Maximum likelihood estimation and Levenberg-Marquardt least-squares fitting approaches, for simulated and experimentally measured few-shot $g^{\left(2\right)}\left(\tau \right)$ functions (∼100 two-photon events) of InP/ZnS/ZnSe and CdS/CdSe/CdS quantum dots. The deep-ensemble model comprises eight individual autoencoders, allowing for probabilistic reconstructions of noise-free $g^{\left(2\right)}\left(\tau \right)$ functions, and we show that the predicted variance scales inversely with number of shots, with comparable uncertainties to computationally intensive Markov chain Monte Carlo sampling. This work demonstrates the advantage of machine learning models to perform uncertainty-aware, fast, and accurate reconstructions of simple Poisson-distributed photon correlation functions, allowing for on-the-fly reconstructions and accelerated materials characterization of solid-state quantum emitters.