The stripe phase, an intertwined order observed in high-temperature superconductors, is regarded as playing a key role in elucidating the underlying mechanism of superconductivity, especially in cuprates. Following Zaanen's early scenario [J. Zaanen, Phys. Rev. Lett. 84, 753 (2000); J. Zaanen et al., Philos. Mag. B 81, 1485 (2001)], the filled charge stripe, with one hole per unit cell of the charge order, can be taken as the interactive elastic quantum strings of holes, stabilized by $\pi$-phase shifts between neighboring magnetic domains. However, this scenario is challenging to explain, particularly in terms of electron pairing, which necessitates hole pairs. In this paper, we propose an effective model for describing the stripe phase in the hole-doped $t-J_z$ model. With respect to the antiferromagnetic background, the model comprises three types of color-labeled point defects coupling to an effective spin field, so-called colored string. Comparing with numerical results from large-scale density matrix renormalization group simulations, we find semiquantitative agreement in local hole density, magnetic moment, and the proposed spectrum features of the effective spin field. By systematically analyzing the hole-density distribution and the scaling of ground-state energy at different system sizes, we determine the effective core radius and the effective hopping amplitude of the quantum string. Furthermore, the local pinning field can be finely adjusted to drag the quantum string, offering a potential method for detecting it in optical lattices. Lastly, we further demonstrate the partially filled stripe with less than one hole per unit cell of the charge order can also be well described by the effective theory.

We perform first-principles electron-phonon interaction (EPI) calculations based on many-body perturbation theory to study the temperature-dependent band-gap and charge-carrier transport properties for ${\mathrm{Mg}}_2\mathrm{Si}$ and ${\mathrm{Ca}}_2\mathrm{Si}$ using the Boltzmann transport equation (BTE) under different relaxation-time approximations (RTAs). For a PBE band gap of $\sim 0.21$ (0.56) eV in ${\mathrm{Mg}}_2\mathrm{Si}$ (${\mathrm{Ca}}_2\mathrm{Si}$), a zero-point renormalization correction of $\sim 29–33$ (37–51) meV is obtained using various approaches, while the gap at 300 K is $\sim 0.15–0.154$ (0.46–0.5) eV. The electron mobility (${\mu }_e$), with a detailed convergence study at 300 K, is evaluated using linearized (self-energy and momentum RTA, or SERTA and MRTA) and iterative BTE (IBTE) solutions. At 300 K, the ${\mu }_e$ values are $\sim 351$ (100), 573 (197), and 524 (163) ${\text{cm}}^2{\text{V}}^{-1}{\text{s}}^{-1}$ from SERTA, MRTA, and IBTE, respectively, for ${\mathrm{Mg}}_2\mathrm{Si}$ (${\mathrm{Ca}}_2\mathrm{Si}$). These respective values at 900 K decrease to $\sim 33$ (11), 48 (21), and 28 (11) ${\text{cm}}^2{\text{V}}^{-1}{\text{s}}^{-1}$. SERTA (MRTA) provides results in better agreement with IBTE at higher (lower) temperatures, while SERTA-derived ${\mu }_e$ closely matches experimental ${\mu }_e$ values for ${\mathrm{Mg}}_2\mathrm{Si}$. All electrical parameters related to thermoelectrics are significantly influenced by the choice of RTA, with SERTA and MRTA yielding improved agreement with experimental results compared to constant RTA (CRTA) for ${\mathrm{Mg}}_2\mathrm{Si}$. Finally, we obtain the figure of merit under various modeling conditions, in which several promising strategies such as nanostructuring (phonon-boundary scattering) and mass-difference scattering are employed to suppress the lattice thermal conductivity computed within phonon-phonon interactions. This study clearly identifies the critical role of different scattering mechanisms (mainly EPI) in accurate transport predictions of thermoelectric silicides.

We apply SU(4)-symmetric model to examine possible ordered states in AB-stacked bilayer graphene (AB-BLG). The Hamiltonian of the system possesses this symmetry under certain assumptions. In such a model the multicomponent order parameter can be presented as a $4\times 4$ matrix $\widehat{Q}$. Using a mean-field approximation, we derive a self-consistency equation for $\widehat{Q}$. Among possible solutions of the obtained equation there are anomalous quantum Hall states, spin, charge, spin-valley density waves, interlayer excitonic phases, and their combinations. We argue that the proposed approach is a useful tool for classification of the ordered states in AB-BLG. The ordered states of the SU(4)-symmetric model demonstrate extensive degeneracies. The degeneracies can be removed by taking into account the neglected non-SU(4)-symmetric terms, disorder, substrate, as well as other perturbations. The ordered states have varying sensitivity to these factors. This suggests that, for AB-BLG, a ground-state ordering type is a nonuniversal property, susceptible to particulars of extrinsic conditions.

Within the Gross-Pitaevskii framework, we reveal the emergence of a crystallized phase of an exciton condensate in an atomically thin anisotropic semiconductor, where screening of exciton-exciton interactions is introduced by a proximal doped graphene layer. While such screened interactions are expected to yield a hexagonal crystal lattice in the excitonic condensate in isotropic semiconductor quantum wells [see, e.g., M. Matuszewski et al., Phys. Rev. Lett. 108, 060401 (2012)], here, we show that, for atomically thin semiconductors with strong electronic anisotropy, such as few-layer black phosphorus, the crystallized exciton phase acquires a parallel stripe structure. The optimal conditions for the emergence of this phase as well as its coexistence with excitonic superfluidity in a striped supersolid phase are identified.

A highly geometrically frustrated lattice structure such as a distorted kagome (or quasikagome) structure enriches physical phenomena through coupling with the electronic structure, topology, and magnetism. Recently, it has been reported that an intermetallic HoAgGe exhibits two distinct magnetic structures with the finite magnetic vector $\mathit{q}=(1/3,1/3,0)$: One is the partially ordered state in the intermediate-temperature region, and the other is the kagome spin ice state in the lowest-temperature region. We theoretically elucidate that the former is characterized by antiferrotoroidal ordering, while the latter is characterized by ferritoroidal ordering based on the multipole representation theory, which provides an opposite interpretation to previous studies. We also show how antiferrotoroidal and ferritoroidal orderings are microscopically formed by quantifying the magnetic toroidal moment activated in a multiorbital system. As a result, we find that the degree of distortion for the kagome structure plays a significant role in determining the nature of antiferrotoroidal and ferritoroidal orderings, which brings about the crossover between the antiferro-type and the ferri-type distributions of the magnetic toroidal dipole. We confirm such a tendency by evaluating the linear magnetoelectric effect. Our analysis can be applied irrespective of lattice structures and magnetic vectors without annoying the cluster origin.

The topological characteristics of Bi and its alloys with Sb have fueled intense debate since the prediction of three-dimensional topological insulators. However, a definitive resolution has not been reached to date. Here, we provide theoretical evidence that surface relaxation conceals the underlying bulk topology of pure Bi. Using density-functional-theory calculations for thin Bi(111) films (up to 17 bilayers), we first demonstrate a substantial interbilayer expansion near the surface. Motivated by this finding, we extend our analysis to thick Bi(111) films (up to 250 bilayers) incorporating relaxation layers, within the framework of a empirical tight-binding model with spin-orbit coupling. Our results reveal that these relaxation layers topologically block the emergence of a surface state and significantly suppress the one-particle spectrum of surface states at the $\overline{M}$ point, thereby obscuring the experimental identification of Bi's topological properties. This phenomenon, which we term “topological blocking,” provides crucial insights into the long-standing difficulty of observing surface states of Bi(111) at the $\overline{M}$ point. Furthermore, it establishes a framework for understanding and predicting the topological behavior in systems where surface relaxation disrupts the bulk-edge correspondence.

Semiconductor SnS with excellent physical properties has attracted wide attention due to its nontoxicity and abundance in the earth. SnS crystallizes in an orthorhombic structure (Pnma) at ambient conditions. Its unit cell comprises double layers stacked with weak van der Waals–like coupling, rendering it sensitive to high temperature ($T$) and high pressure ($P$) conditions. Here we experimentally demonstrate that SnS undergoes two phase transitions under high pressure by in situ x-ray diffraction and Raman spectroscopy. The Pnma SnS transforms into the Cmcm phase above 22.4 GPa, and a CsCl-type structure ($\mathit{Pm}\overline{3}m$) emerges at around 43.2 GPa, coexisting with the Cmcm phase up to about 66 GPa. SnS completely transforms into the $\mathit{Pm}\overline{3}m$ phase by 67.9 GPa. Theoretical calculations are performed to elucidate the structural characteristics of the high pressure Cmcm phase. Optical absorption and electrical transport experiments confirm that high pressure can reduce the band gap of SnS, leading to metallization. Additionally, the $P-T$ phase diagram of SnS has been investigated by in situ Raman spectroscopy. The Pnma to Cmcm phase transition boundary of SnS at high $P-T$ conditions is depicted experimentally. The effects of high temperature and high pressure on crystal structure, and optical and electrical properties of SnS are reversible upon returning to ambient conditions. Our research offers insights into the structures and physical properties of the group IV-VI monochalcogenides under extreme conditions and their potential applications in electronics and optoelectronics.

The ${\mathrm{A}}_2{\mathrm{A}}^{\prime }{\mathrm{B}}_2{\mathrm{O}}_7$-type two-layered Ruddlesden-Popper perovskite oxides as a novel class of ferroelectrics, i.e., hybrid improper ferroelectric (HIF) compounds, have recently been receiving increasing attention. However, the low stability of the ferroelectric state against elevated strain, along with the small spontaneous electric polarization ($P$), remains a major challenge for practical applications. Taking the HIF compound $\mathrm{}{\mathrm{Sr}}_3{\mathrm{Zr}}_2{\mathrm{O}}_7$ as an example, it was revealed in literature that the ferroelectric ground state will lose its stability by structural transition into nonpolar phases upon an epitaxial strain as small as ε∼±2%. The measured polarization in the polycrystalline state is only $P$∼0.30 $\mu \mathrm{C}/\mathrm{c}{\mathrm{m}}^2$ and the predicted maximal $P$ is ∼6.75 $\mu \mathrm{C}/\mathrm{c}{\mathrm{m}}^2$, which are insufficient for practical application. In this work, we address this issue numerically by employing first-principles calculations to explore the possibility to enhance the ferroelectric stability and polarization of $\mathrm{}{\mathrm{Sr}}_3{\mathrm{Zr}}_2{\mathrm{O}}_7$ via effective site-selective isovalent substitutions on the Sr site by a smaller Ca ion. Under a proper substitution scheme, the polar $A{2}_{1}am$ ground state becomes further stabilized relative to the competing nonpolar Pnab phase, and the ground-state polarization can be doubled, while the estimated coercive field slightly increases. Simultaneously, the polar-to-nonpolar transition would not occur unless an unrealistically large strain is imposed. It is thus suggested that a site-selective isovalent substitution scheme would be a valuable way to improve the ferroelectric stability against mechanical fluctuations.

We propose a scenario for superconductivity at strong electron-electron attractive interaction, in the case when the increase of the interaction strength promotes the nucleation of the local Cooper pairs and forms a state with a spatially phase incoherent Cooper pair order parameter. We show that this state can be characterized by a pseudogap which is determined by the electron scattering by phase fluctuations. At low temperatures, however, long-range correlations between the regions with different phases become important and establish global phase coherence and hence superconductivity in the system. We develop a mean-field theory to describe a phase transition between the preformed Cooper pair and superconducting states. This scenario of superconductivity applies not only to conductors with parabolic bands but also to the flat-band systems in which flat and dispersive bands coexist and are responsible for the formation of Cooper pairs as well as their phase synchronization.

The physical nature of doped Mott insulators has been the subject of intensive study for decades. The single-band Hubbard model and the $t\text{−}J$ model on a bipartite lattice are widely recognized as the simplest models to describe these materials. However, the key mechanism of superconductivity in these toy models remains unclear. Here we propose a novel mechanism for the ($d+id$)-wave superconductivity (SC) that occurs in the small-doping region of the honeycomb lattice $t\text{−}J$ model based on the Grassmann tensor product state numerical simulation and spin-charge separation formulation. In the presence of anti-ferromagnetic order near half-filling, we develop a continuum effective field theory for holons, which reveals the competition between repulsive and attractive holon interactions induced by spinon fluctuations and gauge fluctuations, respectively. When $t/J$ is large, the repulsive interaction dominates, leading to a non-Fermi liquid behavior; while in a moderate range of $t/J$, the attractive interaction dominates, leading to the SC order. Potential theoretical and experimental methods to validate the mechanism are discussed.

Flat-band zero-energy surface states of nodal $p$-wave superconductors give rise to striking electromagnetic anomalies, reflecting their high degree of degeneracy at the Fermi level. However, experimental investigations of these states have been limited because of the scarcity of materials exhibiting intrinsic $p$-wave superconductivity. In this paper, we demonstrate that surface flat bands can emerge in a hybrid system consisting of a conventional superconductor and a $p$-wave magnet, a recently proposed class of unconventional magnets that possess a unique composite symmetry, the $\left[C_{2\perp }\right|\left|\mathit{t}\right]$ symmetry. The degeneracy of the flat-band zero-energy surface states is protected by chiral symmetry from the BDI symmetry class, which originates from the $\left[C_{2\perp }\right|\left|\mathit{t}\right]$ symmetry of the $p$-wave magnet. In addition, we predict the robust appearance of a zero-bias conductance peak in a dirty normal-metal–superconductor junction containing a $p$-wave magnet, which serves as an unambiguous signature of anomalous proximity effects associated with the surface flat bands.

We define an infinite class of “frustration-free” interacting lattice quantum Hamiltonians for bosons, constructed such that their exact ground states have a density distribution specified by the Boltzmann weight of a corresponding classical lattice gas problem. By appropriately choosing the classical weights, we obtain boson representations of various known solvable models, including quantum dimer and vertex models, toric code, and certain Levin-Wen string-net models. We also systematically construct solvable models with other interesting ground states, including quantum spin liquids, supersolids, “Bose-Einstein insulators,” Bose liquids with “Bose surfaces,” and Bose-Einstein condensates that permit adiabatic evolution from a noninteracting limit to a Gutzwiller-projected limit.

We introduce a numerical method to study the critical properties of the XY model close to the ferromagnet to paramagnet phase transition. Our method applies ideas of the tensor renormalization group to obtain an improved action. This improved action allows the extraction of universal critical properties through Monte Carlo simulations on relatively small system sizes. We demonstrate the effectiveness of this method on the XY model in three dimensions.

Vacancy defects in isotropic noncollinear antiferromagnets produce long-range spin textures. By developing a magnetic elasticity theory, we demonstrate that a vacancy-induced readjustment in the spin configuration decays algebraically with distance. The power-law exponent depends on the multipole moment of a local spin deformation, which in turn is determined by the lattice symmetry and an equilibrium spin configuration in the absence of defects. The role of these two factors is highlighted for the $J_1$–$J_2$ Heisenberg model on a kagome lattice. A vacancy in this model generates spin deformations that decay as $1/r^2$ for the $q=0$ ground state and as a $1/r$ for the $\sqrt{3}\times \sqrt{3}$ magnetic structure. The analytic conclusions are confirmed by extensive numerical simulations. We also compute the fractional magnetic moments associated with vacancies and other lattice defects. Our results shed light on relative fragility of different magnetic structures with respect to spin glass formation at higher doping levels.

Ferrimagnetic materials provide unique opportunities for different technological applications such as spintronics through the interplay of ferro- and antiferromagnetic interactions. Particularly interesting is their dynamical behavior around the compensation temperature ($T_{\text{comp}}$), where the net magnetization vanishes and thus the ferromagneticlike behavior turns to the pure antiferromagnetic one. Due to the significance of this point, it is important to elucidate the temperature dependence of magnetic properties such as the exchange stiffness $A\left(T\right)$ and the anisotropy constant $K\left(T\right)$ in ferrimagnets. In this study, we use atomistic spin simulations to calculate the temperature dependence of these parameters in ferrimagnetic materials with and without the magnetization compensation point by varying the intersublattice antiferromagnetic exchange parameter. The exchange stiffness $A\left(T\right)$ is extracted from the domain wall width. We found that the domain wall width in ferrimagnetic materials increases with temperature more rapidly than in ferromagnetic materials and discuss its scaling with sublattice magnetizations. The temperature dependence of the anisotropy constant, $K\left(T\right)$, and the inverse attempt frequency are obtained by mapping Langevin dynamics simulations for switching time of a ferrimagnetic nanoparticle to the Arrhenius-Néel law. We found rapid fluctuations of total magnetization near the compensation point which drastically influences the switching probability. Our work deepens the understanding of the behavior of ferrimagnets in technologically relevant regimes (particularly near $T_{\text{comp}}$) and lays the groundwork for their more accurate multiscale modeling.

Controllable and efficient manipulation is always a key challenge for the application of topological magnetic textures in spintronic devices. By first-principles calculations and atomistic simulations, the present work reveals an exotic domain-wall pair in crescent shape, which possesses topology in one dimension and particle-like robustness in two dimensions. Its antiferromagnetic version is observed in the two-dimensional MnOI monolayer with a strong anisotropy, and the ferromagnetic version exists under an appropriate strain. Both of them can be driven efficiently by current to move in a straight line along a certain direction. Hereby, another possible path is provided to realize the application of topological magnetic texture in the next-generation high-speed spintronic devices.

Recently an apical oxygen atoms vibrations exchange mechanism of $d$-wave pairing in cuprates was proposed. The phonon mode in an insulating layer generates attraction of holes in metallic ${\mathrm{CuO}}_2$ plane with potential $V\left(k\right)\propto exp[-2k{d}_a]$, where $d_a$ is the distance to the apical plane. The pairing has a maximum at the crystallographic $\mathrm{\Gamma }$ point leading to $d$-wave channel. The idea is generalized here to include the ${\text{CuO}}_2$ breathing and half-breathing modes in a multilayer cuprate generating the pairing in an adjacent ${\text{CuO}}_2$ layer of the same multilayer. It is demonstrated that the phonon exchange and the spin fluctuation pairing constructively enhance each other since the paramagnon pairing peaks at crystallographic $M$ point. The phonon contribution explains the maximal critical temperature $T_c^{max}$ dependence on the number of layers $N$. It rises equidistantly by $15\text{K}$ from $N=1$ to $N=3$ and then saturates. The strength of the on-site Coulomb on site repulsion at optimal doping is to obtain the observed values of $T_c^{max}$ in the intermediate range of the effective on-site repulsion $U=(1.5-2)\text{eV}$, smaller than commonly used in purely in-plane (spin fluctuation) theory of high $T_c$ superconductivity.

Mott insulators based on $4d$ and $5d$ transition-metal ions, where spin-orbit interaction plays a key role, can exhibit various forms of unusual magnetism. A particular example is the antiferromagnet ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$ containing $d^4{\mathrm{Ru}}^{4+}$ ions. Here the spin-orbit interaction stabilizes the nonmagnetic $J=0$ singlet ionic ground state, which gets dynamically mixed, via exchange interactions, with low-energy $J=1$ ionic excitations. Thanks to a sufficient strength of the exchange, these excitations condense and a long-range order emerges. The resulting ordered moments are soft and prone to fluctuations of their effective length. The corresponding amplitude mode appears as a prominent magnetic excitation and complements the conventional magnons involving rotations of the moments. Motivated by this peculiar kind of magnetic order and the specific spectrum of magnetic excitations, we study their influence on the propagation of doped carriers. To this end, we construct a microscopic model including both $d^4$ and $d^5$ degrees of freedom and address the propagation of an injected electron by employing self-consistent Born approximation. We find that the electron shows a combination of both free and a polaronic type of motion, where the mobile carrier strongly interacts with an accompanying cloud of magnetic excitations. Remarkably, in the latter case it is the exotic excitation, the amplitude mode, that is found to dominate over the contribution of magnons. Our soft-spin situation thus largely contrasts with spin polarons widely discussed in the context of doped Heisenberg-type magnets based on rigid spin moments.

Dirac materials, hosting linearly dispersing quasiparticles at low energies, exhibit an emergent Lorentz symmetry close to a quantum critical point (QCP) separating a semimetallic state from a strongly coupled gapped insulator or superconductor. This feature appears quite robust even in open Dirac systems coupled to an environment, featuring non-Hermitian (NH) Dirac fermions: close to a strongly coupled QCP, a Yukawa-Lorentz symmetry emerges with a unique terminal velocity for both the fermion and the bosonic order-parameter fluctuations. The system can either retain non-Hermiticity or completely decouple from the environment, recovering Hermiticity as an emergent phenomenon. We show that such Yukawa-Lorentz symmetry emerges at quantum criticality even when the NH Dirac Hamiltonian includes a tilt term at the lattice scale. As demonstrated by a leading-order $\epsilon =3-d$ expansion near the $d=3$ upper critical dimension, a tilt term becomes irrelevant near the QCP separating the NH Dirac semimetal and a gapped (insulating or superconducting) phase. This behavior extends to linear-in-momentum nontilt perturbations, introducing velocity anisotropy for the Dirac quasiparticles, which also becomes irrelevant at the QCP. These predictions can be numerically tested in quantum Monte Carlo lattice simulations of NH Hubbard-like models hosting low-energy NH tilted Dirac fermions.