Using machine learning potential, we explore different types of domain walls in the recently unveiled single-element ferroelectric, the bismuth monolayer [Gou et al., Nature (London) 617, 67 (2023)]. Remarkably, our investigation reveals that the charged domain-wall configuration exhibits lower energy compared to the uncharged domain-wall structure. Using the machine learning Hamiltonian, we directly calculate the band structures for large domain-wall systems and demonstrate that the experimentally discovered tail-to-tail domain wall preserves topological interfacial states, which arise from the change in the $Z_2$ topological number between the ferroelectric and paraelectric phases. Our study suggests that domain walls in two-dimensional bismuth hold potential as a promising platform for the development of ferroelectric domain-wall devices.

We develop a theoretical formalism for time-dependent radiative heat flux from one object to another in the case where the former starts radiating at a certain time. The time dependence is demonstrated for the heat flux between two isolated nanoparticles. After one particle starts radiating, the emitted energy first reaches the other one with a delay according to electromagnetic retardation, and afterwards the flux exhibits oscillatory exponential relaxation to its stationary value. For the room- or higher-temperature radiation, the oscillation period and relaxation time are determined by the resonance frequency and damping rate of the particle polarizability, respectively, being equal to dozens of femtoseconds and one picosecond for silicon carbide particles. At cryogenic temperatures, the relaxation time depends on the thermal wavelength.

Scanning tunneling microscopy is the method of choice for characterizing charge density waves by imaging the variation in atomic-scale contrast of the surface. Due to the measurement principle of scanning tunneling microscopy, the electronic and lattice degrees of freedom are convoluted, making it difficult to disentangle a structural displacement from spatial variations in the electronic structure. In this work, we characterize the influence of the displacement of the surface-terminating Se atoms on the 3 × 3 charge density wave contrast in scanning probe microscopy images of $2H\text{−}{\mathrm{NbSe}}_2$. In scanning tunneling microscopy images, we observe the 3 × 3 charge density wave superstructure and atomic lattice at all probed tip-surface distances. In contrast, noncontact atomic force microscopy images show both periodicities only at small tip-surface distances while, unexpectedly, a 3 × 3 superstructure is present at larger tip-surface distances. Using density functional theory calculations, we qualitatively reproduce the experimental findings and indicate that the 3 × 3 superstructure at different tip-surface distances in noncontact atomic force microscopy images is a result from different underlying interactions. In addition, we show that the displacement of the surface-terminating Se atoms has a negligible influence on the contrast in scanning tunneling microscopy images. Our combined experimental and theoretical work presents a method on how to discriminate the influence of the surface corrugation from the variation of the charge density to the charge density wave contrast in scanning probe microscopy images, which can provide insights into the influence of structural disorder to a charge density wave ground state.

Understanding many-body interactions of excitons and charge carriers in monolayer semiconductors is crucial for tuning their unique optical properties and optimizing their performance in optoelectronic devices. However, the sensitivity of these atomically thin semiconductors to doping, defects, and strain–arising from synthesis, substrate, and environmental conditions–hinders consistent observation of many-body effects. In this work, we employed linear and ultrafast transient optical absorption spectroscopy to investigate the influence of background doping on exciton many-body interactions in $\mathrm{Mo}{\mathrm{S}}_2$ monolayers. Using reversible molecular physisorption gating, we achieved a high background doping density of $4.9\times {10}^{13}\mathrm{c}{\mathrm{m}}^{-2}$ in an argon environment, which is significantly higher than those attainable with conventional electrical gating. Our results reveal a photoinduced $A$-exciton resonance redshift, attributed to band-gap renormalization at a low background-doping density of $4.3\times {10}^{12}\mathrm{c}{\mathrm{m}}^{-2}$ in an air environment, transitioning to a blueshift at a high background-doping density of $4.9\times {10}^{13}\mathrm{c}{\mathrm{m}}^{-2}$ due to dominant Pauli blocking effects and vertical excitation shifts. We further observed transient energy splitting between free-exciton and -trion states up to 57 meV due to exciton-electron interactions. The ultrafast spectroscopy further revealed exciton and trion dynamics, including fast energy splitting of exciton and trion resonances within 1 picosecond (ps) followed by a rapid decay having a lifetime of ∼5.4 ps. Our results demonstrate the critical role of background-doping conditions in tuning many-body interactions and quasiparticle dynamics in 2D semiconductors, providing valuable insights for future device design and material engineering.

In this paper, we investigate the Casimir-Lifshitz free energy mechanism that governs both ice growth and melting near metal surfaces, with a particular focus on the role of oxidation. Our study reveals that metals such as gold, iron, and aluminum induce incomplete premelting, resulting in micron-sized liquid water layers when in contact with ice. These layers could have significant implications for the defrosting of metallic surfaces. When exposed to water vapor at the triple point, aluminum and other metals can induce the formation of notably thick layers of either liquid water or ice, which can theoretically become infinitely thick if other interactions are disregarded. However, when aluminum undergoes oxidation to form alumina, its behavior changes dramatically. Alumina surfaces cause complete melting when in direct contact with bulk ice and result in only micron-sized layers of water or ice in vapor conditions. In contrast, magnetite, the oxidized form of iron, retains metalliclike behavior due to its high dielectric constant, similar to other metals, and continues to support thick layers of water or ice. This distinction highlights the significant influence of oxidation on the dynamics of ice growth and melting near different metal surfaces.

The unique electron deficiency of boron makes it challenging to determine the stable structures, leading to a wide variety of forms. In this work, we introduce a statistical model based on grand canonical ensemble theory that incorporates the octet rule to determine electron density in boron systems. This parameter-free model, referred to as the bonding free-energy (BFE) model, aligns well with first-principles calculations and accurately predicts total energies. For borane clusters, the model successfully predicts isomer energies, hydrogen diffusion pathways, and optimal charge quantity for closo-boranes. In all-boron clusters, the absence of B-H bond constraints enables increased electron delocalization and flexibility. The BFE model systematically explains the geometric structures and chemical bonding in boron clusters, revealing variations in electron density that clarify their structural diversity. For borophene, the BFE model predicts that hexagonal vacancy distributions are influenced by bonding entropy, with uniform electron density enhancing stability. Notably, our model predicts borophenes with a vacancy concentration of $\frac{1}{6}$ to exhibit increased stability with long-range periodicity. Therefore, the BFE model serves as a practical criterion for structure prediction, providing essential insights into the stability and physical properties of boron-based systems.

Coexistence of atomic off-center polar distortion and metallicity in polar metals is an intriguing phenomenon of fundamental importance in view of their mutual incompatibility. However, understanding of polar metals remains rather limited. First, since interatomic interaction in polar metals is profoundly weakened by the screening of mobile carriers, it remains unclear how effective the properties of polar metals can be tuned. Second, it remains elusive to determine quantitatively the effects of metallicity on the full spectrum of lattice vibration. Here, we perform linear-response density-functional perturbation calculations on metallic ${\mathrm{NbO}}_2$-doped ${\mathrm{PbTiO}}_3$ under compressive in-plane strains, aimed at understanding the influence of metallicity on ferroelectric-like polar distortion. We find that (i) doping of one layer of ${\mathrm{NbO}}_2$ almost completely eliminates the strong ferroelectricity in bulk ${\mathrm{PbTiO}}_3$, showing drastic impact of metallicity. (ii) Despite the existence of mobile electrons, we show that in-plane strain nevertheless is able to cause a profound (normal-metal to polar-metal) phase transition in ${\mathrm{NbO}}_2\text{−}{\mathrm{PbTiO}}_3$. Furthermore, ${\mathrm{NbO}}_2\text{−}{\mathrm{PbTiO}}_3$ under $-2\%$ in-plane strain is found to be potentially a polar metal at room temperature. (iii) By designing a cloned system (which is an insulator without mobile electrons while keeping the same chemical environment as the original polar metal), we show quantitatively that metallicity affects both structural instability [by changing the number of ${\mathrm{A}}_{2u}\left({\mathrm{TO}}_1\right)$ soft modes] and nonsoft lattice vibration (by altering the broad vibration spectrum). Microscopic knowledge for understanding the structural instability and polar distortion in metallic ${\mathrm{NbO}}_2\text{−}{\mathrm{PbTiO}}_3$ is provided.

We propose a two-dimensional (2D) quantum breakdown model of hardcore bosons interacting with disordered spins which would be classical without the bosons. It resembles particles incident into supersaturated vapor. The model exhibits a set of subsystem symmetries and has a strong fragmentation into Krylov subspaces in each symmetry sector. The Hamiltonian in each Krylov subspace maps to a single-particle problem in a Cayley-tree-like graph. At zero disorder, the Krylov subspaces exhibit either (possible) integrable features or quantum chaos with quantum scar states showing irregular energy and degeneracy patterns. At nonzero disorders, they enter a 2D many-body localization (MBL) phase beyond certain disorder strength $W_{*}$, as indicated by Poisson level spacing statistics and entanglement entropy growing as $logt$ with time $t$. Our theoretical arguments suggest $W_{*}$ is finite or zero for boson number $N_b\lesssim L^{\gamma }/logL$ ($1/2\le \gamma \le 1$) as system size $L\to \infty$. This gives a more stringent condition for MBL than that in the 1D quantum breakdown models. This model reveals the possibility of MBL in systems of quantum particles interacting with classical degrees of freedom.

One of the fundamental effects of laser-matter interaction is the appearance of induced transient magnetization. While the underlying phenomena differ in their microscopic origin and cover a diverse array of materials, here we address a fundamental question about the possibility of driving domain-wall dynamics on the femtosecond timescale of the exchange interactions solely by longitudinal changes of the magnetic moments. We verify the viability of this hypothesis in the case of a generic ferromagnetic system described in the framework of a high-temperature micromagnetic model based on the Landau-Lifshitz-Bloch equation. The effect is investigated in a 1D model at constant temperature as well as in a full micromagnetic framework considering realistic laser-induced heating. Our results demonstrate that domain-wall deformation in a femtosecond time frame leads to the displacement of the wall on a larger timescale up to nanoseconds accompanied by a release of excess energy in the form of spin waves. The domain-wall deformation leads to the appearance of a magnetization gradient across the wall, which promotes the motion towards the region consisting of spins with decreased magnetization length. The total displacement is enhanced at larger temperatures and smaller damping caused by an increase of the longitudinal relaxation time, which ensures the longer presence of the induced magnetization gradient. Our results are important for understanding ultrafast magnetism phenomena on the sub-picosecond timescale.

We report scanning tunneling microscopy/spectroscopy (STM/S) observations of Majorana zero modes (MZMs) and Caroli de Genne–Matricon bound states in the vortex core of stoichiometric iron-based superconductor $\mathrm{CaKF}{\mathrm{e}}_4\mathrm{A}{\mathrm{s}}_4$. Previous STS study on Fe(Se,Te) showed that topologically trivial and nontrivial vortices coexist, possibly due to the inhomogeneities in Fe(Se,Te) as a doped material. In the present study, we demonstrate the presence of a much more regular vortex lattice on a cleaved surface of $\mathrm{CaKF}{\mathrm{e}}_4\mathrm{A}{\mathrm{s}}_4$ single crystal compared with that in Fe(Se,Te). We found that despite the presence of a very regular vortex lattice, the topologically trivial and nontrivial vortices still coexist, and the ratio of the nontrivial vortices is not high. We checked the distribution of the MZMs and found that they are not influenced by the regularity of the vortex arrangements. Consistent with the previous work, we confirmed that higher magnetic field reduces the ratio of topologically nontrivial vortices, highlighting the necessity of limiting the magnetic field to achieve a stable and practical MZM lattice. Other sources of the suppression of a MZM in the vortex core of $\mathrm{CaKF}{\mathrm{e}}_4\mathrm{A}{\mathrm{s}}_4$ are suggested.

We investigated the Re-based kagome superconductor ${\mathrm{Re}}_2\mathrm{Zr}$ through various measurements, including resistivity, magnetization, specific heat, and muon spin rotation and relaxation spectroscopy. These results suggest that ${\mathrm{Re}}_2\mathrm{Zr}$ is a moderately coupled unconventional superconductor. Zero-field muon relaxation data indicate the possible presence of a time-reversal symmetry-breaking state in the superconducting ground state. Our investigation identifies ${\mathrm{Re}}_2\mathrm{Zr}$ as a new unconventional superconductor with a potential complex order parameter that warrants considerable experimental and theoretical interest.

The intricate phonon physics emerges at extreme conditions due to the significant variation in lattice dynamics with high temperature and pressure, proposing challenges for accurate modeling of lattice thermal conductivity (LTC). Here, by combining machine-learning potential with molecular dynamics, the full anharmonic effects are captured efficiently within first-principles accuracy. We reproduce the experimental measurements and lattice dynamics results that consider four-phonon scatterings, thereby demonstrating the non-negligible influences of high-order anharmonicity under extreme conditions. More interestingly, we unraveled the competitive mechanism of high-order phonons with density, which leads to the coupled temperature-density dependence of LTC. We therefore propose an improved LTC relation law that thoroughly considers the density-dependent competing contributions from different phonon transport channels and therefore can be applied across wide thermodynamic ranges across different phases. We show that our improved LTC formula is robust and general to fit the temperature-density dependence of LTC for several solid prototypical cases, where three-phonon scatterings, four-phonon scatterings, and wavelike phonon tunneling simultaneously exist. In addition, we report the formula of the thermal conductivity of MgO in the interior of giant planets. We also explore the mechanism of the abrupt thermal conductivity decrease at the B1-B2 phase boundary. Our work provides fundamental insights into phonon transport mechanisms under extreme conditions and provides guidance for modeling thermal conductivity in the interior of planetary physics.

In this study, we investigate Anderson localization in a one-dimensional lattice with mosaic off-diagonal quasiperiodic hopping. Our findings reveal that the localization behavior of zero-energy states is highly dependent on the parity of the mosaic modulation period, denoted as $\kappa$. Specifically, when $\kappa$ is an odd integer, there is no Anderson localization transition even for large quasiperiodic hopping strengths, and the zero-energy state remains in a critical state. On the other hand, for an even $\kappa$ and generic quasiperiodic hopping, the zero-energy state becomes a localized edge state at either the left or right end of the system. Additionally, we observe that the geometric mean value of the energy spectrum is equal to the constant hopping for an even $\kappa$, while for an odd $\kappa$, it is equal to the geometric mean value of the hopping. This odd-even effect of the mosaic period also extends to other eigenstates near zero energy. More specifically, for an odd $\kappa$, an energy window in which the eigenstates remain critical even for strong quasiperiodic hopping exists. In contrast, for an even $\kappa$, an Anderson localization transition occurs as the hopping strength increases. Furthermore, we are able to accurately determine the Lyapunov exponent $\gamma \left(E\right)$ and the mobility edges $E_c$. By analyzing the Lyapunov exponent, we identify critical regions in the hopping-energy parameter planes. Additionally, as the energy approaches the mobility edges, we observe a critical index of the localization length of $\nu =1$. Finally, we demonstrate that different systems can be characterized by their Lyapunov exponent $\gamma \left(E\right)$ and Avila's acceleration $\omega \left(E\right)$.

Previous studies of $(1+1)$-dimensional random Clifford circuits and Haar random circuits indicate that the quantum error correction threshold occurs concurrently with measurement-induced phase transitions. This implies the area-law phase cannot be used for quantum error correction in nonunitary quantum channels. The situation might be changed when the many-body measurements and feedback operations are introduced into circuits. The channel invariant subspace generated by the combination of many-body measurement and feedback operations can support the quantum error correction in the area-law phase. To show these properties, four quantum circuits consisting of noncommuting four-body measurements and feedback operations have been put forward as a prominent example. The study of these circuits also shows that the nondeterminism (determinism) of the final state after many-body measurements (single-body measurements) plays an important role in the quantum phase transition, which also leads to the quantum error correction in the area-law phase.

Information can be stored magnetically in antiferromagnets ultrafast since their characteristic times are on the picosecond scale. Various spin torques have proven to be important for efficient and high-speed magnetic memories. So far, this has been understood on the classical level by solving the equations of motion for macrospins describing the collective motion of the sublattice magnetizations. Since spins and hence magnetizations are deeply rooted in quantum mechanics, we show that the exchange-enhanced manipulation of sublattice magnetizations extends to quantum antiferromagnets as well. To this end, we solve the time-dependent mean-field equations for the Schwinger boson theory under external alternating magnetic fields. Exchange enhancement persists on the quantum level which includes dephasing effects. Significantly lower fields are sufficient to control the sublattice magnetization than for uniform fields, which holds great promise for the realization of ultrafast magnetic storage devices.

We investigate the ground-state properties and the effects of temperature and magnetic field on elementary magnetic excitations in the $s=1/2$ rouaite ${\mathrm{Cu}}_2{\left(\mathrm{OH}\right)}_3{\mathrm{NO}}_3$ using bulk magnetization and high-field Raman spectroscopic experiments. The unique exchange topology of rouaite, consisting of weakly coupled alternating ferromagnetic and antiferromagnetic chains, gives rise to a rich array of field-induced phases, including a 2/3-plateau phase at ${\mu }_0{H}_{2/3}\approx 15\mathrm{T}$, corresponding to a fully polarized ferromagnetic chain. Across ${\mu }_0{H}_{2/3}$, the field dependence of low-energy phonons shows marked anomalies, indicating the presence of strong magnetoelastic coupling. In addition, as an applied field approaches ${\mu }_0{H}_{2/3}\approx 15\mathrm{T}$, one-magnon excitations exhibit an order-parameter-like softening, while depleted continuum excitations become gapless. In the 2/3-plateau phase, magnetic excitations are dominated by a fractionalized spinon continuum pertaining to the decoupled antiferromagnetic chains and a spin-flip excitation arising from the polarized ferromagnetic chains. Our results demonstrate that a dimensional reduction occurs at ${\mu }_0{H}_{2/3}\approx 15\mathrm{T}$, transiting from a three-dimensional magnet to a one-dimensional antiferromagnet through the magnetic quenching of the ferromagnetic chain subsystem.

Motivated by the growing interest in band structures featuring higher-order Van Hove singularities (HOVHS), we investigate a spinless fermion kagome system characterized by nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping amplitudes. While NN hopping preserves time-reversal symmetry, NNN hopping, akin to chiral hopping on the Haldane lattice, breaks time-reversal symmetry and leads to the formation of topological bands with Chern numbers ranging from $C=\pm 1$ to $\pm 4$. We perform analytical and numerical analysis of the energy bands near the high-symmetry points $\mathrm{\Gamma }, \pm \mathbf{K}$, and ${\mathbf{M}}_i$ ($i=1,2,\text{and}3$), which uncover a rich and complex landscape of HOVHS, controlled by the magnitude and phase of the NNN hopping. We observe power-law divergences in the density of states (DOS), $\rho \left(\epsilon \right)\sim {\left|\epsilon \right|}^{-\nu }$, with exponents $\nu =1/2,1/3,1/4$, which can significantly affect the anomalous Hall response at low temperatures when the Fermi level crosses the HOVHS. Additionally, the NNN hopping induces the formation of higher Chern number bands $C=\pm 2,\pm 4$ in the middle of the spectrum obeying a sublattice interference whereupon electronic states are maximally localized in each of the sublattices when the momentum approaches the three high-symmetry points ${\mathbf{M}}_i$ ($i=1,2,\text{and}3$) on the Brillouin zone boundary. This classification of HOVHS in kagome systems provides a platform to explore unconventional electronic orders induced by electronic correlations.

We study the nonequilibrium dynamics of the superconducting order parameter in the Hatsugai-Kohmoto (HK) model. In the absence of superconductivity, its ground state is a non-Fermi liquid, whose properties are controlled by the HK interaction. Our protocol involves quantum quenching the HK interaction but leaving the interaction responsible for superconductivity unchanged. We map out the nonequilibrium dynamical phase diagram of the interacting model which contains three phases where, at long times, the order parameter amplitude vanishes, approaches a constant value, or persistently oscillates. We also investigate the Loschmidt echo in searching for dynamical quantum phase transition and find that its nonanalytic temporal behavior is close but does not match exactly the vanishing of the order parameter. The momentum space entanglement entropy between positive and negative momentum modes, relevant for Cooper pairing, is calculated. Counterintuitively, this momentum space entanglement does not change significantly during the quench dynamics and its value remains reasonably large even for a vanishing superconducting order parameter. Nevertheless, its derivative with respect to the HK interaction signals the dynamical phase transition associated to the late time vanishing of superconductivity.

We show that the two-dimensional ${\mathbb{Z}}_2$ invariant for time-reversal invariant insulators can be formulated in terms of the boundary-condition dependence of the ground state wave function for both noninteracting and strongly correlated insulators. By introducing a family of quasi-single-particle states associated to the many-body ground state of an insulator, we show that the ${\mathbb{Z}}_2$ invariant can be expressed as the integral of a certain Berry connection over half the space of boundary conditions, providing an alternative expression to the formulations that appear in S.-S. Lee and S. Ryu [Phys. Rev. Lett. 100, 186807 (2008)]. We show the equivalence of the different many-body formulations of the invariant and show how they reduce to known band-theoretic results for Slater determinant ground states. Finally, we apply our results to analytically calculate the invariant for the Kane-Mele model with nonlocal (orbital) Hatsugai-Kohmoto (HK) interactions. This rigorously establishes the topological nontriviality of the Kane-Mele model with HK interactions and represents one of the few exact calculations of the ${\mathbb{Z}}_2$ invariant for a strongly interacting system.