Interlayer coupling plays a critical role in tuning the electronic structures and magnetic ground states of two-dimensional materials, influenced by the number of layers, interlayer distances, and stacking order. However, its effect on the orientation of the magnetic easy axis remains underexplored. In this study, we demonstrate that interlayer coupling can significantly alter the magnetic easy-axis orientation, as shown by the magnetic easy axis of monolayer $1T-\mathrm{Mn}{\mathrm{Se}}_2$ tilting 67° from the $z$ axis, while aligning with the $z$ axis in the bilayer. This change results from variations in orbital occupations near the Fermi level, particularly involving nonmetallic Se atoms. Contrary to the traditional focus on magnetic metal atoms, our findings reveal that Se orbitals play a key role in influencing the easy-axis orientation and topological Chern numbers. Furthermore, we validate our conclusions by changing stacking orders, introducing charge doping, applying in-plane biaxial strains, and substituting nonmetallic atoms. Our results highlight the pivotal role of interlayer coupling in tuning the magnetic properties of layered materials, with important implications for spintronic applications.

We introduce a geometrically frustrated classical Ising model, dubbed the “spin-vorticity model,” whose ground-state manifold is a classical spin liquid: a 2-form Coulomb phase. We study the thermodynamics of this model both analytically and numerically, exposing the presence of algebraically decaying correlations and an extensive ground-state entropy, and give a comprehensive account of its ground-state properties and excitations. Each classical ground state may be decomposed into collections of closed two-dimensional membranes, supporting fractionalized string excitations attached to the edges of open membranes. At finite temperature, the model can then be described as a gas of closed strings in a background of fluctuating membranes. The emergent gauge structure of this spin liquid is naturally placed in the language of 2-form electrodynamics, which describes one-dimensional charged strings coupled to a rank-2 antisymmetric gauge field. After establishing the classical spin-vorticity model, we consider perturbing it with quantum exchange interactions, deriving an effective “membrane exchange” model of the quantum dynamics, analogous to ring exchange in quantum spin ice. We demonstrate the existence of a Rokhsar-Kivelson point where the quantum ground state is an equal-weight superposition of all classical ground-state configurations, i.e., a quantum spin liquid. The quantum aspects of this spin liquid are exposed by mapping the membrane exchange model to a strongly coupled frustrated 2-form U(1) lattice gauge theory. We further demonstrate how to quantize the string excitations by coupling a 1-form string field to the 2-form U(1) gauge field, thus mapping a quantum spin model to a 2-form U(1) gauge-Higgs model. We discuss the stability of the gapless deconfined phase of this gauge theory and the possibility of realizing a class of quantum phases of matter: 2-form U(1) quantum spin liquids.

The localized holes generated from the substitution of lattice $\mathrm{T}{\mathrm{i}}^{4+}$ in titanium-based metal oxides for $\mathrm{A}{\mathrm{l}}^{3+}$ ions can deplete the excess electrons localized near oxygen vacancies $\left({\mathrm{V}}_{\mathrm{O}}\right)$, thereby suppressing $\mathrm{T}{\mathrm{i}}^{3+}$ recombination centers. Interestingly, despite the strongly localized features of the holes and excess electrons, the suppression is highly effective even when $\mathrm{A}{\mathrm{l}}^{3+}$ and ${\mathrm{V}}_{\mathrm{O}}$ are distantly separated in certain titanium-based metal oxides such as anatase ${\mathrm{TiO}}_2$. However, this unexpected effectiveness is poorly understood, since the underlying mechanism of suppressing the $\mathrm{T}{\mathrm{i}}^{3+}$ recombination center by Al doping remains elusive. To resolve this, taking ${\mathrm{TiO}}_2$ polymorphs as model systems, we have comprehensively studied the electronic structures of $\mathrm{Al}/{\mathrm{V}}_{\mathrm{O}}$-codoped ${\mathrm{TiO}}_2$ by combining density functional theory calculations with machine learning methods. The results indicate that the effective suppression of the $\mathrm{T}{\mathrm{i}}^{3+}$ recombination center observed in anatase ${\mathrm{TiO}}_2$ mainly originates from the strong $p\text{−}d$ coupling between $\text{Ti-}{t}_{2g}$ and $\mathrm{O}\text{−}{p}_{\pi }$ orbitals, which facilitates electron hopping from ${\mathrm{V}}_{\mathrm{O}}$ to distant holes. Furthermore, based on symmetry analysis, this $p\text{−}d$ coupling mechanism was generalized to Al-doped ${\mathrm{SrTiO}}_3$, as well as for comprehending the carrier dynamics of deeply trapped electrons in wide-bandgap metal oxides. Overall, the uncovered $p\text{−}d$ coupling mechanism provides a solid theoretical basis for improving photocatalytic performances of metal oxides by suppressing deep trap states.

We introduce the concept of “tetris chains,” which are linear arrays of four-site molecules that differ by their intermolecular hopping geometry. We investigate the fermionic symmetry-protected topological Haldane phase in these systems using Hubbard-type models. The topological phase diagrams can be understood via different competing limits and mechanisms: strong coupling $U\gg t$, weak coupling $U\ll t$, and the weak intermolecular hopping limit $t^{\prime }\ll t$. Our particular focus is on two tetris chains that are of experimental relevance. First, we show that a “Y-chain” of coarse-grained nanographene molecules (triangulenes) is robustly in the Haldane phase in the whole $t^{\prime }\text{−}U$ plane due to the cooperative nature of the three limits. Secondly, we study a near-homogeneous “${\mathrm{Y}}^{\prime }$-chain” that is closely related to the electronic model for poly(p-phenylene vinylene). In the latter case, the above mechanisms compete, but the Haldane phase manifests robustly and is stable when long-ranged Pariser-Parr-Popple interactions are added. The site-edged Hubbard ladder can also be viewed as a tetris chain, which gives a very general perspective on the emergence of its fermionic Haldane phase. Our numerical results are obtained by large-scale, SU(2)-symmetric tensor network calculations. We employ the density-matrix-renormalization group as well as the variational uniform matrix-product state (VUMPS) algorithms for finite and infinite systems, respectively. The numerics are supplemented by analytical calculations of the band-structure winding number.

We investigate the fractional quantum anomalous Hall (FQAH) effect in rhombohedral multilayer graphene (RnG) in the presence of a strong applied displacement field. We first introduce the interacting model of RnG, which includes the noninteracting continuum model and the many-body Coulomb interaction. We then discuss the integer quantum anomalous Hall (IQAH) effect in RnG and the role of the Hartree-Fock approach in understanding its appearance. Next, we explore the FQAH effect in RnG for $n=3-6$ using a combination of constrained Hartree-Fock and exact diagonalization methods. We characterize the stability of the FQAH phase by the size of the FQAH gap and find that RnG generally has a stable FQAH phase, although the required displacement field varies significantly among different $n$ values. Our work establishes the theoretical universality of both IQAH and FQAH in RnG.

This paper explores the topological properties of altermagnets, a class of collinear magnetic materials. We employ equivariant K-theory of magnetic groups and Hamiltonian models to formulate a robust $C_4^z\mathbb{T}$ topological invariant to classify 2D and 3D altermagnetic systems. Our findings demonstrate that the spin Chern number serves as a robust topological index, corresponding to the half-quantized Chern number of the divided Brillouin zone. This indicator enables the prediction of a topologically protected 2D altermagnetic insulators and 3D Weyl altermagnetic semimetals, highlighting the relationship between altermagnetism and topological phases. Furthermore, our results provide a pathway to the exploration of topological applications in $d$-wave altermagnetic materials.

Motivated by the recent development of the quantum twisting microscope, we formulate a theory of elastic momentum-resolved tunneling across a planar tunnel junction between a monolayer graphene layer situated on a tip and a twisting graphene-based sample. We elucidate features in the dependence of the tunnel current on bias and twist angle, which reflect the sample band structure and allow the tip to probe the momentum-and energy-resolved single-particle excitations of the sample. While the strongest features originate from the Fermi edge of the tip, we argue that features associated with the tip Dirac points provide a more immediate and precise map of the sample band structure. We specifically compute the low-temperature tunneling spectrum of magic-angle twisted bilayer graphene (MATBG) rotated relative to the tip by nearly commensurate angles, highlighting the potential of Dirac-point spectroscopy to measure single-particle spectral functions of flat bands along specific lines in reciprocal space. Furthermore, our analysis of tunneling matrix elements suggests a method to extract the ratio of the intrasublattice and intersublattice tunneling parameters $w_0/w_1$ of MATBG from the differential tunneling conductance. Finally, we discuss signatures of $C_{3z}$-symmetry breaking in the tunneling spectrum using strained MATBG as an example. Our work establishes a general theoretical framework for Dirac-point spectroscopy of flat-band systems using the quantum twisting microscope.

We demonstrate that a bianisotropic response associated with a broken mirror symmetry of a dielectric resonator allows opening a band gap in simple square lattice arrays of such resonators. Realizing the proposed system as an array of high-index ceramic resonators working at GHz frequencies, we numerically and experimentally demonstrate the presence of topological edge states at the interface between two domains with opposite orientations of the bianisotropic resonators, as well as at the boundary between a single domain and free space. For both cases, we experimentally characterize the dispersion of edge states, and we examine their propagation along sharp bends, their resilience to various types of geometrical defects, and a spin-momentum-locked unidirectional propagation in the case of circularly polarized excitation. Also, we develop a theoretical model based on a Green's function approach that describes the square lattice of resonators and features a quadratic degeneracies in the vicinity of $\mathrm{\Gamma }$ and $M$ high-symmetry points that are removed upon the introduction of bianisotropy, and apply this model to evaluate Berry curvature. The considered design extends possibilities in the construction of optical and microwave structures simultaneously featuring topological edge states at the interfaces between distinct resonator domains or a resonator domain and free space.

We theoretically study topological superconductivity in elongated planar Josephson junctions. In the presence of spin-orbit coupling and an in-plane magnetic field, the Josephson junction can enter the topological phase and host zero-energy Majorana bound states over a range of the superconducting phase difference centered around $\pi$, with the span of this range determined by the strength of the magnetic field. We demonstrate that the topological superconducting phase range can be greatly increased by elongation of the junction, which causes an amplification of the Zeeman-induced phase shift of Andreev bound states. We show that the appearance of trivial in-gap states that occurs in elongated junctions can prohibit the creation of Majorana modes, but it can be mitigated by further proximitization of the junction with additional superconducting contacts. The topological transition in this system can be probed by measurements of the critical current and we show that the elongation of the junction leads to a linear decrease of the transition critical magnetic field beneficial for experimental studies.

We study the nonequilibrium dynamics of the dissipative quantum East model via numerical tensor networks. We use matrix product states to represent evolution under quantum-jump unravellings for sizes beyond those accessible to exact diagonalization. This allows us to demonstrate that dynamical heterogeneity accompanies slow relaxation, in analogy with what is seen in classical glassy systems. Furthermore, using variational matrix product operators we (i) compute the spectral gap of the Lindbladian and show that glassiness is enhanced in the presence of weak quantum fluctuations compared to the pure classical case, and (ii) obtain the dynamical large deviations by calculating the leading eigenvector of the tilted Lindbladian and find clear evidence for a first-order active-inactive dynamical phase transition. We also show how to directly sample the rare quantum trajectories associated to the large deviations.

In the current work, we have performed multiscale structural analysis of a Pb-free sodium niobate-based smart system, i.e., $0.9{\mathrm{NaNbO}}_3-0.1{\mathrm{Ba}}_{0.9}{\mathrm{Ca}}_{0.1}{\mathrm{TiO}}_3$ (NN-10BCT) reported earlier for its high ferroelectric response. We have investigated the temperature-dependent evolution of crystal structure at long, medium, and short ranges using synchrotron x-ray diffraction (SXRD), Raman scattering, and pair distribution function(PDF) techniques in conjunction with dielectric studies. Temperature-dependent synchrotron x-ray diffraction data combined with dielectric analysis suggest two unique polymorphic phase boundaries (PPB) with two coexisting ferroelectric phases stable in the wide temperature ranges. These PPBs are stable in different regions viz. (i) cryogenic temperatures with coexisting R3c and $Pmc{2}_1$ phases (ii) vicinity of room temperatures with coexisting $Pmc{2}_1$ and Amm2 phases. In contrast to the conclusions drawn from SXRD, PDF reveals structures having lower symmetry (with coexisting Cc$+$ $Pmc{2}_1$ phases at 1.7 $\le r\le$ 20 Å) at short ranges for these PPBs. The presence of different long- and short-range symmetries (accommodating tilt-oriented ferroelectric phases) in the unique polymorphic phase boundaries makes them thermally stable and advantageous for technological applications.

Recent investigations have revealed a new phenomenon involving the transfer of charges between metallic as well as dielectric particles and the surfaces of photovoltaic crystals under illumination. Given its potential relevance to microfluidic and nanotrapping applications, understanding and controlling this phenomenon is of considerable interest. In this study, we examine the potential for manipulation of this charge transfer by customizing the induced electric field in terms of its strength and shape. In addition, we explore a method to mitigate this charging effect by introducing a thin layer between the crystal and the particle suspension. Specifically, we investigate the controlled trapping and repulsion of metallic micro-objects and nano-objects using a slowly increasing electric field induced by light in an iron-doped lithium niobate crystal. By employing structured light patterns with modulated amplitudes, we analyze the influence of shape and exposure of the light patterns on the dynamic movement of the particles. Our observations reveal two distinct regimes characterized by an initial attraction followed by repulsion. We present a model based on an electrical resistor-capacitor circuit that explains these two regimes and provides a good estimate of the temporal transition between them. These findings contribute to the advancement of controlled optoelectronic manipulation techniques for particles that utilize ferroelectric crystals.

Magnetic skyrmions, typically stabilized by the Dzyaloshinskii-Moriya interaction (DMI), are promising candidates as the information carriers for advanced spintronic applications. In conventional micromagnetic theory, formation and morphology of skyrmion are generally thought to be restricted by symmetries associated with specific point groups. Here, through symmetry analysis and first-principles-based spin Hamiltonian calculations, we demonstrate that even in systems with zero net DMI, local DMI contributions can result in energy gains that stabilize noncollinear skyrmionic states. Symmetry constraints on global DMI, for example, confirm that systems with $D_{3h}$ and $D_{3d}$ point group symmetries yield zero net DMI. We identify two two-dimensional magnets, ${\mathrm{Mn}}_2{\mathrm{AgTe}}_4$ and ${\mathrm{In}}_2{\mathrm{Cr}}_2{\mathrm{Te}}_5$, with $D_{3h}$ and $D_{3d}$ symmetries, respectively, where magnetic atoms exhibit $3m.$ site symmetry with their nearest neighbors. In these systems, local DMI stabilizes Néel-type skyrmions, forming a skyrmionic phase in ${\mathrm{Mn}}_2{\mathrm{AgTe}}_4$ and a metastable excitation state in ${\mathrm{In}}_2{\mathrm{Cr}}_2{\mathrm{Te}}_5$. This study expands the search for skyrmionic phases in materials with unconventional point group symmetries, enriching the landscape of skyrmionic systems.

Momentum dependent spin splitting in antiferromagnetic (AFM) crystals and the resultant phenomena, such as magneto-optical and Hall effects, have attracted considerable attention for potential spintronics applications. Here, based on symmetry analysis, we proposed that specific crystal symmetry breaking through an electric field in layered A-type AFM materials results in magneto-optical (MOE) and layer-polarized anomalous Hall effects (LP-AHE). We further validate this in representative A-type AFM bilayer $\mathrm{CrP}{X}_4$ $(X=\mathrm{S}\mathrm{and}\mathrm{Se})$ systems using first-principles calculations. The results demonstrate that the electric-field-induced magneto-optical effects in these bilayer systems are comparable to those of the ferromagnetic monolayer counterparts, and the spin-layer-locking character of A-type AFM gives rise to the LP-AHE. Overall, the electric field induces Zeeman-like spin splitting and the asymmetry-related spin-orbit coupling effect; the former is crucial for the manifestation of those phenomena, while the latter counts for the larger magnitude of MOE/LP-AHE. These highly tunable effects with gate voltage modulation not only offers an approach to detect and manipulate the layered AFM materials, but also expand the range of materials available for miniaturized low-dissipative spintronics based on two-dimensional antiferromagnets.

The Kitaev magnets with bond-dependent interactions have garnered considerable attention in recent years for their ability to harbor exotic phases and nontrivial excitations. The topological magnons, which are indicated by a nonzero Chern number that can enhance the thermal Hall conductivity, are proposed to partially explain thermal Hall measurements in real materials. Hitherto, topological magnons have been extensively explored when the magnetic field is normal to the honeycomb plane, but their topological characteristics are less studied in the presence of in-plane magnetic field. Here, we study two distinct in-plane field induced spin-flop phases in the $\mathrm{\Gamma }\text{−}{\mathrm{\Gamma }}^{\prime }$ model, both of which are off-diagonal couplings that have intimate relation to the Kitaev interaction. The two spin-flop phases are distinguished by their out-of-plane spin components which can be either antiparallel or parallel, thus dubbing antiferromagnetic (AFM) or ferromagnetic (FM) spin-flop phases, respectively. We map out topological phase diagrams for both phases, revealing a rich pattern of the Chern number over exchange parameters and magnetic field. We analytically calculate the boundaries of topological phase transitions when the magnetic field is along the $a$ and $b$ directions. We find that the thermal Hall conductivity and its derivative display contrasting behaviors when crossing different topological phase transitions. The striking difference of the two phases lies in that when the magnetic field is along the $b$ direction, topological magnons are totally absent in the AFM spin-flop phase, while they can survive in the FM analog in certain parameter regions.

We report high-pressure Raman spectra and resistance measurements of black arsenic (b-As) up to 58 GPa, along with phonon density of states and enthalpy calculations for four reported arsenic phases up to 50 GPa. It is found that metastable b-As transforms into gray arsenic (g-As) phase at a critical pressure of 1.51 GPa, followed by subsequent transitions to simple cubic arsenic (c-As) and incommensurate host-guest arsenic (hg-As) phases at 25.9 and 44.8 GPa, respectively. Superconductivity emerges above 25 GPa in the c-As phase, with the superconducting transition temperature ($T_c$) remaining nearly a constant of 3 K. On further compression, $T_c$ steeply increases to a higher value around 4.5 K in the incommensurate hg-As phase above 43 GPa. We use our results to update the structural and superconducting phase diagrams under pressure for the novel semiconductor, black arsenic.

Topological boundary state is the hallmark feature of topological physics. Recently, non-Hermicity was found to dramatically expand the scope of topological physics, and provides an exotic strategy to manipulate the topological boundary states. Here, we realize the non-Hermitian winding and braiding of topological edge states in electric circuits. The topological edge states originate from the nontrivial bulk polarization. The twisted winding of a topological edge band and the ensuing bipolar hybrid skin-topological effect, and the Hopf link and Solomon link braidings between two topological edge bands, are visualized by measuring the admittances in circuit experiments. Our findings deepen the insight into the interaction between the Hermitian and non-Hermitian topologies, and inspire a mechanism in topological boundary wave manipulation.

We investigate a gapped two-dimensional nodal-line semimetal subjected to a perpendicular magnetic field. We identify an unusual pattern for Landau levels, where the energy of Landau levels first decreases and then starts increasing versus the level index. These descending/ascending Landau levels form a stretched checkmark shape. Tuning the magnitude of the magnetic field changes the spacing between Landau levels. At fixed chemical potential in the low-doped regime, the Landau levels move below the chemical potential and get filled from one side, while they move out and get vacant from the other side. Using the Kubo formalism in the linear response theory, we analytically study a gapped nodal-line semimetal's longitudinal and Hall conductivities. In the dc limit, we observe that as the magnetic field is varied at a fixed chemical potential, the Chern number swings back and forth between two consecutive integer numbers, giving rise to bumpy Hall plateaus in a low-doped system. We also find that the longitudinal optical conductivity displays different series of the Shubnikov–de Haas oscillations, corresponding to interband and intraband transition among the descending and ascending sets of the Landau levels.