Using density functional calculations and multiorbital, multiatom cluster exact diagonalization that includes local exchange and Coulomb interactions, we explored the local low-energy electronic states of trilayer ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$ via a minimal ${\mathrm{Ni}}_3{\mathrm{O}}_{14}$ cluster. We find that, at ambient pressure, starting with all three Ni being nominally $2+$ valence, one of the two extra holes is localized in the central ${\mathrm{NiO}}_2$ layer forming a Zhang-Rice singlet (ZRS) with $d_{x^2-y^2}$ orbital. The other hole mainly occupies the antibonding combination of the two interplane apical O $p_z$ orbitals and thereby hybridizes with an out-of-plane three-spin-polaron (3SP) formed by the $d_{z^2}$ orbitals of three ${\mathrm{NiO}}_2$ layers. At high pressure, however, the two extra holes are concentrated on one of two outer layers and the inner layer separately forming the ZRS with $d_{x^2-y^2}$ orbitals. We highlight the similarities between the bilayer ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ and trilayer ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$ via speculated possible charge and spin configurations as well as the in-plane 3SP on two neighboring clusters suggested by our isolated cluster results. We thereby propose that the hole transfer from apical to in-plane oxygen orbitals of outer layer generates in-plane 3SP-like quasiparticles that act as mobile carriers coupled by interlayer superexchange; while the interplane 3SP-like states may provide the pairing glue. Since the low-pressure phase lacks freely propagating in-plane quasiparticles, this scenario naturally favors SC in the high-pressure phase.

Recently developed extended Kohn-Sham theory and extended quasiparticle (QP) theory are both fundamental and important, in particular, in treating the initially excited eigenstates from first-principles. However, still the QP theory including $GW\left(\mathrm{\Gamma }\right)$ methods has been applied only to the initial ground state by almost all authors. In this paper, we want to emphasize that these theories allow one to apply $GW\left(\mathrm{\Gamma }\right)$ methods directly to an initially excited eigenstate. Using only basic and elementary arguments without using the Green's function, we explicitly demonstrate that the QP wave functions can be normalized to unity and the self-energy can be hermitized for the initially excited eigenstate. Our paper supports the conventional procedure commonly used in first-principles calculations. These theories hold when relaxation from excited states can be ignored. We propose the normalized $GW$ (NGW) approach and perform self-consistent calculations for initially excited (cationic and photoabsorbed) states of several light atoms. The resulting QP energies show good agreement with the available experimental data for excited states, as well as with the expected relationships among different QP energies, supporting the validity of the method.

In this study, one-dimensional nanoribbons of single-layer manganese phosphorus trisulfide (${\mathrm{MnPS}}_3$) are investigated using density functional theory based calculations, complemented by experimental Raman spectroscopy measurements. Cutting the ${\mathrm{MnPS}}_3$ single layers along the high-symmetry crystallographic directions yields the formation of four possible nanoribbon types: Mn-Mn-, P-P-, and Mn-P-edged armchair and a zigzag-edged one. Structural analyses reveal clear edge- and width-dependent reconstructions in armchair nanoribbons: S-S dimerization emerges selectively at Mn-terminated edges (odd-width Mn-Mn and Mn-P nanoribbons with even Mn rows), while tilted P-P dumbbells consistently form at all P-terminated edges across the entire width range. The edge reconstructions are directly observable in scanning tunneling microscopy images. Magnetically, armchair nanoribbons stabilize either Néel or dimerized Néel antiferromagnetic order, depending on the formation of S-S dimers at Mn-terminated edges, whereas zigzag nanoribbons generally favor a ferromagnetic configuration, with the exception of the two narrowest cases. Electronic band dispersion calculations show that all armchair nanoribbons exhibit semiconducting behavior, whereas all zigzag nanoribbons are metallic, except for the two narrowest ones. In armchair nanoribbons, S-S dimerization at Mn-terminated edges reduces the band gap relative to nondimerized ribbons, whereas in nondimerized ribbons the band gap increases with width. Frequency-dependent Raman activity calculations reveal the presence of characteristic vibrational modes—originating from S-S dimers, S-P bonds, and nondimerized S atoms—that serve as fingerprint signatures of the edge type of ${\mathrm{MnPS}}_3$ nanoribbons. Overall, these results demonstrate that the electronic, magnetic, and vibrational properties of ${\mathrm{MnPS}}_3$ nanoribbons are strongly governed by edge geometry and ribbon width, highlighting their potential for edge-engineered low-dimensional spintronic and nanoelectronic applications.

We investigate the higher-order bulk-boundary correspondence in a family of chiral-symmetric Bloch Hamiltonians with anticommuting mirror symmetries. These models generalize the $\pi$-flux square lattice, the prototypical topological quadrupole insulator, and include both separable and nonseparable models with extended and diagonal hopping. For separable systems, the product of subsystem chiral winding numbers correctly predicts the number of zero-energy corner states. However, this invariant fails in nonseparable models, motivating the development of new momentum-space diagnostics. We introduce gauge-independent mirror-filtered winding numbers for Wannier Hamiltonians, constructed by projecting mirror eigenstates onto the occupied subspace. Furthermore, by adapting periodicized Wilson lines from chiral Floquet theory to the case with momentum-dependent chiral operator, we define new invariants associated directly with Wannier gaps. These invariants provide a detailed characterization of Wannier band topology. Our results clarify the interplay between chiral symmetry, mirror symmetries, and Wilson loops in higher-order topological phases and point to open challenges in formulating momentum-space invariants for general nonseparable models.

Strange metals are highly entangled gapless states of matter that exhibit anomalous transport, such as linear-in-temperature resistivity, over more than a decade of temperature. Why a single power law should be so robust is an open question. We propose a scenario in which interactions enhance the domain of certain scattering regimes, effectively suppressing other “would-be regimes.” We test this proposal in a one-dimensional Luttinger liquid coupled to a one-dimensional acoustic phonon. We use the memory matrix formalism to calculate the dc electrical and thermal conductivities at low and high temperatures, relative to the Debye cutoff on phonon frequencies, in both the “clean” (umklapp scattering) and “dirty” (disorder scattering) limits. We find the crossover temperature separating the low- and high-temperature regimes to be interaction dependent, with repulsive interactions increasing it, sometimes by more than an order of magnitude, depending on the scattering type. This provides a concrete illustration for how interactions can extend a single transport regime over a wider temperature range.

Conformal field theory (CFT) offers a modern viewpoint for understanding phase transitions. However, directly accessing the conformal algebra and microscopically uncovering the emergent conformal symmetry, especially in higher dimensions, remains a significant challenge. Motivated by recent advances in revealing CFT features via the fuzzy two-sphere, here we generalize this approach to higher dimensions and aim to expose the conformality at the $(3+1)$-D quantum critical point. We demonstrate this framework by investigating quantum phase transitions belonging to the Ising and Yang-Lee universality classes in a $(3+1)$-D quantum model (equivalent to a classical four-dimensional system), realized via Landau level projection on the fuzzy three-sphere. By computing the energy spectra at criticality, we explicitly verify the state-operator correspondence, a hallmark of conformal invariance. Together with prior advances, this work establishes a new pathway for the microscopic study of emergent conformality in higher-dimensional phase transitions.

Coupling effects between self-assembled quantum dots in different layers separated by approximately $200\mathrm{nm}$ are studied by transient capacitance spectroscopy. This coupling manifests itself via interdependent time constants of the transients. Two different coupling mechanisms that act over such large spacings are identified. The first one is electrostatic coupling, caused by electrons in the first layer that modify the electric field at the site of the second layer and with it the lifetime of the discrete states in the quantum dots therein. The second mechanism is cascade coupling, where electrons emitted by the first layer are recaptured by the second layer. A rate equation model combined with self-consistent band structure calculations provides a quantification of the proposed mechanisms.

Topological insulators (TIs) are highly attractive platforms for next-generation optoelectronic and photonic devices. Spin-momentum locking of topological surface states enhances their nonlinear optical responses and sensitivities, especially to circularly polarized light. Until now, theoretical investigations of nonlinear responses in TIs have been limited to microscopic calculations on analytical continuum models, or leveraging density-functional-theory-based Hamiltonians. In this work, we expand beyond these two approaches by employing a nonlinear Kubo formalism to calculate second-order nonlinear optical conductivity in a slab geometry using symmetry-informed tight-binding models that accurately reproduce the conduction, valence, and topological surface bands in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. Our methodology enables us to study the layer-resolved contribution to injection currents coupled to the incident electric field. We demonstrate that our technique can reveal how device engineering modifies elements of the nonlinear optical response such as the circular and linear photogalvanic effects by breaking inversion and time-reversal symmetry. In particular, magnetization-induced symmetry breaking enables nonlinear conductivity tensor components (e.g., ${\sigma }_{xyz}$) that are normally forbidden by symmetry, thereby directly modifying the circular photogalvanic effect. We find, in line with experiments, that the photogalvanic current is sensitive to field effects, Fermi level energy, gate voltage, and the energy of incident light. Our computed midwave infrared responsivity $R\approx 0.170\mu \mathrm{A}/\mathrm{W}$ is comparable to reported TI and intrinsic two-dimensional-material photodetectors. Finally, we simulate experimentally unexplored methods to modify the circular photogalvanic effect, such as proximitizing a magnetic field to one of the TI surface materials, suggesting a mechanism for optoelectronic tuning.

The electronic and magnetic properties of two-dimensional $\mathrm{Ni}{\mathrm{Br}}_2$ bilayer are systematically investigated using first-principles calculations. We find that the metastable antialigned stacking $\mathrm{Ni}{\mathrm{Br}}_2$ bilayer exhibits sliding ferroelectricity, where reversible out-of-plane polarization is enabled by interlayer sliding. In contrast, the ground-state aligned AB-stacked bilayer is an $A$-type antiferromagnetic (AFM) semiconductor. Upon applying a vertical electric field, this AFM semiconductor can be converted into a half-metal with 100% spin polarization. This transition is driven by the field-induced potential gradient, which triggers opposite energy shifts in the spin-resolved bands of the two layers. Furthermore, the conducting spin channel can be effectively switched by reversing the electric field direction. To achieve nonvolatile control, we propose a van der Waals heterostructure by integrating the $\mathrm{Ni}{\mathrm{Br}}_2$ bilayer with a ferroelectric ${\mathrm{Ga}}_2{\mathrm{S}}_3$ bilayer. Our results demonstrate that half-metallicity with 100% spin-down polarization is realized when the ${\mathrm{Ga}}_2{\mathrm{S}}_3$ polarization is upward ($\mathrm{P}\uparrow$), while the system reverts to a semiconducting state upon polarization reversal ($\mathrm{P}\downarrow$). Based on this polarization-dependent phase transition, a nonvolatile ferroelectric memory device is proposed, offering a promising platform for next-generation AFM spintronics.

We systematically analyze both the intrinsic and extrinsic spin Hall conductivity in Janus monolayers using an effective minimal Hamiltonian and the Kubo-Streda formalism with Feynman diagrams. Our analytical and numerical results reveal that the vertex cancellation distinguishes Janus monolayers from the pristine counterparts, i.e., the transition metal dichalcogenide, because of the existence of Rashba- and Zeeman-type spin-orbit couplings. The interplay between intravalley and intervalley scattering processes significantly modifies the extrinsic spin Hall conductivity in the conduction bands for different occupations. These intervalley scattering processes play a crucial role and provide us an experimentally accessible way to tune the extrinsic spin Hall effect in Janus.

We develop a general algebraic scheme to decompose fractional quantum Hall (FQH) wave functions based on the operator contraction multiplication. By introducing fermionic and bosonic operators and establishing three fundamental contraction rules, we achieve an exact decomposition of the Laughlin states. This approach naturally extends to multicomponent systems by factorizing coupled Jastrow factors via resultants and elementary symmetric polynomials, enabling a complete decomposition of the Halperin states. For the Halperin (2,2,1) state, we explicitly derive its basic expansion, identify root configurations, and reveal intra- and intercolor squeezing operators, thereby uncovering the underlying generalized Pauli principle. Using this method, we compute orbital entanglement spectra for up to 16 particles with decomposition dimensions exceeding ${10}^{11}$, obtaining edge excitation sequences that precisely match chiral Luttinger liquid theory. Our framework breaks through the long-standing limitations of Jack polynomials, provides a unified decomposition for both single- and multicomponent FQH states, and opens an alternative avenue for exploring wave functions for more complex FQH states.

Integrating atomically thin transition metal dichalcogenides (TMDCs) with metallic surfaces is an effective strategy to leverage their exceptional properties in advanced devices and catalysts, as it promotes efficient charge carrier injection and extraction from TMDC monolayers. Light-matter interactions in TMDC monolayers predominantly occur at the $K$ point, making the charge carrier dynamics at this point essential for optimizing charge transfer efficiency. However, direct probing of the dynamics at the $K$ point of TMDCs interfaced with metal substrates remains challenging. In this Letter, we employed pump-probe azimuth- and polarization-dependent final-state sum frequency generation spectroscopy to investigate the ultrafast dynamics of charge transfer at the $K$ point of a ${\text{MoS}}_2$ monolayer on an Au substrate. We observed ultrafast injection of photoexcited hot electrons from Au into the monolayer ${\text{MoS}}_2$ conduction band minimum, followed by a fast return ($\sim 2$ ps) and a trap-state-mediated slow return ($\sim 60$ ps) processes, driven by an internal electric field. The direct optical observation of the full electron dynamics at the $K$ point of ${\text{MoS}}_2$ monolayer in ambient conditions provides valuable insights into optimizing the transfer of charge carrier across the TMDC/metal interface through optimized contacts, informing the design of advanced TMDC-based devices with enhanced charge transfer rates.

Metal-organic frameworks (MOFs) combine high porosity with structural fragility, raising important questions about their mechanical stability. We develop a rigidity-based formalism in which spring networks parameterized by universal force field for metal-organic frameworks are used to construct rigidity and dynamical matrices. Large-scale analysis of 5682 MOFs from the computation-ready, experimental MOF 2019 database shows that most frameworks are formally overconstrained yet cluster sharply near the isostatic threshold, revealing accidental geometric modes and placing many MOFs near mechanical instability. In the representative case of UiO-66, we show that auxiliary long-range constraints introduced by tuning the neighbor cutoff lift these modes into soft, flat, finite-frequency bands. The results show that rigidity-matrix analysis can rapidly identify MOFs likely to remain mechanically stable. This near-criticality mirrors behavior known from topological mechanics and points to a deeper design principle in porous crystals.

Predicting the thermodynamic and electronic properties of halide perovskite (HP) alloys remains challenging due to their polymorphous character and the complex landscape of density-functional theory (DFT) calculated properties arising from local structural and chemical variations. Establishing clear links between atomic-scale distortions and macroscopic behavior is particularly difficult under alloyed conditions, where composition and symmetry vary continuously across configuration space. Through Natural Intelligence, we show that this landscape can be effectively mimicked by two simple yet physically grounded structural descriptors: the excess of cation–anion–cation ($B-X-B^{\prime }$) bond angles and the average cation–anion (B–X) bond length. Systematic DFT calculations across alloy families involving halogen ($X$-site), alkali ($A$-site), and group IV ($B$-site) substitutions reveal that excess $B-X-B^{\prime }$ angles capture octahedral distortions and correlate with mixing enthalpy. Meanwhile, the average B–X bond length emerges as a predictive metric for band-gap evolution in HP alloys.

The directional transport of magnetic skyrmions under microwave magnetic fields, known as the skyrmion ratchet effect, offers a promising approach for driving skyrmions in materials with poor electrical conductivity. While ratchet effects affected by disorders, biharmonic magnetic fields, and biased microwave fields have been widely discussed, the ratchet effect of magnetic skyrmions in systems with anisotropic Dzyaloshinskii-Moriya interaction (DMI) has not been investigated yet. In this work, we investigate the ratchet motion of skyrmions driven by a biharmonic magnetic field in systems with anisotropic DMI. Based on micromagnetic simulations, we demonstrate that anisotropic DMI effectively modulates the velocity and direction of skyrmion motion. Moreover, by inducing skyrmion deformation and altering its symmetry, the anisotropic DMI can lead to either nearly isotropic or highly anisotropic ratchet motion of skyrmions. Specifically, the skyrmion can exhibit identical ratchet velocities along different directions, or its motion can be confined to a specific direction, enabling highly direction-selective behavior. Based on the analysis of the frequency spectrum and the analytical theory, we attribute such directional anisotropy effects to the combined contributions of two factors, the anisotropic mass term and variation in the damping oscillation. These findings provide further insight into precise control of skyrmion motion based on the ratchet effect in insulating systems.

We study the proximity effect in the Hubbard model coupled to BCS superconductors describing a single-layer strongly correlated electron system in a phase-biased Josephson junction. We find two distinct gapped solutions, a Mott-like insulating (M phase) and a proximitized superconducting phase (S phase), separated by a first-order transition with hysteresis. In the M phase, the large correlation-induced charge gap strongly suppresses the critical current, while the S phase behaves as a 0-junction, with a proximitized gap that closes for $\varphi =\pi$ to yield a correlated metal. Phase bias and junction transparency can thus serve as tuning knobs to switch between conducting and insulating regimes. Working within the dynamical mean-field theory using the numerical renormalization group as the impurity solver, we associate M- and S-phase solutions with the doublet and singlet fixed points of the underlying superconducting Anderson impurity problem. We obtain detailed insight into the spectral structure on all energy scales. In the M phase, the self-energy has sub-gap resonances symmetrically located around the Fermi level resulting from the splitting of the “mid-gap pole” found in Mott insulators; this structure accounts for phase insensitivity.

Ab initio pseudoatomic orbital (PAO) Hamiltonians express the electronic structure of a solid in a compact, localized basis that spans the same Hilbert space as a conventional Slater-Koster tight-binding model, thereby providing an exact ab initio representation without any loss of accuracy. Building on this correspondence, we develop an environment-dependent tight-binding framework in which Slater-Koster hopping integrals are augmented with bond-screening functions that capture the local coordination environment. All parameters are determined by fitting to the PAO eigenvalue spectrum across multiple atomic configurations simultaneously, which breaks the degeneracy between screening and hopping parameters and yields physically meaningful, transferable models capable of generating Hamiltonians for large systems with ab initio precision. We demonstrate the efficiency and accuracy of the approach on four prototypical systems: bulk platinum, silicon surfaces, Si/Ge [001] superlattices, and twisted bilayer graphene with up to 4324 atoms. The method is implemented in the paoflow code and integrates seamlessly with its full postprocessing suite, enabling the evaluation of a broad range of electronic, optical, and transport properties.

We systematically investigate the nonlinear photogalvanic effect in few-layer graphene with various stacking orders, including AA- and AB-stacked bilayers, and AAA-, ABA-, and ABC-stacked trilayers. Using a tight-binding model to describe the electronic states, the shift current conductivity and jerk current conductivity are calculated over a broad spectral range from terahertz to visible frequencies. Our symmetry analysis reveals that a nonvanishing shift current emerges only in ABA-stacked trilayer graphene due to its broken inversion symmetry, with a peak conductivity reaching approximately $1.21\times {10}^{-13} \mathrm{A}\mathrm{m}/{\mathrm{V}}^2$ at optimal doping. In contrast, the jerk current, permitted in all structures, requires an in-plane static electric field and exhibits pronounced spectral tunability with chemical potential. These findings provide design principles for tunable, polarization-sensitive photodetection and energy-harvesting devices based on van der Waals few-layer films.