We propose dipole and quadrupole indices for interacting insulators with point group symmetries. The proposed indices are defined in terms of many-body quantum multipole operators combined with the generator of the point group symmetry. Unlike the original multipole operators, these combined operators commute with the Hamiltonian under symmetry and therefore their eigenvalues are quantized. This enables a clear identification of nontrivial multipolar states. We calculate the multipole indices in representative models and show their effectiveness as order parameters. Furthermore, we demonstrate a bulk-boundary correspondence: a nonzero index implies the existence of edge/corner states under the point group symmetry.

Uranium ions in the sesquinitride α-${\mathrm{U}}_2{\mathrm{N}}_3$ occupy independent acentric and centrosymmetric sites according to conventional x-ray diffraction patterns [R. Troć, J. Solid State Chem. 13, 14 (1975)]. We submit that polar uranium multipoles in acentric sites are revealed in resonant x-ray diffraction data recently published by Lawrence Bright et al. [Phys. Rev. B 100, 134426 (2019)]. To this end, their diffraction data gathered with a primary x-ray energy in the vicinity of the uranium $M_4$ absorption edge are compared to symmetry-informed diffraction amplitudes calculated for the bixbyite α-${\mathrm{Mn}}_2{\mathrm{O}}_3$ lattice structure. Bragg spots forbidden in this lattice diffraction pattern appear to provide clear-cut evidence for high-order polar uranium multipoles.

In this paper, we examine the magnetoelectric response of Ising pyrochlores, focusing on both the ordered antiferromagnetic state and the frustrated ferromagnetic case known as “spin ice.” We employ a model which accounts for magnetoelastic effects by considering the interplay between oxygen distortions and superexchange magnetic interactions within pyrochlores. This, together with numerical simulations, provides a tool to make quantitative comparisons with experiments. Our main target is then to see how to extract relevant information from this simple model, and to explore its limitations. We obtain a direct estimation of quantities such as the electric dipole moment, the central oxygen displacement, and the effective magnetoelastic energy for the canonical spin-ice material ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. We also inquire about the possibility of using the electric dipole carried by magnetic monopoles to obtain a direct measure of their density. In each studied scenario the correlations between monopoles, induced by their number or by the magnetic background, render these findings less straightforward than initially anticipated. Furthermore, the coupling between electrical and magnetic degrees of freedom provides additional tools to investigate magnetic order in these systems. As an example of this we discuss the phase diagram of the antiferromagnetic pyrochlore under applied magnetic field along the [111] direction. We find an instance where the phase stability at nonzero temperatures is not dictated by the energy associated with different ground states but (akin to the phenomenon of “order by disorder”) is instead determined by their accessibility to thermal fluctuations.

We study theoretically cubic anisotropy of Zeeman splitting of a hole confined in a semiconductor nanocrystal. This anisotropy originates from three contributions: crystallographic cubically symmetric spin and kinetic energy terms in the bulk Luttinger Hamiltonian and the spatial wave function distribution in a cube-shaped nanocrystal. From symmetry considerations, an effective Zeeman Hamiltonian for the hole's lowest even state is introduced, containing a spherically symmetric and a cubically symmetric term. The values of these terms are calculated numerically for spherical and cube-shaped nanocrystals as functions of the Luttinger Hamiltonian parameters. We demonstrate that the cubic shape of the nanocrystal and the cubic anisotropy of hole kinetic energy (so-called valence band warping) significantly affect effective $g$ factors of hole states. In both cases, the effect comes from the cubic symmetry of the hole wave functions in a zero magnetic field. Estimations for the effective $g$ factor values in several semiconductors with zinc-blende crystal lattices are made. Possible experimental manifestations and potential methods for measuring of the cubic anisotropy of the hole Zeeman splitting are suggested.

Recently, an atomic-scale two-dimensional silicon carbide monolayer has been synthesized [Polley et al., Phys. Rev. Lett. 130, 076203 (2023)], which opens up new possibilities for developing next-generation electronic and optoelectronic devices. Our study predicts the pristine SiC monolayer to have an “indirect” band gap of 3.38 eV $(K\to M)$ and a “direct” band gap of 3.43 eV $(K\to K)$ calculated using the HSE06 functional. We performed a detailed investigation of the various possible defects (i.e., vacancies, foreign impurities, antisites, and their various combinations) on the structural stability, electronic, and optical properties of the SiC monolayer using a first-principles-based density-functional theory (DFT) and molecular dynamics (MD) simulations. A number of physical quantities, such as the formation energy, electronic band gap, and the effective masses of charge carriers, have been calculated. We report that the SiC monolayer has a very low formation energy of 0.57 eV and can be stabilized on TaC{111} film by performing the surface slab energy and interfacial adhesion energy calculations. Nitrogen doping is predicted to be the most favorable defect in silicon carbide monolayer due to its very low formation energy, indicating high thermodynamic stability. The analysis of the electronic band structure and the density of states shows that the additional impurity states are generated within the forbidden region in the presence of defects, leading to a significant reduction in the band gap. An interesting transition from semiconducting to metallic state is observed for ${\text{N}}_{\text{C}}$ and ${\text{Al}}_{\text{Si}}$ defective systems. For the pristine SiC monolayer, we find that the conduction band is nearly flat in the $M\to K$ direction, leading to a high effective mass of $3.48m_o$. A significant redshift in the absorption edge, as well as the occurrence of additional absorption peaks due to the defects, have been observed in the lower energy range of the spectrum. The calculated absorption spectra span over the visible and ultraviolet regions in the presence of defects, indicating that the defective SiC monolayers can have potential optoelectronic applications in the UV-visible region.

Negative piezoelectrics contract in the direction of an applied electric field, which is opposite to the behavior of normal piezoelectrics and rare in dielectric materials. The advent of low-dimensional ferroelectrics, with unconventional mechanisms of polarity, opens a fertile branch in the search for candidates with prominent negative piezoelectricity. Here, the distorted $\alpha$-Bi monolayer, a newly identified elementary ferroelectric with a puckered black-phosphorus-like structure [Gou et al., Nature (London) 617, 67 (2023)], is computationally studied, which manifests a large negative in-plane piezoelectricity (with $d_{33}\sim -26$ pC/N). Its negative piezoelectricity originates from its unique buckling ferroelectric mechanism, namely intercolumn sliding. Consequently, a moderate tensile strain can significantly reduce its ferroelectric switching energy barrier, while compressive strain can significantly enhance its prominent nonlinear optical response. The physical mechanism of in-plane negative piezoelectricity also applies to other elementary ferroelectric monolayers.

The interplay between different quantum phases plays an important role in strongly correlated systems such as high-$T_c$ cuprates, quantum spin systems, and ultracold atoms. In particular, the application of effective-field theory and renormalization group analysis suggests that the coexistence of density wave (DW) and superfluid (SF) orders can lead to a supersolid phase of ultracold bosons. Here we revisit the problem by considering weakly coupled wires, where we treat the intrawire interactions exactly via bosonization and interwire couplings using a mean-field theory which becomes asymptotically exact in the limit of high dimensionality. We obtain and solve the mean-field equations for the system near the self-dual point, where each wire has the Luttinger parameter $K=1$ and the interwire DW and SF coupling strengths are identical. This allows us to find explicit solutions for the possible supersolid order. An energy comparison between different possible solutions shows that the supersolid order is energetically unfavorable at zero temperature. This suggests that the density wave and superfluid phases are connected by a first-order transition near the self-dual point. We also discuss the relation between our work and the intertwining of charge density wave and superconducting orders in cuprates.

The Su-Schrieffer-Heeger (SSH) model is fundamental in topological insulators and relevant to understanding higher-order topological phases. This study explores the relationship between the $n$-dimensional SSH model and its $(n-1)$-dimensional counterpart, identifying a hierarchical structure in the Hamiltonian that allows us to solve an arbitrary $n$-dimensional SSH model analytically. By generalizing the bulk-edge correspondence principle to arbitrary dimensions in a higher-order fashion using the vectored Zak phase, we reveal a type of topological insulator called hierarchical topological insulators. In this hierarchical topological insulator, there exist intermediate-order topological interfacial states that are protected by subsymmetry and energy band topology in a partial Brillouin zone. Furthermore, we compare the $n$-dimensional SSH model with the Benalcazar-Bernevig-Hughes (BBH) model, another essential model in higher-order topological phases similar to the two-dimensional SSH model with an extra flux of $\pi$ in each plaque. We find that the BBH model is another example of hierarchical topological insulators.

The planar Hall effect (PHE) in topological materials has been a subject of great interest in recent years. Generally, it is understood to originate from the chiral anomaly (CA) induced charge pumping between doubly degenerate Weyl nodes. However, the occurrence of PHE in materials with positive and anisotropic orbital magnetoresistance has raised questions about the CA being the sole origin of this effect. Here, we report the PHE, magnetoresistance, and thermal transport properties (Seebeck and Nernst coefficients) of Ag intercalated ${\mathrm{PdTe}}_2$. We observe positive longitudinal magnetoresistance, linear field dependence of the amplitude of PHE, and a prolate pattern in the parametric plots. The planar Hall resistivity and anisotropic magnetoresistance fit well with the theoretical study of CA being the origin of PHE. So our observations are consistent with Weyl physics dominating the PHE in ${\mathrm{PdTe}}_2, {\mathrm{Cu}}_{0.05}{\mathrm{PdTe}}_2$, and ${\mathrm{Ag}}_{0.05}{\mathrm{PdTe}}_2$. We further support our data with a theoretical model that reproduces the qualitative experimental features. In addition, we calculate the Seebeck ($\mathit{S}$) and Nernst ($\nu$) coefficients for ${\mathrm{PdTe}}_2$ and Cu and Ag intercalated compounds. The estimated values of the Fermi energy for the Cu and Ag intercalated compounds are, respectively, 2 times and 3 times larger than that of ${\mathrm{PdTe}}_2$.

In this paper we explore the properties of a one-dimensional spin chain in the presence of chiral interactions, focusing on the system's transition to distinct chiral phases for various values of the chiral coupling. By employing the mean-field theory approximation we establish a connection between this chiral system and a Dirac particle in the curved spacetime of a black hole. Surprisingly, the black-hole horizon coincides with the interface between distinct chiral phases. We examine the chiral properties of the system for homogeneous couplings and in scenarios involving position-dependent couplings that correspond to black-hole geometries. To determine the significance of interactions in the chiral chain we employ bosonization techniques and derive the corresponding Luttinger liquid model. Furthermore, we investigate the classical version of the model to understand the impact of the chiral operator on the spins and gain insight into the observed chirality. Our findings shed light on the behavior of the spin chain under the influence of the chiral operator, elucidating the implications of chirality in various contexts, including black-hole physics.

Introducing quasiparticle anisotropy in graphene via uniaxial strain has a profound effect on the polarization charge density induced by external impurities, both Coulomb and short range. In particular, the charge distribution induced by a Coulomb impurity exhibits a power-law tail modulated by a strain-dependent admixture of angular harmonics. The appearance of distributed charge is in sharp contrast to the response in pristine or isotropic graphene, where for subcritical impurities the polarization charge is fully localized at the impurity position. It is also interesting to note that our results are obtained strictly at zero chemical potential, and the behavior is distinct from the familiar Friedel oscillations observed at finite chemical potential. We find that over a wide range of strain, the $d$-wave symmetry is dominant. The presence of Dirac cone tilt, relevant to some two-dimensional materials beyond graphene, can also substantially affect the induced charge distribution. Finally, we consider impurities with short-range potentials and study the effect of strain on the charge response. Our results were obtained in the continuum via perturbation theory valid for weak (subcritical) potentials and are supported by numerical lattice simulations based on density functional theory.

The quantum electrodynamics of particles constrained to move on a plane is not a fully dimensionally reduced theory because the gauge fields through which they interact live in higher dimensions. By constraining the gauge field to the surface of the bulk, we obtain a fully reduced planar Abelian Chern-Simons Higgs model that can describe the vortex dynamics and second-order superconducting-normal phase transitions in planar Chern-Simons superconductors. Dual analyses performed before and after dimensional reduction yield the same Lagrangian for describing the vortex dynamics, indicating the self-consistency of our reduced theory. Compared to ordinary $(2+1)$-dimensional electrodynamics, we obtain anomalous fermion statistical vortices, consistent with results considering boundary effects. An additional electric charge constraint and different Chern-Simons parameter constraints are also found, which may help define a self-dual conformal field theory. Our renormalization group analysis shows that the quantized critical exponent depends on the Chern-Simons parameter. Quench disorder can bring more stable fixed points with different dynamical critical exponents. If we dimensionally reduce to a curved surface, our theory can also be extended to curved spacetimes, where geometric flow will be introduced and compete with vortex flow.

We present results of investigations on the correlated nature of electronic states crossing the Fermi level in ${\mathrm{Pb}}_9\mathrm{Cu}{\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$ (also referred to as LK-99) obtained within the $\mathrm{DFT}+\mathrm{DMFT}$ approach. We found that the band structure in the vicinity of the Fermi level is formed by extremely narrow $\mathrm{Cu}d$ states and $p$ states of extra O weakly hybridized with each other. Coulomb correlations between $\mathrm{Cu}d$ electrons open the band gap between Cu $d_{xz}/d_{yz}$ and the extra-O $p$ states that form the top of the valence band. Our conclusion is that the extra-oxygen $p$ states play a significant role in the electronic properties and LK-99 cannot be mapped onto a two-band Hubbard model. We also conclude that doping with electrons will turn the stoichiometric ${\mathrm{Pb}}_9\mathrm{Cu}{\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$ into a metal, whereas the result of doping with holes is less certain.

Transverse spin, an intriguing aspect of spin angular momentum, has gained considerable attention in recent years. However, transverse spin is typically accompanied by longitudinal spin in electromagnetic fields. This work aims to generate a series of optical fields with pure transverse spin. We present analytical and numerical demonstrations showing that when multiple linearly polarized plane waves interfere in the same plane, the longitudinal spin vanishes, leaving only the transverse spin, which is perpendicular to both the wave propagation and the inhomogeneous field plane. This transverse spin is demonstrated to be related to the imaginary part of the complex Poynting momentum. Furthermore, we show that pure transverse spin is also observed in the interference of multiple Gaussian beams, offering practical applications in optical field preparation and enhancing our understanding of spin-related physics.

We study the scaling properties of entanglement entropy (EE) near the quantum critical points in interacting random antiferromagnetic (AFM) spin chains. Using density-matrix renormalization group, we compute the half-chain EE near the topological phase transition between the Haldane and random singlet phases in a disordered spin-1 chain. It is found to diverge logarithmically in system size with an effective central charge $c_{\mathrm{eff}}=1.17\left(4\right)$ at the quantum critical point (QCP). Moreover, a scaling analysis of EE yields the correlation length exponent $\nu =2.28\left(5\right)$. Our unbiased calculation establishes that the QCP is in the universality class of the infinite-randomness fixed point predicted by previous studies based on the strong disorder renormalization group technique. However, in the disordered spin-1/2 Majumdar-Ghosh chain, where a valence bond solid phase is unstable to disorder, the crossover length exponent obtained from a scaling analysis of EE disagrees with the expectation based on the Imry-Ma argument. We provide a possible explanation.

Superconductivity and ferroelectricity, representing two distinct forms of ordered states, are typically not found together in the same system, making it even more difficult to create a connection between them. Here, supported by first-principles calculations, we propose that Anderson-Blount's ferroelectriclike metal or, more accurately, a polar metal can manifest in electron-doped polar $Pca{2}_1 {\mathrm{HfO}}_2$. In this system, polar phonons and consequently the structural asymmetry are not affected by the presence of itinerant electrons. We find that an optical phonon, featuring atomic displacements orthogonal to the ferroelectric polarization direction, is strongly coupled to doped electrons and can acquire a pronounced electron-phonon coupling strength to activate conventional Bardeen-Cooper-Schrieffer superconductivity. The displacements of polar oxygen atoms in $Pca{2}_1 {\mathrm{HfO}}_2$ create a link between ferroelectricity and superconductivity, enabling a tunable superconducting temperature ranging from approximately 10 to 30 Kelvin. Owing to hafnia's compatibility with silicon, we suggest that the ${\mathrm{HfO}}_2$-based polar superconductor presents an opportunity to construct high-performing hybrid integrated systems utilizing switchable quantum states.

Su-Schrieffer-Heeger (SSH) chains are paradigmatic examples of one-dimensional topological insulators hosting zero-energy edge modes when the bulk of the system has a nonzero topological winding invariant. Recently, high-harmonic spectroscopy has been suggested as a tool for detecting the topological phase. Specifically, it has been shown that when the SSH chain is coupled to an external laser field of a frequency much smaller than the band gap, the emitted light at harmonic frequencies strongly differs between the trivial and the topological phase. However, it remains unclear whether various nontrivial topological phases—differing in the number of edge states—can also be distinguished by the high-harmonic generation (HHG). In this paper, we investigate this problem by studying an extended version of the SSH chain with extended-range hoppings, resulting in a topological model with different topological phases. We explicitly show that HHG spectra are a sensitive and suitable tool for distinguishing topological phases when there is more than one topological phase. We also propose a quantitative scheme based on tuning the filling of the system to precisely locate the number of edge modes in each topological phase of this chain.

We use semianalytic methods to model a periodic structure of plate-array cylinders (metacylinders), and derive several of the medium's effective material properties in the quasistatic limit. Subject to $s$-polarized [transverse-electric (TE)] light, the anisotropic dispersion of the crystal manifests as a Maxwell Garnett equation for the effective permittivity at leading order. This is performed both for the case of no material contrast between interior and exterior regions, and a nonunity normalized refractive index. In each case, the leading order effective permittivity is a function of the difference between Bloch wave and plate-array angles. As such, we envisage the metamaterial as being mechanically tunable through uniform mechanical rotation of the constituent metacylinders.

We systematically demonstrate the temperature-dependent thermal transport properties in crystalline ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ via first-principles density functional theory informed linearized Boltzmann transport equation. The investigation, covering a wide temperature range (30–600 K), reports the emergence of an unusual optical-phonon-dominated thermal transport in crystalline ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$. Further, a significant contribution of four-phonon scattering is recorded which markedly alters the lattice thermal conductivity. Therefore, the combined effect of cubic and quartic phonon anharmonicity is seen to navigate the underlying physical mechanism and open up intriguing phononic interactions in ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ at high temperature. Irrespective of three- and four-phonon processes, umklapp is seen to prevail over normal scattering events. Consequently, four-phonon scattering is found to notably reduce the lattice thermal conductivity of ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ to $28\%$ at room temperature and $42\%$ at higher temperature. This quartic anharmonicity further manifests in the breakdown of $T^{-1}$ scaling of thermal conductivity and challenges the idea of a universal lower bound to phononic thermal diffusivity at high temperature. The faster decay of thermal diffusivity compared to $T^{-1}$ is rationalized encompassing the quartic anharmonicity via a modified timescale. These results invoke better understanding and precision to the theoretical prediction of thermal transport properties of ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$. Concomitantly, this also triggers the possibility to explore the manifestations of the lower bound of thermal diffusivity in materials possessing pronounced four-phonon scattering.