Deriving structure-property relationships for multicomponent ferroelectric materials has always been a challenging problem because the properties are mostly driven by subtle nanoscale correlations which are hard to detect. Here we have studied the famous Pb-free material $x\left({\mathrm{Ba}}_{0.7}{\mathrm{Ca}}_{0.3}\right){\mathrm{TiO}}_3\text{−}(1-x)\mathrm{Ba}\left({\mathrm{Zr}}_{0.2}{\mathrm{Ti}}_{0.8}\right){\mathrm{O}}_3$ $(x\mathrm{BCT}\text{−}\mathrm{BZT})$ which has been at the center of attention for approximately the last 10 years because of its unprecedented piezoelectric properties. However, the structure-property relationship for $x\mathrm{BCT}$-BZT remains elusive as neither the common concepts nor the experimental results lead to satisfactory models which can fully explain its unusual piezoelectric properties as a function of composition as well as recognize its uniqueness compared to other similar systems. Hence we have applied total neutron-scattering and Raman-scattering methods to examine the local structural correlations of $x\mathrm{BCT}$-BZT in the range $0.40\le x\le 0.60$ at ambient conditions. By refining large-box atomistic models against the neutron pair distribution functions, we have observed an emerging coherence in the polar displacements of the cations at $x=0.50$, leading to an increased structural ergodicity at the key orthorhombic-tetragonal phase boundary. Given the very similar level of local structural disorder and spontaneous polarization found in the system with $x$, we propose that the abrupt amplification of piezoelectric properties in this material at a region of phase instability is a consequence of enhanced collaboration amongst the all cations in a strain-reduced local environment. It also indicates that the popular structure-property concept entailing a low-symmetry crystal structure cannot be a generic concept or a precondition.

In this study, dielectric constant and pyroelectric current measurements under high pressure up to 16.7 kbar have been performed for the interacting spin dimer system ${\mathrm{TlCuCl}}_3$, which exhibits spin-driven ferroelectricity in the magnon Bose-Einstein condensation (BEC) phase with strong quantum spin fluctuation. When pressure is applied, the magnon BEC phase becomes significantly stabilized, whereas the value of the electric polarization decreases in high-pressure regions. It is also observed that electric polarization becomes harder under pressure. Analyses based on both a Landau theory and a microscopic spin Hamiltonian demonstrate that the suppression of quantum fluctuation on the application of pressure caused the observed pressure effects. Consequently, it is revealed that the ferroelectricity in ${\mathrm{TlCuCl}}_3$ is highly governed by the quantum spin fluctuation.

We study disorder-induced ergodicity breaking transition in high-energy eigenstates of interacting spin-1/2 chains. Using exact diagonalization, we introduce a cost function approach to quantitatively compare different scenarios for the eigenstate transition. We study ergodicity indicators such as the eigenstate entanglement entropy and the spectral level spacing ratio, and we consistently find that an (infinite-order) Berezinskii-Kosterlitz-Thouless transition yields a lower cost function when compared to a finite-order transition. Interestingly, we observe that the ergodicity breaking transition in systems studied by exact diagonalization (with around 20 lattice sites) takes place at disorder values lower than those reported in previous works. As a consequence, the crossing point in finite systems exhibits nearly thermal properties, i.e., ergodicity indicators at the transition are close to the random matrix theory predictions.

We investigate the longitudinal conductance of a disordered three-dimensional (3D) quantum Hall system within a tight-binding lattice model using numerical Thouless conductance calculations. For the bulk, we confirm that the mobility edges are independent of the propagating directions in this anisotropic system. As disorder increases, the conductance peak of the lowest subband in the horizontal direction floats to the central subband as in the two-dimensional (2D) case, while there is no clear evidence of floating in the vertical direction. We thus conclude that for extended states, the longitudinal conductance in the vertical direction behaves like a quasi-one-dimensional (1D) normal metal, while the longitudinal conductance in the horizontal direction is controlled by layered conducting states stacked coherently. Inside the quantum Hall gap, we study the novel 2D chiral surface states at the sidewalls of the sample. We demonstrate the crossover of the surface states between the quasi-1D metal and insulator regimes, which can be achieved by modifying the interlayer hopping strength and the disorder strength in the model. The typical behaviors of the Thouless conductance and the wave functions of the surface states in these two regimes are investigated. Finally, in order to predict the regime of the surface states for arbitrary parameters, we determine an explicit relationship between the localization length of surface states and the microscopic parameters of the model.

The three-dimensional quenched random bond diluted $(J_1-J_2)$ quantum Heisenberg antiferromagnet is studied on a simple-cubic lattice. Using extensive stochastic series expansion quantum Monte Carlo simulations, we perform very long runs for an $L\times L\times L$ lattice up to $L=48$. By employing a standard finite-size scaling method, the numerical values of the Néel temperature are determined with high precision as a function of the coupling ratio $r=J_2/J_1$. Based on the estimated critical exponents, we find that the critical behavior of the considered model belongs to the pure classical three-dimensional $O\left(3\right)$ Heisenberg universality class.

The spin-wave dispersions in iron and nickel along the [111] direction are determined using soft x-ray resonant inelastic x-ray scattering (RIXS). For iron, a 10-nm thin film was studied and, over the limited $q$ range accessible, the peaks disperse as expected for a spin wave and in agreement with inelastic neutron scattering (INS) results. At the higher $q$ values damping is observed with the peaks weakening and broadening. This damping is less pronounced than in the INS studies. The RIXS results are also compared with ab initio spin fluctuation calculations. The calculations slightly underestimate the energy dispersion and the damping is larger than in the measurement. Nevertheless, the agreement between the RIXS results, INS studies, and the theory is quite satisfactory. For the single crystal of nickel, the measured $q$ dispersion flattens out rapidly and the peaks broaden. The strong damping effect is reproduced by the spin fluctuation calculations but the energy of the peaks is largely overestimated. Nevertheless, the flattening of the dispersion is not reproduced by the calculations and, although similar effects were observed in early INS experiments, they are not seen in more recent work. Possible reasons for this are discussed. These measurements show that using soft x-ray RIXS to study spin fluctuations in metallic systems, which are in general very challenging for the technique, has much promise. More interestingly, since the iron measurements were performed on a 10-nm thin film, the study opens the possibility to study tailor-made thin-film samples, which cannot be easily studied by other techniques. Combining these studies with state-of-the-art ab initio calculations opens up interesting prospects for testing our understanding of spin waves in metallic systems.

Metasurfaces, the two-dimensional analogs of metamaterials, are ideal platforms for sensing molecular chirality at the nanoscale, e.g., of inclusions of natural optically active molecules, as they offer large accessible surfaces and can provide the necessary strong resonances for coupling the probing radiation with the chiral inclusions. Here, by employing a less familiar but more convenient formalism, we examine chiral inclusions in achiral isotropic metasurfaces; the latter sustain the electric and magnetic resonant dipoles to enhance the chirality features. We derive analytically, and verify numerically, expressions that provide insight to the enhancement mechanism of the magnetoelectric coupling and explain why circular dichroism signals (difference in absorption between left and right circularly polarized waves) can arise from both the real and the imaginary part of the chirality parameter $\kappa$, correcting thus existing misconceptions. Our analysis demonstrates distinct chiroptical signals where the contributions from both the real and imaginary part of $\kappa$ can be independently observed and, based on such measurements, we propose a scheme for the unambiguous determination of an unknown chirality.

We theoretically analyze the effect of the inversion symmetry breaking on the structure of the impurity molecular states in Weyl metals. We show that for the case of a highly noncentrosymmetric Weyl metallic host, the standard picture of the alternating bonding and antibonding orbitals breaks down, and a qualitatively different frustrated atomic state emerges. This is a consequence of the pseudogap closing and related delicate Fano interplay between intra- and interimpurity scattering channels.

Two-dimensional MXenes continue to receive much research attention owing to their versatility and predicted topological phase, which are yet to be fully explored. Here, we conduct a rigorous search on $M_2^{\prime }{M}^{″}{\mathrm{C}}_2$ $(M^{\prime }=\mathrm{V}, \mathrm{Nb}, \mathrm{or} \mathrm{Ta};M^{″}=\mathrm{Ti}, \mathrm{Zr}, \mathrm{or} \mathrm{Hf})$ with various surface terminations, $X_2$ $(X=\mathrm{F}, \mathrm{Cl}, \mathrm{Br}, \mathrm{I}, \mathrm{O}, \mathrm{H}, \mathrm{or} \mathrm{OH})$, using first-principles calculations. The majority of the systems exhibit the topological phase with semimetallic band structures. Most importantly, fluorinated MXenes, $M_2^{\prime }{M}^{″}{\mathrm{C}}_2{\mathrm{F}}_2$, are topological insulators. They possess sizable nontrivial band gaps from 34 to 318 meV using Heyd-Scuseria-Ernzerhof (HSE) hybrid functional calculations which are within the range capable of realizing quantum spin-Hall effects even at room temperature. Furthermore, the $d$ orbitals of $M^{\prime }$ and $M^{″}$ atoms mostly contribute to the spin-orbit coupling-induced band gaps. Selecting ${\mathrm{V}}_2\mathrm{Ti}{\mathrm{C}}_2{\mathrm{F}}_2$ as an exemplar, we demonstrate the presence of edge states, verifying the calculated $Z_2$ invariant, and reveal its robustness against tensile strain. Finally, we propose SiC(0001) as a candidate substrate for material realization as it can preserve the nontrivial band topology.

We propose a topological nodal-ring superconductor (TNRSC) by inducing superconductivity on a topological nodal-ring semimetal (NRSM). Such a TNRSC can map to a one-dimensional BDI class topological superconductor and host both $N_{\mathrm{BDI}}=1$ and 2 topological phases in the Brillouin zone. These two topological phases support one and two Majorana drumhead surface states, respectively. By virtue of these novel Majorana modes, we find (i) the presence of drumhead surface states can be identified inside the nodal ring, and the radius of the nodal ring can be accurately determined by the zero-bias conductance of a normal-metal (NM)/TNRSC junction; and (ii) the spin-polarized and correlated currents can be generated in the leads of a NM/TNRSC/NM junction. The conclusions are robust even for NRSMs with dispersive drumhead surface states, and they can also apply to the topological NRSM ${\mathrm{HgCr}}_2{\mathrm{Se}}_4$.

The design of two-dimensional superconductors has attracted great research interest owing to their wide application in nanoscale devices. Here, we combine first-principles calculations with structure searching technology to identify a unique stable hexagonal $h\text{−}{\mathrm{MnB}}_3$ monolayer, exhibiting a slightly higher energy with respect to the reported tetragonal $t\text{−}{\mathrm{MnB}}_3$. Interestingly, $h\text{−}{\mathrm{MnB}}_3$ contains two boron kagome layers sandwiched with Mn atoms. It exhibits metallic properties and has a superconducting transition temperature of 24.9 K, which is much higher than 2.9 K in $t\text{−}{\mathrm{MnB}}_3$. Its superconductivity mainly originates from the coupling between in-plane vibrational phonons of boron kagome layers and electrons of Mn atoms. $h\text{−}{\mathrm{MnB}}_3$ exhibits a tunable superconductivity, and reaches a maximum of 34 K at 2% tensile strain resulting from the softening in-plane modes of boron kagome layers. The Si (111) surface may be an ideal substrate for the growth of superconductive $h\text{−}{\mathrm{MnB}}_3$. The unique superconducting mechanism observed here could inspire the searching of more boron kagome based two-dimensional superconductors.

Neutron diffraction and magnetic susceptibility studies show that orthorhombic single-crystals of topological semimetals $\mathrm{Sr}\left({\mathrm{Mn}}_{0.9}{\mathrm{Cu}}_{0.1}\right){\mathrm{Sb}}_2$ and $\mathrm{Sr}\left({\mathrm{Mn}}_{0.9}{\mathrm{Zn}}_{0.1}\right){\mathrm{Sb}}_2$ undergo three-dimensional C-type antiferromagnetic (AFM) ordering of the ${\mathrm{Mn}}^{2+}$ moments at $T_N=200\pm 10$ and $210\pm 12$ K, respectively, significantly lower than that of the parent ${\mathrm{SrMnSb}}_2$ with $T_{\mathrm{N}}=297\pm 3$ K. Magnetization versus applied magnetic field (perpendicular to MnSb planes) below $T_{\mathrm{N}}$ exhibits slightly modified de Haas van Alphen oscillations for the Zn-doped crystal as compared to that of the parent compound. By contrast, the Cu-doped system does not show de Haas van Alphen magnetic oscillations, suggesting that either Cu substitution for Mn changes the electronic structure of the parent compound substantially, or that the Cu sites are strong scatterers of carriers that significantly shorten their mean free path thus diminishing the oscillations. Density functional theory (DFT) calculations including spin-orbit coupling predict the C-type AFM state for the parent, Cu-, and Zn-doped systems and identify the $a$-axis (i.e., perpendicular to the Mn layer) as the easy magnetization direction in the parent and 12.5% of Cu or Zn substitutions. In contrast, 25% of Cu content changes the easy magnetization to the $b$-axis (i.e., within the Mn layer). We find that the incorporation of Cu and Zn in ${\mathrm{SrMnSb}}_2$ tunes electronic bands near the Fermi level resulting in different band topology and semimetallicity. The parent and Zn-doped systems have coexistence of electron and hole pockets with opened Dirac cone around the Y-point whereas the Cu-doped system has dominant hole pockets around the Fermi level with a distorted Dirac cone. The tunable electronic structure may point out possibilities of rationalizing the experimentally observed de Haas van Alphen magnetic oscillations.

Influence of short-range four-fermion interactions on quadratic and cubic nodal-line fermion systems is studied by renormalization group theory. It is found that arbitrarily weak four-fermion interaction could drive quadratic or cubic nodal-line fermion system to a new phase. According to the initial conditions and value of fermion flavor, the system may appear three kinds of instabilities. First, quadratic or cubic nodal line is split into conventional nodal lines, thus the system becomes nodal-line semimetal. Second, finite excitonic gap is generated, and the system becomes an excitonic insulator. Third, the system is driven into superconducting phase. Thus quadratic and cubic nodal line fermion systems are rare strong correlated fermion systems in three dimensions under the influence of four-fermion interactions. These theoretical results may be verified in the candidates for quadratic and cubic nodal-line fermion systems.

Here we comprehensively investigate Landau levels, Hofstadter's butterfly, and transport properties of a semi-Dirac nanoribbon in a perpendicular magnetic field using a recently developed real-space implementation of the Kubo formula based on the kernel polynomial method. A Dirac ribbon is considered to compare and contrast our results for a semi-Dirac system. We find that with the Landau levels being nonequidistant from each other for the semi-Dirac case (which is true for a Dirac case as well), the flatness of the energy bands vanishes in the bulk and becomes dispersive for a semi-Dirac ribbon in contrast to a Dirac system. This feature is most discernible for intermediate values of the external field. We further compute the longitudinal $({\sigma }_{xx} \mathrm{and} {\sigma }_{yy})$ and the transverse or Hall $\left({\sigma }_{xy}\right)$ conductivities, where the Hall conductivity shows a familiar quantization, namely, ${\sigma }_{xy}\propto 2n$ (the factor of 2 includes the spin degeneracy), which is highly distinct from a Dirac system, such as graphene. We also observe anisotropic behavior in magnetotransport in a semi-Dirac ribbon owing to the dispersion anomalies in two different longitudinal directions. Our studies may have important ramifications for monolayer phosphorene.

Thin films of amorphous $\left(\mathrm{a}\right)\text{–}{\mathrm{TiO}}_2$ are ubiquitous as photocatalysts, protective coatings, photo-anodes, and in memory applications, where they are exposed to excess electrons and holes. We investigate trapping of excess electrons and holes in the bulk of pure amorphous titanium dioxide, $\mathrm{a}\text{–}{\mathrm{TiO}}_2$, using hybrid density-functional theory (h-DFT) calculations. Fifty 270-atom $\mathrm{a}\text{–}{\mathrm{TiO}}_2$ structures were produced using classical molecular dynamics and their geometries fully optimized using h-DFT simulations. They have the density, distribution of atomic coordination numbers, and radial pair-distribution functions in agreement with experiments. The calculated average $\mathrm{a}\text{–}{\mathrm{TiO}}_2$ band gap is $3.25\mathrm{eV}$ with no states splitting into the band gap. Trapping of excess electrons and holes in $\mathrm{a}\text{–}{\mathrm{TiO}}_2$ is predicted at precursor sites, such as elongated Ti–O bonds. Single electron and hole polarons have average trapping energies $\left(E_T\right)$ of $-0.4\mathrm{eV}$ and $-0.8\mathrm{eV}$, respectively. We also identify several types of electron and hole bipolaron states and discuss their stability. These results can be used for understanding the mechanisms of photo-catalysis and improving the performance of electronic devices employing $\mathrm{a}\text{–}{\mathrm{TiO}}_2$ films.

In layer-structured $\mathrm{S}{\mathrm{r}}_2\mathrm{Ir}{\mathrm{O}}_4$, strong crystal electric field and spin-orbit coupling result in an intriguing spin-orbit entangled $J_{\mathrm{eff}}=1/2$ state, resembling the spin $S=1/2$ state of high-temperature superconducting cuprates. Our study unravels the intricate relationship between the lattice and the pseudospin interactions using uniaxial strain. Applied along the [1 1 0] direction, a compressive strain does not induce any effect. In contrast, the strain along [1 0 0] triggers a dramatic detwinning of the magnetic domains bringing the system to a single domain at around 0.04% strain. The strain driven detwinning rate is temperature independent showing that it does not exhibit a spontaneous orthorhombic lattice distortion driven by the pseudo-Jahn-Teller effect.

In this work, we train neural networks to predict transport properties of a quasi-one-dimensional tight-binding model with disordered on-site energies. In the case where the on-site energies of all sites in the scattering region pick up values randomly and independently from a given interval (model I), it is found that the performance of the neural network depends strongly on the system size. For a small system size, the neural network can predict accurately the conductance at the Fermi energy. With an increase in the system size, the mean absolute error ($\mathrm{MAE}$) increases. This tendency persists under an increase in the number of training samples and the number of neurons in the neural network. The physical mechanism behind this phenomenon can be ascribed to the universal conductance fluctuation. To reduce the effective dimension of features fed into the neural network, we consider the case of substitutional doping where the impurities have a fixed on-site energy, random position distribution, and variable concentration (model II). It is found that even for a relatively large system size, the trained neural network in model II performs much better in predicting the conductance at the Fermi energy. When the prediction target is changed to the average conductance under a finite bias (average value of 10 conductances at energies near the Fermi energy), the $\mathrm{MAE}$ can be reduced by almost a half. The small fluctuation of the average conductance reduces further the prediction difficulty of the neural network. The trained neural network can predict quickly and accurately the disorder-averaged transport properties for model II.