We investigate interacting Su-Schrieffer-Heeger (SSH) chains with two- and three-site unit cells using density matrix renormalization group (DMRG) simulations. By selecting appropriate filling fractions and sweeping across interaction strength $J_z$ and dimerization $\delta$, we map out their phase diagrams and identify transition lines via entanglement entropy and magnetization measurements. In the two-site model, we observe the emergence of an interaction-induced antiferromagnetic intermediate phase between the topologically trivial and nontrivial regimes, as well as a critical region at negative $J_z$ with suppressed magnetization and finite-size scaling of entanglement entropy. In contrast, the three-site model lacks an intermediate phase and exhibits asymmetric edge localization and antiferromagnetic ordering in both positive and negative $J_z$ regimes. We further examine the response of edge states to Ising perturbations. In the two-site model, zero-energy edge modes are topologically protected and remain robust up to a finite interaction strength. However, in the three-site model, where the edge states reside at finite energy, this protection breaks down. Despite this, the edge-localized nature of these states survives in the form of polarized modes whose spatial profiles reflect the noninteracting limit.

We study the entanglement and bipartite fluctuations of fractonic phases in a one-dimensional dipole-conserving Bose-Hubbard chain using the density matrix renormalization group method. We demonstrate that bipartite charge fluctuations fail to detect quantum phase transitions in fractonic systems. Instead, we introduce bipartite dipole fluctuations, ${\mathcal{F}}^d$, which exhibit scaling laws identical to the entanglement entropy $S$. For example, at integer filling $n=2$, both ${\mathcal{F}}^d$ and $S$ show logarithmic scaling in dipole Luttinger liquids and area-law scaling in dipole Mott insulators. Interestingly, in the dipole supersolid phase at noninteger filling $n=3/2$, we reveal that ${\mathcal{F}}^d$ and $S$ obey area laws despite the phase being compressible and hosting long-range dipole-dipole order. Moreover, we identify another phase at $n=3/2$, previously called the fractional Mott insulator phase, as a dipole-conserving charge density wave state. In this phase, ${\mathcal{F}}^d$ and $S$ follow area laws, but ${\mathcal{F}}^d$ exhibits an additional period-2 oscillation. These findings provide insights into the interplay between dipole conservation, quantum fluctuations, and entanglement in the fractonic phases.

The negatively charged boron vacancy center in two-dimensional (2D) hexagonal boron nitride has emerged as a promising quantum sensor. However, its sensitivity is constrained due to ubiquitous nuclear spins in the environment. The nuclear spins, hyperfine coupled with the central electron spin, effectively behave as magnetic field fluctuators, leading to rapid decoherence. Here, we explore the effectiveness of static magnetic field strength and orientation in realizing peculiar subspaces that can lead to enhanced spin coherence. Specifically, using detailed numerical simulations of the spin Hamiltonian, we identify specific field configurations that minimize energy gradients and, consequently, are expected to facilitate decoherence suppression. We also develop an approximate analytical model based on the perturbation theory that accurately predicts these low-gradient subspaces for magnetic fields aligned with the electron spin quantization axis, applicable not only to boron vacancies but to any spin-1 electronic system coupled to nearby nuclear spins. Furthermore, to stimulate experimental validation, we estimate coherence lifetimes as a function of various bias field configurations and demonstrate that significant decoherence suppression can indeed be achieved in certain regions. These findings and the developed methodology offer valuable insights for mitigating decoherence in a low-field regime.

Hexagonal ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ crystals consist of symmetric building blocks, in which Ge and Sb atoms are randomly distributed in two kinds of atomic layers with different compositions. Their physical properties are strongly influenced by the chemical disorder arising from both Ge/Sb intermixing and deviations from the perfect stoichiometry, which are responsible for the high $p$-type doping observed experimentally. We present a systematic first-principles study of the effects of chemical disorder on the structural, electronic, and transport properties of doped ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ crystals. Crystals with a Ge/Sb intermixing rate below 50% have a lower energy and are all expected to exist in the same samples, in accordance with experimental observations. The modification of their structural parameters, electronic band dispersion, and electronic conductivity is described as functions of the Ge/Sb intermixing rate and doping. In particular, we show that conductivity changes depend on a subtle balance between disorder-induced carrier scattering events and modifications of the carrier density, which themselves depend on Ge/Sb intermixing and on the nature and concentration of the point defects responsible for doping. Our results provide insight into the microscopic origins of the electronic properties of GeSbTe materials for phase change memories, whose microstructure contains hexagonal ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ grains.

We present a microscopic and fully quantized model to investigate the interaction between semiconductor nanostructures and quantum light fields including the many-body Coloumb interaction between photoexcited electrons and holes. Our approach describes the coupled dynamics of the quantum light field and single and double electron-hole pairs, i.e., excitons and biexcitons, and exactly accounts for Coulomb many-body correlations and carrier band dispersions. Using a straightforward yet exact approach, we study a one-dimensional two-band system interacting with a single-mode, two-photon quantum state within a Tavis-Cummings framework. By employing an exact coherent factorization scheme, the computational complexity is reduced significantly enabling numerical simulations. We also derive a simplified model that includes only the bound $1s$-exciton and biexciton states for comparison. Our simulations reveal distinct single- and two-photon Rabi oscillations, corresponding to photon-exciton and exciton-biexciton transitions. We demonstrate, in particular, that biexciton continuum states significantly modify the dynamics in a way that cannot be captured by simplified models that consider only bound states. Our findings emphasize the importance of a comprehensive microscopic modeling in order to accurately describe quantum optical phenomena of interacting electronic many-body systems.

Spin-momentum locking (SML) excitons in two-dimensional semiconductors are appealing to programmable optical control of spin-polarized carriers in ultrafast spintronics. To address the current thirsty for long-lived excitons with zero-external-field stability and room-temperature spin polarization, we predict the existence of intrinsically SML excitons in altermagnetic ${\mathrm{V}}_2{X}_2\mathrm{O}$ ($X=\mathrm{S}$, Se) driven by giant nonrelativistic spin splittings ($>1.2$ eV). First-principles calculations reveal SML excitons with binding energies exceeding 1400 meV in monolayers and 430 meV in their van der Waals heterobilayers, along with stacking-dependent optical selection rules for tunable interlayer excitons. These remarkable physical properties, combined with their long radiative lifetimes, strongly suggest the feasibility of SML excitons with robust spin polarization at room temperature. Our work introduces a paradigm for SML exciton physics via altermagnetism, opening possibilities for all-optical manipulation in advanced opto-spintronics.

Pseudospin models are proposed for the description of the phase transitions, dielectric characteristics, and polarization switching in two crystals of the phenyltetrazole family. One of them, APHTZ, is a canted ferroelectric, whereas the other, MPHTZ is a simple antiferroelectric. In APHTZ, the electric field, applied perpendicularly to the axis of spontaneous polarization, flips the polarization in one of the two sublattices, effectively rotating the nonzero net polarization by ${90}^{\circ }$ and switching the system between two different ferroelectric configurations. The temperature-electric field phase diagrams are constructed. The diagram topology appears to be typical for the Ising-like antiferroelectric systems.

Two-dimensional (2D) antiferromagnets hold great promise for application in next-generation computational devices. A critical challenge of the application of antiferromagnets lies in the detection of the Néel vector to enable an antiferromagnetic (AFM) state readout. Recently, a time-reversal-odd ($\mathcal{T}$-odd) second-harmonics generation (SHG) signal was experimentally discovered in 2D antiferromagnets. However, opposite Néel vectors generate identical SHG intensities without phase information, hindering magnetic domain discrimination. To address this problem, we propose to use a nonmagnetic substrate together with the antiferromagnet to form a heterojunction. This introduces $\mathcal{T}$-even SHG that interferes with the intrinsic $\mathcal{T}$-odd SHG of AFM materials, generating giant nonlinear magneto-optical (NLMO) effects that enable the detection of the Néel vector. Taking heterojunctions formed by antiferromagnetic bilayer ${\mathrm{CrBr}}_3$ and monolayer and bilayer ${\mathrm{MoS}}_2$ as examples, through symmetry analysis and first-principles calculations we reveal the mechanism of SHG responses and derive conditions to achieve a most notable NLMO effect under linearly and circularly polarized light. Theoretically, we find that the strict equality between the $\mathcal{T}$-even and $\mathcal{T}$-odd SHG is not necessary. Practically, we discover that the $\mathcal{T}$-even SHG originated from interlayer coupling interferes strongly with the $\mathcal{T}$-odd SHG from 2D antiferromagnets, demonstrating exceptional advantages for generating giant NLMO effects. Our work provides a unique strategy for probing AFM order and advances the development of ultrathin magnetic storage devices.

The Griffiths phase (GP), a state of magnetic disorder persisting above the Curie temperature $\left(T_C\right)$, is frequently observed in rare-earth and transition-metal oxides, often leading to anomalous quantum critical fluctuations near $T_C$. In this study, we investigate the ordered double perovskite ${\mathrm{Er}}_2{\mathrm{NiMnO}}_6$ (ENMO), uncovering similar critical instabilities through detailed magnetic, magnetocaloric, and heat capacity measurements and analysis. The derived critical exponents near the critical region, $T_C$ $[\alpha =-0.942(1),$ $\beta =1.081\left(8\right),$ $\gamma =0.765\left(6\right), \text{and} \delta =1.731\left(7\right)]$ deviate significantly from all known universality classes of magnetism, yet they satisfy the magnetic scaling equation of state. Complementary magnetocaloric effect (MCE) analysis confirms these critical exponents while revealing a substantial low-temperature magnetic entropy change and adiabatic temperature values ($-\mathrm{\Delta }{S}_{\text{max}}$ $\approx$ 15 J/kg K and $\mathrm{\Delta }{T}_{\text{ad}}$ $\approx$ 15 K for $\mathrm{\Delta }H=70$ kOe), further supported by heat capacity data. The anomalous critical behavior is attributed to quantum GP formation above $T_C$, consistent with predictions from both the Bray model and Yang-Lee zeros theory. Additionally, ENMO maintains a robust insulating character across the measured temperature range, well-described by polaron hopping mechanisms. These findings challenge conventional models of magnetic phase transitions in disordered systems, emphasizing the necessity for new theoretical frameworks to account for clustered-phase dynamics and the development of revised universality classes to explain such unconventional critical phenomena.

Altermagnets exhibit spin-split bands without net magnetization, making them attractive for spintronics. However, in most conventional altermagnets, local inversion symmetry of sublattice hinders the intrinsic electrical switching. In this work, we propose a design strategy to realize a distinct class of altermagnets: by deliberately breaking sublattice inversion symmetry, staggered Rashba-type spin-orbit fields with opposite signs emerge, producing asymmetric local torques that enable deterministic, field-free switching of the Néel vector. The resulting class of altermagnets features noncentrosymmetric sublattices connected by improper rotations, preserving the hallmark altermagnetic spin-split band structure while unlocking full electrical controllability. Symmetry analysis, tight-binding modeling, and linear response theory confirm this mechanism, establishing a general design principle for electrically controllable altermagnetic spintronics.

The superconducting behavior of transition-metal-embedded hexagonal boron-carbon (${\mathrm{B}}_2{\mathrm{C}}_2$) and boron-phosphorus (${\mathrm{B}}_2{\mathrm{P}}_2$) monolayers is systematically explored in both face-to-back (FB) and face-to-face (FF) stacking configurations. Embedding 3d and 4d transition metals into ${\mathrm{B}}_2{\mathrm{C}}_2$ and ${\mathrm{B}}_2{\mathrm{P}}_2$ frameworks induces robust metallicity, enabling superconductivity in these two-dimensional systems. Structural, dynamic, and energy stability are confirmed via formation energy analysis, phonon dispersion calculations, and ab initio molecular dynamics simulations, revealing several dynamically stable and nonmagnetic metallic phases: six $M\mathrm{BC}$ ($M=\mathrm{Sc}$, V, Y, Zr, Nb, Mo), seven $\mathrm{FF}\text{−}\mathrm{M}{\mathrm{B}}_2{\mathrm{C}}_2$, five $\mathrm{FB}\text{−}\mathrm{M}{\mathrm{B}}_2{\mathrm{P}}_2$, and eight $\mathrm{FF}\text{−}\mathrm{M}{\mathrm{B}}_2{\mathrm{P}}_2$ structures. By combining electron–phonon coupling analysis with the McMillan-Allen-Dynes formula and anisotropic Migdal–Eliashberg equations, we predict superconducting transition temperatures ($T_c$) of up to 71.0 K for $\mathrm{FF}\text{−}\mathrm{Cu}{\mathrm{B}}_2{\mathrm{C}}_2$—featuring a distinct two-gap signature—and 31.5 K for MoBC with a single-gap profile, attributed to σ-bonding states and van Hove singularities, respectively. In comparison, ${\mathrm{B}}_2{\mathrm{P}}_2$-based systems show lower $T_c$ values up to 27.1 K (e.g., $\mathrm{FF}\text{−}\mathrm{Zr}{\mathrm{B}}_2{\mathrm{P}}_2$), attributed to weaker bonding interactions. A comprehensive comparison of atomic composition (C vs P) and stacking geometry highlights the critical role of covalency and electronic topology in governing superconducting properties, offering valuable guidance for the design of $\mathrm{high}-T_c$ two-dimensional superconductors.

Information about the crystal structures in the range of morphotropic phase boundary of ferroelectric perovskite solid solutions is important for understanding their intricate properties, which result in wide opportunities for practical applications. However, for the $(1-x)\mathrm{Pb}\left(\mathrm{M}{\mathrm{g}}_{1/3}\mathrm{N}{\mathrm{b}}_{2/3}\right){\mathrm{O}}_3–x\mathrm{PbTi}{\mathrm{O}}_3$ solid solution system, this information is contradictory. Different composition-temperature phase diagrams have been reported for this system in literature based on the investigations of single crystals and ceramics using various experimental techniques. In this work, we apply polarized light microscopy (PLM), x-ray diffraction (XRD) and dielectric spectroscopy to study the crystal structure and phase transitions in the $0.68\mathrm{Pb}\left(\mathrm{M}{\mathrm{g}}_{1/3}\mathrm{N}{\mathrm{b}}_{2/3}\right){\mathrm{O}}_3–0.32\mathrm{PbTi}{\mathrm{O}}_3$ single crystal. We confirm the monoclinic ${\mathrm{M}}_{\mathrm{B}}$ symmetry (space group $\mathit{Cm}$) of the room-temperature phase. According to PLM, it transforms with increasing temperature into a triclinic (Tr) phase rather than the previously reported monoclinic ${\mathrm{M}}_{\mathrm{C}}$ or tetragonal phase. XRD data are consistent with the presence of Tr phase. The Tr phase transforms to the monoclinic ${\mathrm{M}}_{\mathrm{C}}$ ($Pm$) phase and then to the cubic phase. Ergodic relaxor behavior is observed above the Curie temperature. The unit cell in the ${\mathrm{M}}_{\mathrm{C}}$ phase is pseudotetragonal with the lattice parameters $a=b<c$ and a small monoclinic angle β. In the ${\mathrm{M}}_{\mathrm{B}}$ phase, the direction of spontaneous polarization is temperature independent and close to the $\langle 111\rangle$ pseudocubic direction. In the Tr and ${\mathrm{M}}_{\mathrm{C}}$ phases, it changes with temperature so that near the Curie point it is close to the [001] axis. No significant anomalies in the dielectric properties or changes in the domain structure are observed at the ${\mathrm{M}}_{\mathrm{B}}\to \mathrm{Tr}$ and $\mathrm{Tr}\to {\mathrm{M}}_{\mathrm{C}}$ phase transitions. The domain structure changes dramatically when the temperature varies within the Tr phase, causing a sharp change in birefringence.

We show how to construct Landau-like free-energy potentials using a machine learning approach. For concreteness, we focus on perovskite oxide ${\mathrm{PbTiO}}_3$, representative of a large class of materials that undergo nonreconstructive structural phase transitions; in this case, a proper ferroelectric transformation with improper ferroelastic features. We work with a training set obtained from Monte Carlo simulations based on an atomistic “second-principles” potential for ${\mathrm{PbTiO}}_3$. We rely exclusively on data that would be experimentally accessible—i.e., temperature-dependent polarization and strain, both with and without external electric fields and stresses applied—to explore scenarios where the training set could be obtained from laboratory measurements. We introduce a scheme that allows us to identify optimal polynomial models of the temperature-dependent free-energy surface, mapped as a function of the homogeneous electric polarization and homogeneous strain. Typically, our method evaluates thousands of possible models, ranking them by accuracy and predictive power. Our results for ${\mathrm{PbTiO}}_3$ show that a very simple polynomial—where only two parameters depend linearly on temperature—is sufficient to yield a correct description of the material's behavior. We thus validate the usual approximations made in phenomenological studies of phase transitions of this kind. Remarkably, the obtained models also capture the subtle couplings by which elastic strain controls key features of ferroelectricity in ${\mathrm{PbTiO}}_3$, such as the symmetry of the polar phase and the discontinuous character of the transition, despite the fact that no effort was made to include such information in the training set. We emphasize the distinctive aspects of our methodology (which relies on an original form of validation step) by comparing it with the usual machine learning approach for model construction. Our results illustrate how physically motivated models can have remarkable predictive power, even if they are derived from a limited amount of data. We argue that such “third-principles” models can be the basis for predictive macroscopic or mesoscopic simulations of ferroelectrics and other materials undergoing nonreconstructive structural transitions.

Linear magnetoresistance is a hallmark of three-dimensional (3D) Weyl metals in the quantum limit. Recently, a pronounced linear magnetoresistance has also been observed in 2D graphene [Xin et al., Nature (London) 616, 270 (2023)]. However, a comprehensive theoretical understanding remains elusive. By employing the self-consistent Born approximation, we derive the analytical expressions for the magnetoresistivity of 2D massless Dirac fermions in the quantum limit. Notably, our result recovers the minimum conductivity in the clean limit and reveals a linear dependence of resistivity on the magnetic field for Gaussian impurity potentials, in quantitative agreement with experiments. These findings shed light on the magnetoresistance behavior of 2D Dirac fermions under ultrahigh magnetic fields.