Nowadays the vibrational Stark effect (VSE) of adsorbates at the electrochemical interfaces is generally investigated using the Lambert theory, in which the strong electric field across the interfaces can be treated as some kind of perturbation. Lambert found that the VSE arises mainly from the classical effect, and the quantum effect is negligible. This idea is accepted by almost all current first-principles calculations for this issue. Here we revisit this problem by addressing the fundamental question of to what extent the quantum effect is important for VSE, and if it is observable, then which physical quantity determines this effect. We use the Morse, Lennard-Jones, and Dunham potentials as basic potentials to explore this problem using quantum perturbation theory. We define the relative difference between quantum and classical VSE slopes to define the quantum effect, yielding $\eta \sim 7\hslash \omega /12D_e$, where $\hslash$, $\omega$, and $D_e$ are the Planck constant, vibrational frequency, and binding energy, respectively. With this formula we show that for CO, $\eta \sim 2–3$%, while for adsorbed hydrogen on Pt electrode, $\eta \sim$ 8–10%, using the experimental measurable data. We find that $\eta$ is directly determined by the anharmonic coefficient ${\chi }_e$. With these results we present a new understanding of the VSE as a function of electric field and potential in electrochemical experiments, showing that the nonlinear slope of VSE as a function of potential should arise from the nonlinear relation between electric field and potential across the interfaces, which may resolve the longstanding controversial in experiments.

Higher-order topological states in sound have played a pivotal role in advancing our understanding of the intricate physics underlying sound transport, leading to new strategies for manipulating sound. In this study, we report a tunable structure for hinge skin states in a non-Hermitian acoustic metamaterial exhibiting a hybrid skin-topological effect. Our findings show that when on-site gain and loss are exquisitely introduced into acoustic topological insulators, chiral edge modes in their Hermitian counterparts are respectively amplified or attenuated at zigzag boundaries. By intentionally constructing adjacent gain and loss boundaries, hinge skin states emerge at their intersections. Through the strategic combination of non-Hermitian and topological physics, we successfully reveal how higher-order hinge modes originate from lower-order surface states and demonstrate flexible acoustic steering in a tunable non-Hermitian acoustic metamaterial. Our findings unveil that skin-topological effect could have significant applications in the design of innovative acoustic devices with unconventional functions such as multidimensional acoustic control and precise energy harvesting.

Motivated by recent experiments, we study the coupling of quantum Hall (QH) hydrodynamics to quantum electrodynamics within a resonance cavity. In agreement with experimental observations, we find that the Hall conductivity remains unchanged. However, the coupling to the cavity induces a second-order quantum reactance effect, contributing distinctly to the longitudinal AC conductivity. This effect arises from the exchange of energy between the QH fluid and cavity photons. Beyond the topological response, we show that the cavity couples to collective excitations, resulting in a shift of the Kohn mode frequency. Our methods are broadly applicable to both integral and fractional QH liquids, and our results offer a universal perspective on the protection of topological properties against long-range interactions induced by electromagnetic cavity modes.

We investigate the influence of quantum fluctuations in a chiral cavity on the quantum Hall (QH) state, extending previous studies of QH liquids in linearly polarized cavities. Using the Schrieffer-Wolff transformation for perturbative cavity-matter interaction, we identify the system's normal modes, which correspond to the elementary excitations of the dressed electrons and photons. In contrast to the linear case, we find that the chiral cavity modifies the Kohn mode frequency by a contribution proportional to the cyclotron frequency, which can be interpreted as a renormalization of the magnetic field by cavity fluctuations. We show that the AC conductivities display cavity-induced corrections, including an isotropic quantum reactance effect and a rotating total-current response under applied AC fields. These findings are also derived from a hydrodynamic approach, which extends their validity to fractional quantum Hall states. Finally, we examine the role of finite cavity quality factor and find that while photon losses introduce resistive contributions to the impedance, these vanish in the DC limit. Our results provide insights into the interplay between quantum Hall states and chiral cavities, with significant implications for material engineering and cavity-induced topological effects.

ABCB-stacked tetralayer graphene, with intrinsic spontaneous polarization, offers a unique platform to explore electron correlation effects, whose interplay with spin-orbit coupling may engender topological phases. Here, employing a $\mathbf{k}·\mathbf{p}$ model with self-consistent Hartree-Fock calculations, we investigate its electronic ground states. Remarkably, we find that the intrinsic polarization, in conjunction with strong interactions ($U=8\text{eV}$) and spin-orbit coupling (SOC), is sufficient to drive a $C=3$ quantum anomalous Hall state, obviating the need for an external electric field typical in ABCA stacks. Conversely, at moderate interactions ($U=6\text{eV}$), a minimal electric field is necessary. Furthermore, calculations predict other correlation-driven metallic phases such as quarter- and three-quarter-filled states. These results establish that the synergy of intrinsic polarization, correlations, and SOC governs the rich topological phenomena, suggesting ABCB-stacked graphene as a highly tunable platform for exploring emergent topological phenomena.

Excitonic properties of two-dimensional (2D) crystals are of broad interest for luminescent devices. In 2D inversion-symmetry-breaking tetragonal crystals, a robust linear scaling holds between exciton binding energy ($E_{\mathrm{b}}$) and quasiparticle band gap ($E_{\mathrm{QP}}$), namely, $E_{\mathrm{b}}=3/8E_{\mathrm{QP}}$. However, how the built-in potential difference in 2D inversion-symmetry-breaking tetragonal crystals affects the scaling coefficient and the exciton radiative lifetimes remains unclear. Therefore, we systematically investigate excitonic properties and carrier mobility in such crystals using k·p perturbation theory, the screened hydrogen model, high-precision $G_0{W}_0$, and the Bethe-Salpeter equation (BSE). Our results indicate that the built-in potential difference weakens electron-hole coupling, reducing both $E_{\mathrm{QP}}$ and $E_{\mathrm{b}}$, and leading to a slightly shorter exciton radiative lifetime. Importantly, the exciton lifetime (up to 2.15 ps) remains significantly larger than in 2D hexagonal crystals, and the linear scaling between $E_{\mathrm{b}}$ and $E_{\mathrm{QP}}$ persists in the inversion-symmetry-breaking tetragonal crystals. Furthermore, all the materials exhibit high carrier mobility, which is more than two orders of magnitude higher than that of ${\mathrm{MoS}}_2$ and ${\mathrm{WS}}_2$. Our findings not only deepen the fundamental understanding of exciton properties in 2D tetragonal crystals but also suggest a viable strategy for exploring high-performance optoelectronic devices.

Graphullerene, an emerging class of two-dimensional (2D) carbon allotropes constructed by covalently interlinked fullerene molecules, holds great promise for electronics, photocatalysis, and energy storages. Using first-principles calculations, we design three stable graphullerene monolayers based on the smallest fullerene ${\mathrm{C}}_{20}$—quasitetragonal GrF1-${\mathrm{C}}_{20}$ and GrF2-${\mathrm{C}}_{20}$, along with quasihexagonal LOPC-${\mathrm{C}}_{20}$. Their successful stabilization provides a valuable reference for understanding the formation mechanisms of fullerene-based networks. Unlike large-band-gap ${\mathrm{C}}_{60}$-based graphullerenes, these ${\mathrm{C}}_{20}$ systems exhibit widely tunable electronic properties dictated by their bonding patterns: GrF1-${\mathrm{C}}_{20}$ possesses an ultranarrow band gap, while GrF2-${\mathrm{C}}_{20}$ and LOPC-${\mathrm{C}}_{20}$ are wide-gap semiconductors. Remarkably, GrF2-${\mathrm{C}}_{20}$ demonstrates suitable band edge alignment for photocatalytic overall water splitting under neutral conditions. The most striking finding is the strain-induced magnetic transition in GrF1-${\mathrm{C}}_{20}$. Compressive strain polarizes the unpaired ${\mathrm{p}}_{\mathrm{z}}$ electrons, mediating the emergence of magnetism. At a critical uniaxial strain of ∼4%, the system transitions into a half-metallic state. Furthermore, the band gap magnitude and direct/indirect nature of LOPC-${\mathrm{C}}_{20}$ are highly susceptible to mechanical strain. Our work not only pioneers the exploration of ${\mathrm{C}}_{20}$-based graphullerenes but also highlights strain engineering as a powerful tool for tailoring their electronic and magnetic properties, offering key design strategies for future carbon-based optoelectronic and spintronic devices.

Intrinsic large, flat saturation surfaces of two-dimensional materials are ideal optical and sliding ferroelectric films. Here, we propose the inversion symmetry of a $\mathrm{PtS}{\mathrm{e}}_2$ bilayer can be broken in the ${60}^{\circ }$ twisted structure with an energy difference of 0.05 eV/($\mathrm{PtS}{\mathrm{e}}_2$), compared to the original AA stacking structure. In addition, it exhibits a strong second harmonic generation response as high as 369 pm/V, more than 2.6 times greater than that of hexagonal boron nitride (h-BN) and 1.5 times greater than that of $\mathrm{Mo}{\mathrm{S}}_2$. The out-of-plane component is 162 pm/V, exceeding even that of difficult-to-synthesize Janus MoSSe. Moreover, it also introduces strong ferroelectric polarization of 1.72 pC/m with a low switch barrier of only 32 meV. These characteristics imply it is easier to identify and tune ferroelectrics than widely explored h-BN. In addition, ${\mathrm{PtSe}}_2$ bilayer in the ${60}^{\circ }$ twisted structure also shows a strong bulk photovoltaic effect with a tunable shift current up to $14.9\mu \mathrm{A}\text{/}{\mathrm{V}}^2$. Such a twisting operation can trigger the emergence of physical properties from nothingness and achieves significant regulation. It has excellent potential for both ferroelectric devices and nonlinear optics.

Dynamical quantum phase transitions reveal singularities in quench dynamics, characterized by the emergence of Loschmidt echo zeros at critical times, which usually exist only in the thermodynamic limit but are absent in finite-size quantum systems. In this Letter, we propose a theoretical scheme to probe Loschmidt echo zeros in finite-size systems by applying a two-step quenching protocol, which offers an experimentally feasible approach to study Loschmidt echo zeros. Using the transverse Ising model as a test bed, we identify that the exact Loschmidt echo zeros can be always accessed by tuning the quench rate, when the quench is across the phase transition point. The associated rate function displays divergence at critical times, accompanying with the change of the dynamical topological order parameter. The critical times are influenced by the quench rate, system size, and momentum modes, embodying the interplay between finite-size effects and critical dynamics. Moreover, the generality of these observations is further confirmed in the XY and Haldane models.

A central challenge in spintronics is the efficient generation and control of spin currents for information processing. Here we investigate ultrashort spin transport and the resulting terahertz (THz) emission in a hybrid structure comprised of gold nanoparticles (GNPs), a ferromagnet (FM), and a normal metal (NM), and show that plasmon excitation in the GNPs significantly enhances the electron-magnon scattering rate through heating effects, thereby amplifying spin current generation at the $\mathrm{FM}|\mathrm{NM}$ interface. This enhancement becomes even more pronounced when the FM is an ultrathin insulator with a thickness much smaller than the GNP size. In this case, the GNPs and NM substrate form a plasmonic nanocavity with the FM acting as a dielectric spacer, trapping plasmons inside the gap. The resulting spin current can be boosted by up to two orders of magnitude compared to the structure without plasmon excitations. Our findings reveal a pathway to design efficient spintronic THz devices and further open the door to the interdisciplinary field of spintronics and nanophotonics.

Fractional Chern insulators (FCIs) typically emerge in topological flat bands and are regarded as lattice analogs of fractional quantum Hall states. Conventionally, the flat-band wavefunctions that support FCIs are expected to mimic the lowest Landau level, a condition that can be quantified by the quantum-geometric indicators. In realistic systems, however, FCIs often compete with lattice symmetry-breaking orders, especially when the hosting flat bands not ideal. In this work, we propose stabilizing FCIs by exploiting the intrinsic incommensurability of alternating twisted trilayer graphene, which naturally suppresses competing charge-density-wave (CDW) phase while FCIs are less effected. Within an adiabatic approximation at the supermoiré scale, the effect of incommensuration on local physics can be quantified as phase shifts of interlayer coupling. Using exact diagonalization, we compute ground states in different local patches and uncover a strikingly counterintuitive result: the FCI gap increases as the quantum-geometric indicators worsen. Within certain parameter ranges, we further identify mixed phases where FCIs coexist with CDWs, but with CDWs confined only to patches of weak incommensurability. Finally, we provide experimental protocols and discuss how incommensuration enrich the system's topology and quantum geometry. Not only do our results establish incommensuration as a robust stabilizer of FCIs, but also provide a general paradigm for exploring strong-correlation physics in incommensurate systems.

In the quantum magnet ${\mathrm{SrCu}}_2{\left({\mathrm{BO}}_3\right)}_2$, an anomalous thermal broadening of the triplon modes has been measured at relatively low temperatures compared to the triplon gap $\mathrm{\Delta }$ using both inelastic neutron scattering and Raman spectroscopy. Given how accurately a broad variety of physical phenomena in ${\mathrm{SrCu}}_2{\left({\mathrm{BO}}_3\right)}_2$ are captured by the spin $S=1/2$ Shastry-Sutherland model, it remains an open question whether the anomalous thermal broadening is also an intrinsic feature of this minimal model. However, few techniques are available for computing the finite-temperature dynamics of strongly interacting many-body systems. To address this problem, we have developed a broadly applicable numerical simulation method based on matrix-product states to simulate dynamical spectral functions at nonzero temperatures accurately, detailed in a companion paper [Phys. Rev. B 113, 024406 (2026)]. Using this technique, we demonstrate that the experimentally observed broadening is captured by the Shastry-Sutherland model. Perturbative calculations identify the origin of this phenomenon as singlet bound two-triplon states being thermally excited at an energy scale small compared to the gap $\mathrm{\Delta }$ to the single triplon excitations at the experimentally relevant model parameters.

We observe anomalous charge modulations induced by ionized indium impurities on the surface of the semiconductor black phosphorus by scanning tunneling microscopy (STM). When the impurities are switched into a negatively charged state by the STM tip, periodic charge modulations emerge around the impurity center, but strictly confined by the nanoscale impurity potential. These modulations form a distorted triangular pattern, whose periodicity remains unchanged in a wide range of positive bias. Furthermore, these local charge orders exhibit an anisotropy opposite to that expected based on the anisotropy of the Fermi surface, challenging a simple band-structure interpretation. Our experiment demonstrates the possibility of creating and manipulating macroscopic charge orders through impurity engineering.

The lack of inversion symmetry at the surface of a bulk material can give rise to confined surface states, offering a quasi-two-dimensional platform for investigating electronic correlation effects, even in weakly correlated materials. Here, we report the observation of an electronic liquid-crystal smectic order at a Co-terminated surface of monoclinic ${\mathrm{CoSb}}_2$. Our low-temperature scanning tunneling microscopy measurements reveal a bias-dependent behavior of the smectic charge order, exhibiting checkerboard and stripe patterns at positive and negative bias voltages, respectively. Theoretical calculations indicate that the charge order arises from pronounced quasi-one-dimensional Fermi-surface nesting of the emergent surface bands. These findings highlight the potential to induce exotic correlated states on the terminated surfaces of conventional materials, broadening the spectrum of candidates with strong correlation.

The cuprate superconductors are among the most widely studied quantum materials, yet there remain fundamental open questions regarding their electronic properties and the role of structural degrees of freedom. Recent neutron and x-ray scattering measurements uncovered exponential scaling with temperature of the strength of orthorhombic fluctuations in the tetragonal phase of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ and ${\mathrm{Tl}}_2{\mathrm{Ba}}_2\mathrm{Cu}{\mathrm{O}}_{6+\delta }$, unusual behavior that closely resembles prior results for the emergence of superconducting fluctuations, and that points to a common origin rooted in inherent correlated structural inhomogeneity. Here we use neutron and x-ray diffuse scattering to provide further insight into structural fluctuations in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$. We perform measurements up to temperatures that approach the melting point of the undoped parent compound, and we investigate the effects of in situ in-plane uniaxial elastic stress and plastic deformation. Our neutron scattering results for the parent compound ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ reveal that short-range orthorhombic fluctuations persist to the maximum experimental temperature of nearly 1000 K, i.e., to a significant fraction of the crystallization temperature. At this temperature, the spatial characteristic length extracted from the momentum-space data is still about three lattice constants. The neutron scattering experiment enables quasistatic discrimination and reveals that the response is increasingly dynamic at higher temperatures. We also find that neither compressive elastic stress along the tetragonal [110] direction nor irreversible plastic deformation activating the $\langle 100\rangle \left[001\right]$ slip system significantly alter the robust orthorhombic fluctuations. Overall, these results support the notion that these fluctuations couple to subtle, underlying inhomogeneity that underpins the cuprate phase diagram. Finally, in ${\mathrm{La}}_{1.8}{\mathrm{Sr}}_{0.2}\mathrm{Cu}{\mathrm{O}}_4$, we uncover low-energy structural fluctuations at a nominally forbidden reflection that are distinct from the orthorhombic distortions. While the origin of these fluctuations is not clear, they might be related to the presence of extended defects such as dislocations or stacking faults.

Spin-orbit coupling (SOC) in noncentrosymmetric materials is the source of incommensurate magnetic structures. In semiconductors, it drives the Rashba spin splitting and spin momentum locking, while in magnetic insulators based on transition metals, it induces anisotropic spin exchange interactions like the Dzyaloshinskii-Moriya (DM) interaction which drives chiral magnetism and skyrmion formation. Here, we establish a direct connection between SOC and spin exchange interactions by deriving an effective spin model from the SOC Hubbard model at half-filling. Using a strong-coupling expansion up to fourth-order by including the full set of terms, we identify Heisenberg, Ising-like, and ring exchange interactions, as well as a variety of four-body terms for realistic Hubbard parameters, which impose strong constraints on the relative strengths of the spin interactions. Our spin model shows excellent agreement in energy with the SOC Hubbard model down $U/t\sim 5$ near the metal-insulator transition point, providing insight to which kind of magnetic interactions relevant across this regime are responsible for the emergence of complex magnetic textures.

Altermagnets, a class of collinear magnetic materials, have become a thriving topic in the fields of condensed matter physics and material science due to their unusual properties and potential applications. Recently, the study of topological states has been extended to the altermagnetic materials. In this work, we investigate altermagnetic topological insulators in the square model constructed based on the anisotropic Qi-Wu-Zhang (QWZ) model. To clearly identify the topological properties of these altermagnetic states, we first consider the anisotropic QWZ model which hosts the Chern insulator marked with nonzero Chern numbers and the Zak insulator characterized by the Zak phase. We focus on the altermagnetic Zak insulator which is characterized by the spin-dependent Zak phase. Additionally, the model exhibits rich phase transitions which can be identified based on the spin Chern number and the spin Zak phase.