The deposition of a two-dimensional material on the surface of a three-dimensional crystal can generate superlattices with electronic properties modified through the proximity spin-orbit effect. In this paper, we found that Kekulé graphene superlattices are obtained by placing graphene on Cd-terminated (001)-($1\times 1$) cadmium sulfide (CdS) surface. From an effective model of Kekulé superlattices, which is corroborated by density functional theory calculations, we identified that the puckered surface of CdS modifies the on-site energies (staggered potential) and C-C bonds, giving rise to two possible $\sqrt{3}\times \sqrt{3}$ hexagonal superlattices, which are known as Kekulé-O graphene and Kekulé-Y with a quadratic band crossing point. Both Kekulé superlattices present spin-orbit coupling due to the interaction of graphene with the CdS surface. To guide the experimental realization of Kekulé superlattices based on graphene/CdS heterostructures, we simulate electron diffraction patterns as well as images from high-resolution transmission electron microscopy and scanning transmission electron microscopy in the mode of high-angle annular dark field.

The phenomenon of spontaneous formation of quasihexagonal arrays of electric bubbles in systems of electric dipoles subjected to an external electric field bias is studied via ab initio-based simulations of ultrathin ferroelectric films. We find that the formation of such topologically nontrivial superstructures is driven by development and evolution of soft-mode triplets with equal wavelengths and eigenfrequencies. The concurrent development of these soft-modes takes place above the transition point and the soft-modes become frozen-in near the transition temperature, where frequencies of the soft modes attain a minimum value. A further gradual cooling (or heating) of the superstructures leads to an increase in the soft-mode frequencies, following a square root law around the transition point. We quantify the thermal behavior of the degree of quasihexagonal ordering and find that the dipole structure factor intensities show the same critical behavior around the transition point as the soft-mode frequencies. The critical behavior, associated with the topological changes, is consistent with the Landau theory of phase transitions.

Interacting crystalline SPT phases were first classified by Thorngren and Else through the crystalline equivalence principle, suggesting that a spatial group symmetry can be treated as if it were an internal symmetry group. Using techniques from topology, we elucidate how this principle holds for one of the proposals for the interacting bosonic case and yet fails for weak free-fermion phases. Lastly, we show how a variant of the principle does hold for strong crystalline free-fermion phases, showing that it is not necessary for the cohomology theory to be of Borel type.

Going beyond the bistability paradigm of the charge polarization in ferroelectrics is highly desired for ferroelectric (FE) memory devices toward ultrahigh-density information storage. Here, we propose to build multistates by combining the intrinsic and sliding-induced polarizations. The physics is that there is at least one order of magnitude difference in the energy barriers between these two types of polarizations, which leads to a significant difference in the electric fields for reversing the polarization. This difference, along with the symmetry breaking, allows for a unique flipping mechanism involving layer-by-layer sliding followed by layer-by-layer flipping during the transformation of the multistates. As a result, six and ten switchable states can be achieved for the $1T^{″}$ bilayers and trilayers, respectively. We further illustrate the concept in $H$-stacking bilayers and trilayers of $1T^{″}$ transition-metal dichalcogenides by first-principles calculations. Our study provides a route to design polarization multistates for developing next-generation memory devices.

We put forward a methodology to identify phase transitions in condensed matter without the need to rely on any preexisting physical background. Specifically, we use graph limit theory to construct order parameters that leverage the outcomes of molecular dynamics simulations. We apply this approach to investigate the phase transitions of a Lennard-Jones system and the glass-forming ability of the Kob-Andersen binary Lennard-Jones mixture. This methodology rigorously links graph limit theory, a cutting-edge field in combinatorial mathematics, with condensed matter physics.

We theoretically study the open quantum system dynamics (in the Trotterized limit) of integrable quantum circuits in the presence of on-site dephasing noise with a spin-1/2 “impurity” interacting at the edge. Using a combination of Bethe ansatz (BA) and exact diagonalization (ED), we study the dynamics of both the bulk and the impurity for the XXX (Heisenberg) and the XX qubit chains with and without bulk noise. In the absence of noise, we show that the impurity exhibits two distinct phases: the bound-mode phase, where the impurity undergoes persistent oscillations, and the Kondo phase, where it decays with Kondo time $t_K$. Turning on the bulk dephasing noise, we find for the two models that in the long-time limit in both regimes, the quantum Zeno effect takes place where the dynamics of the impurity magnetization slows down as the noise strength $\gamma$ increases. In contrast, the impurity magnetization in the bound-mode regime shows the opposite effect, decaying faster as the noise strength increases at short times $(t\ll 1/\gamma )$. We show that the Zeno effect slows down the impurity dynamics in the long-time limit, driven by the transition in bulk dynamics from ballistic (KPZ) universality class in the XX (XXX) chain to diffusive dynamics in the presence of noise.

The maximum unitarily extractable work from a quantum system—ergotropy—is the basic principle behind quantum batteries, a rapidly emerging field. This work studies ergotropy in two quantum chaotic systems, the quantum kicked top and the kicked Ising spin chain, to illustrate the effects of chaotic dynamics. In an ancilla-assisted scenario, chaos enhances ergotropy when the state is known, a consequence of large entanglement production in the chaotic regime. When the state is unknown, we need to at least partially characterize the state using coarse-grained measurements for useful extraction of work. In this case, chaos impedes ergotropy by suppressing information gained from coarse-grained measurements, while entanglement with an ancilla still facilitates ergotropy. In this scenario, we study the interplay between chaos and entanglement and find a sweet spot in the chaos parameter for optimal work. Our results point to the potential of quantum chaos-assisted batteries for better work extraction.

In order to explore the high-temperature superconductivity of novel carbon structures at ambient pressure, we have investigated the crystal structures, electronic states, dynamics, and electron-phonon interactions of carbon-hydrogen (carbon-rich) system by means of structural search predictions as well as first-principles calculations. A novel three-dimensional carbon structure intercalated by hydrogen atoms, $P{6}_3/mcm{\mathrm{HC}}_6$, is obtained. The results show that $P{6}_3/mcm{\mathrm{HC}}_6$ is thermodynamically and dynamically stable at ambient pressure. This is a carbon-based structure, and its stability mainly comes from the strong covalent hybridization between carbon and carbon. The role of hydrogen is mainly to introduce hybrid energy bands in the band gap to promote metallization, and the electron-phonon coupling is mainly contributed by carbon. The superconducting transition temperature of $P{6}_3/mcm{\mathrm{HC}}_6$ reaches 107 K at ambient pressure. Comparing carbon and carbonlike structured superconductors, we point out that three-dimensional carbon or carbonlike structures are an interesting direction for exploring ambient-pressure high-temperature superconductivity.

Three-dimensional reconstruction of atomic structure, known as atomic electron tomography (AET), has found increasing applications in materials science. The AET has been limited to objects of very small size due to the challenges of obtaining accurate atomic positions for large objects, for which the projection approximation generally assumed in AET is no longer valid due to the evolution of the electron probe along the beam direction. To address these challenges, we have developed a method that represents atoms as local orbitals and implements a depth-dependent probe-object interaction. Compared to conventional tomographic methods, the accuracy of atomic positions is improved by more than a factor of three and provides a solution for the tomographic reconstruction of large objects.

In the present study, nuclear quantum effects (NQEs) on proton diffusivity in oxides were evaluated by molecular dynamics (MD) simulations with a quantum thermal bath based on Langevin dynamics. We employed the proton diffusion in barium zirconate ($\mathrm{BaZr}{\mathrm{O}}_3$) with the cubic perovskite structure as the model system, in which protons migrate by rotation around single oxide ions and by hopping between adjacent oxide ions. MD simulations with the standard classical thermal bath and phonon calculations were also conducted to verify the conventionally used classical harmonic transition state theory (classical h-TST), in which the transition state theory, the harmonic approximation, and the classical approximation are assumed. As a result, the h-TST is reasonable for the proton rotation, while significantly overestimating the activation energy and the preexponential factor of the jump frequency for the proton hopping. Furthermore, the classical approximation makes the proton jump frequencies close to linear in the Arrhenius plots, which should actually be nonlinear by the NQEs in the temperature range of 500–2000 K. This suggests the necessity of the treatment beyond the classical h-TST for accurate evaluation of the proton diffusivity in oxides even in the intermediate temperature range (573–873 K).

Recently, there has been interest in the dynamics of monitored quantum systems using linear jump operators related to the creation or annihilation of particles. Here, we study the dynamics of the entanglement entropy under quantum jumps that induce local particle losses in a model of free fermions with hopping and ${\mathbb{Z}}_2$ pairing. We solve the nonunitary dynamics using the recently developed Faber polynomial method and explore the different steady-state entanglement regimes by tuning the pairing strength, thus interpolating between monitored free fermions coherently driven by a particle-number-conserving Hamiltonian and a parity-conserving one. In the absence of pairing, all quantum trajectories approach the vacuum at long times, with the entanglement entropy showing nonmonotonic behavior over time that we capture with a phenomenological quasiparticle ansatz. In this regime, quantum jumps play a key role, and we highlight this by exactly computing their waiting-time distribution. On the other hand, the interplay between losses and pairing gives rise to quantum trajectories with entangled steady states. We show that by tuning the system parameters, a measurement-induced entanglement transition occurs, where the entanglement entropy scaling changes from logarithmic to area law. We compare this transition with the one derived in the no-click limit and observe qualitative agreement in most of the phase diagram. Furthermore, the statistics of entanglement gain and loss are analyzed to better understand the impact of the linear jump operators.

We discuss a two-band model for two-dimensional superconductors with electron and hole bands separated by an energy gap and singlet $d$-wave pairing in each band. This type of model exhibits a V-shaped to U-shaped transition in the density of the states of the superconductor, and was phenomenologically used as a possible interpretation of recent tunneling experiments in magic-angle twisted trilayer graphene (MATTG) [H. Kim et al., Nature (London) 606, 494 (2022)]. Performing a microscopic investigation, we find that such a qualitative difference in behavior occurs when the electron and hole chemical potentials change, leading to topological quantum phase transitions (TQPTs) between gapless and gapped $d$-wave superconducting states, due to the annihilation of chiral Dirac fermions at the phase boundaries. This transition requires the vanishing of the coherence peaks in the density of states at zero energy when the phase boundary is crossed, but this is not seen in the experimental data of Kim et al. We also show that direct thermodynamic signatures of these topological quantum phase transitions arise in the theoretical compressibility, which exhibits logarithmic singularities at the transition points. Measurements of the compressibility may illuminate the interpretation of the experimental data of Kim et al. and provide additional information about topological quantum phase transitions in the superconducting state of MATTG. Based on our analysis, we are led to conclude that the V-shaped to U-shaped transition observed is not related to the annihilation of Dirac fermion quasiparticles and its associated TQPTs, but is possibly connected to a change in symmetry of the order parameter from a nodal to a non-nodal superconducting phase.

Multifractal analysis is a powerful tool for characterizing the localization properties of wave functions. Despite its utility, this tool has been predominantly applied to disordered Hermitian systems. Multifractal statistics associated with the non-Hermitian skin effect remain largely unexplored. Here, we demonstrate that the tree geometry induces multifractal statistics for the single-particle skin states on the Cayley tree by deriving the analytical expression of multifractal dimensions. This sharply contrasts with the absence of multifractal properties for conventional single-particle skin effects in crystalline lattices. Our work uncovers the unique feature of the skin effect on the Cayley tree and provides a novel mechanism for inducing multifractality in open quantum systems without disorder.

${\mathrm{Mg}}_3{\mathrm{Bi}}_2$ is a candidate type-II nodal-line semimetal (a novel category of topological semimetals). However, the exotic transport properties of ${\mathrm{Mg}}_3{\mathrm{Bi}}_2$ single crystals are yet to be elucidated. Herein, we report the magnetotransport properties of an $n$-type ${\mathrm{Mg}}_3{\mathrm{Bi}}_2$ single crystal grown from a melt. The results revealed that the single crystal exhibited a very large, nonsaturating magnetoresistance (5000%) under an 8-T field, significantly exceeding that of polycrystals. The combined analysis of Shubnikov–de Haas (SdH) oscillations, Hall resistivity, and first-principles calculations suggest that SdH oscillations originate from trivial electron bands rather than hole bands, which contain an almost linear dispersion. We confirmed that the electron mobility reached 10 000 $\mathrm{c}{\mathrm{m}}^2$/Vs by analyzing Hall resistivity and magnetoresistance based on a two-band model. The electron/hole concentration and mobility were used to investigate the measured transport properties, such as the Nernst coefficient. Overall, these results are critical for elucidating the electronic structure and transport properties of ${\mathrm{Mg}}_3{\mathrm{Bi}}_2$.

The realization of spin field-effect transistors requires robust spin-orbit splitting and coherent spin precession in the presence of ferroelectric polarization, which can be observed in two-dimensional noncentrosymmetric systems. To control the spin-orbit coupling (SOC) parameters, we adopted strain engineering. Within the framework of the density functional theory, we investigated the electronic structure, spontaneous electric polarization, and spin texture of $X{\mathrm{O}}_2{Y}_2$ ($X=\mathrm{W}$, Mo; $Y=\mathrm{Cl}$, Br, I) monolayer under uniaxial strain from $-1$% to 5%. We obtained tunable spin splitting in the conduction band minimum of all the monolayers. Among them, ${\mathrm{WO}}_2{\mathrm{Cl}}_2$ monolayer shows considerable SOC strength reaching up to 2.16 $\mathrm{eV}$ Å, allowing the device to function at room temperature. We also found that the spontaneous electric polarization is substantially influenced by the applied strain, which is increased from 156.2 pC/m to 255.3 pC/m. Additionally, we highlight the emergence of a reversible persistent spin helix (PSH) across all the compounds, maintained across strained variants. For practical applications, we confirm the fully reversed PSH under external electric $-0.8$ V/nm. The highly tunable spontaneous electric polarization and the SOC strength as well as the emergence and reversibility of the PSH state in $X{\mathrm{O}}_2{Y}_2$ ($X=\mathrm{W}$, Mo; $Y=\mathrm{Cl}$, Br, I) monolayer underscore the potential for the application to the spin diffusion channel in spin-field effect transistors.

Exploration of novel topologically excited states is one of the core topics in topology physics, yet nontrivial nodal surfaces have garnered insufficient research attention. In this paper, we discover that open nodal surfaces can be categorized into two types based on their symmetry conditions: ones situated on the boundary surface of the first Brillouin zone (BZ), and the others within the BZ. The former have been extensively researched and are known as conventional type, whereas the latter, which are less studied, are termed the unconventional type. Through symmetry analysis, we identify two unconventional nodal surfaces in space group (SG) 194, each composed of Weyl degenerate points. Using first-principles calculations, we further reveal that several real materials in this SG exhibit unconventional nodal-surface phonons, accompanied with conventional nodal surfaces and type-I linear and quadratic nodal-line phonons in the first BZ. Significantly, the coexistence of two types of open nodal surfaces and various nodal lines gives rise to a composite nontrivial phonon state, which we term the topological nodal line-surface hybrid phonon. Our findings not only enrich the classification of topological nodal surfaces but also introduce a material platform for exploring composite nontrivial phonons.

We present a linear response theory for stationary density accumulations in anomalous transport phenomena, such as the orbital Hall effect, where the transported density is odd under time reversal and the underlying charge is not conserved. Our framework applies to both metals and insulators, topologically trivial or nontrivial, and distinguishes between contributions from bulk and edge states, as well as undergap and dissipative currents. In time-reversal invariant systems, we prove a microscopic reciprocity theorem showing that only dissipative currents at the Fermi level contribute to density accumulation, while undergap currents do not. In contrast, in non-time-reversal invariant systems, nondissipative density accumulations, such as magnetoelectric polarization, can appear in both the bulk and edges. Importantly, we find that the net density accumulation does not always vanish, pointing to a global nonconservation that implies the existence of a nonvanishing integrated “net torque” in addition to a “distributed torque,” which has zero spatial average. We show that the distributed torque can be absorbed in the divergence of a redefined current that satisfies Onsager reciprocity, while the net torque must be explicitly accounted for. Finally, we apply our theory to two-dimensional models with edge terminations.

Chiral symmetry plays an essential role in condensed matter physics. In tight-binding models, it is often attributed to bipartite lattice structures, and its typical consequence is the “particle-hole symmetric” band structures, where positive and negative eigenenergies appear in a pairwise manner. In this paper, we address chiral symmetry for nonbipartite lattice models with flat bands. Our argument relies on what we call the molecular-orbital representation, by which we can guarantee the existence of the flat band. We show that chiral symmetry is preserved for the nonflat bands when the molecular orbitals are normalized and divided into two sets, within which they do not overlap. The chiral operator is constructed by the same molecular orbitals as the Hamiltonian. This results in the characteristic relation between the chiral operator and the Hamiltonian, which we call the Pythagoras relation. We present examples of such models, including the kagome lattice and its one-dimensional analog, and address the characteristics originating from chiral symmetry, such as the emergence of the topological edge modes. We also show an example where the numbers of molecular orbitals in each set are different, resulting in multiple flat bands with different energies.