In 1991, it was proposed that fourfold-degenerate Landau levels formed by a single species of electrons could host a non-Abelian fractional quantum Hall (FQH) state with Fibonacci anyons at filling fraction $\nu =\frac{2}{3}$. In this work, we investigate how such degenerate Landau levels can be realized in rhombohedral-stacked tetralayer graphene. We identify the following key conditions which may stabilize the Fibonacci state: (1) A magnetic field of around 20 T is required if surface and interior carbons have the same energy level. If substrate hybridization raises the surface carbon energy level by ${\mathrm{\Delta }}_2=30\mathrm{meV}$ relative to interior carbon, the required field will have a larger range: 15–20 T. For ${\mathrm{\Delta }}_2=45\mathrm{meV}$, the range reaches a maximum: 7–20 T. (2) The displacement field must be tuned to achieve Landau level degeneracy. $\nu =\frac{3}{5}$ Fibonacci FQH states may also be realized in pentalayer rhombohedral graphene with a magnetic field of 12 T, and $\nu =\frac{1}{2}$ states with Ising anyons may occur in trilayer graphene for magnetic fields of 12–20 T at ${\mathrm{\Delta }}_2=0$ or 5–20 T at ${\mathrm{\Delta }}_2=45\mathrm{meV}$. We also study a simple interaction model to explore spin/valley polarization effects, and we see that the Fibonacci state may occur at $\nu =2/3+$ integer filling fractions, where the integer is 0 and 4 for sufficiently weak interaction, or can shift to 2 and 5 under a stronger interaction. The case ${\mathrm{\Delta }}_2=45\mathrm{meV}$ also produces states at negative filling fraction, e.g., $-\frac{2}{3}, -4\frac{2}{3}$. Here $\nu$ is defined with respect to the Hall conductance, ${\sigma }_{xy}=\nu \frac{e^2}{h}$.

Topological materials have attracted immense research interest as a fertile ground for realizing exotic quasiparticles, such as Dirac/Weyl/Majorana fermions. Symmetry plays a vital role in classifying and diagnosing topological states of matter. Among the 230 space groups (SGs), 65 chiral SGs have been shown to enforce the existence of Weyl points at time-reversal invariant momenta through Kramers degeneracy in the electronic band structures of nonmagnetic materials with spin-orbit coupling (SOC). Current research on the correlation between topological quasiparticles and chiral crystal structures has mainly focused on nonmagnetic electronic systems, while studies on chiral phononic and magnetic materials remain scarce. In this work, we summarize the properties of topological quasiparticles at high-symmetry points and along high-symmetry lines in the 65 chiral SGs and their enantiomers, both with and without SOC. We also identify the achiral supergroups that share the same translational symmetry with the corresponding chiral SGs, providing guidance for realizing a chiral SG through symmetry breaking from an achiral supergroup. Using the nonmagnetic chiral materials ${\mathrm{Al}}_2{\mathrm{Nb}}_3\mathrm{N}$, ${\mathrm{Al}}_2{\mathrm{Nb}}_3\mathrm{C}$, and ${\mathrm{Al}}_2{\mathrm{Ta}}_3\mathrm{C}$ in SG 213, as well as the experimentally synthesized chiral collinear ferromagnet ${\mathrm{NaMnFeF}}_6$ in SG 150, as examples, we further reveal the correlation between structural chirality and quasiparticle chirality in both phononic and electronic systems. Our work provides a new platform for studying the manipulation of topological quasiparticles in chiral systems.

As-, Sb-, and Bi-hyperdoped $n$-type Si layers are fabricated by ion implantation followed by pulsed laser annealing to systematically investigate dopant-dependent transport behavior. The resulting single-crystalline $n^{++}$ layers, with dopant concentrations up to $2.0\times {10}^{21} {\mathrm{cm}}^{-3}$, exhibit metalliclike behavior with carrier densities above $7.5\times {10}^{19} {\mathrm{cm}}^{-3}$, and mobilities exceeding 50 ${\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$. Phase-coherence lengths are extracted from magnetoconductance measurements using the two-dimensional Hikami-Larkin-Nagaoka model and reach 45–120 nm at low temperatures. A clear competition between weak localization (WL) and weak antilocalization (WAL) is observed in Bi-hyperdoped samples. Moreover, Si:Sb retains longer phase coherence at elevated temperatures, whereas structural disorder shortens low-temperature coherence in Si:Bi and strong spin-orbit scattering drives its observed WL-WAL crossover. In Si:Bi, the spin-orbit length ranges from 30 to 67 nm and shows no clear monotonic temperature dependence. These dopant-dependent transport characteristics may inform the design of silicon-based quantum and spintronic devices.

The interplay between band topology and nonlinear optical responses presents a promising platform for discovery, particularly for second-harmonic generation (SHG), which requires broken inversion symmetry. Here, we theoretically investigate the topological constraints on SHG in “essentially noncentric insulators” in which the topologically nontrivial phase of matter exists only in crystal classes without a center of inversion. Using the Floquet formalism combined with the Keldysh Green's function method, we derive explicit analytic expressions for the interband contributions to the SHG response driven by linearly polarized light in a 2D two-band model. Our analysis identifies that the transverse SHG response is intrinsically characterized by the shift vector. Based on the theory of “essentially noncentric insulators”, we show that the shift obstruction relation imposes a topological constraint, namely, that in a nontrivial phase the shift vector cannot be continuously tuned to zero across the entire Brillouin zone. As a result, the $T1a$ component of the transverse SHG response, which depends on this shift vector, is topologically constrained rather than quantized and cannot be globally eliminated. We further obtain the topological phase diagram for a representative 2D two-band model and compute its SHG response using both our formalism and Sipe's method. Our numerical results are in good agreement with Sipe's method and reveal a positive correlation trend between the SHG response and the average intercellular shift. These findings suggest that the identified topological invariants may serve as a design principle for engineering enhanced nonlinear optical responses.

A comprehensive study of second harmonic generation on thermally oxidized ${\mathrm{MoS}}_2$ flakes with the thickness ranging from monolayer up to seven layers is presented. Observing the fundamental nonlinear behavior for nontreated and oxidized ${\mathrm{MoS}}_2$ reveals that oxidation causes significant changes in the second harmonic response for all investigated structures. Excitation-power-dependent measurements to analyze the nonlinear behavior with respect to the oxidation time show progressive oxidation within the maximum oxidation time of 6 h under the considered oxidation conditions. Here, polarization-dependent measurements reveal the structural changes due to oxidation. Additionally, it is found that the oxidation depth is restricted to the topmost S layer and the oxidation behavior exhibits a layer dependency. These findings are supported by theoretical band structure calculations. The results demonstrate that the thermal oxidation progress of two-dimensional ${\mathrm{MoS}}_2$ can be monitored with nonresonant and noninvasive SH microscopy by following the distinct fingerprints of structural modification in the nonlinear response.

The recently synthesized quasihexagonal-phase fullerene network (${\mathrm{qHPC}}_{60}$) offers opportunities for 2D electronics. Through first-principles calculations, we reveal that ${\mathrm{qHPC}}_{60}/\mathrm{graphene}$ van der Waals heterostructures exhibit unique electronic properties, including the opening of a small band gap in graphene due to symmetry breaking. Specifically, while the band structure of ${\mathrm{qHPC}}_{60}$ remains essentially unchanged upon heterostructure formation, its Fermi level is shifted upward by interlayer charge transfer, leading to the formation of an $n$-type Schottky contact. Notably, a negative exciton formation energy is obtained, indicating a possible excitonic instability within the investigated quasiparticle band gap range. The Schottky barrier height can be effectively tuned by varying the interlayer distance or applying an external electric field. Furthermore, the periodic cage structure of ${\mathrm{qHPC}}_{60}$ induces spatially periodic charge-transfer sites in graphene, generating a substrate-modulated charge-order potential that modifies the graphene Dirac cone. These findings establish ${\mathrm{qHPC}}_{60}/\mathrm{graphene}$ heterostructures as a versatile platform for exploring emergent quantum phenomena and designing alternative electronic and optoelectronic devices.

Naturally oxidized copper (${\mathrm{CuO}}_x$) was cited as an exceptionally strong orbital current source despite the keen debate over the concept of orbital current. Here, we report unambiguous experimental evidence for the absence of a detectable orbital current torque in the Fe/Pt/${\mathrm{CuO}}_x$ trilayers. Using a magnetic metal detector of Fe thin film with a negligible self-induced torque, the dampinglike torque due to Pt/${\mathrm{CuO}}_x$ bilayers is clarified to entirely arise from the spin Hall spin current of the Pt. As the Pt thickness increases, the torque for Fe/Pt/${\mathrm{CuO}}_x$ and Fe/Pt/MgO increases coherently and monotonically, as exactly expected from the spin Hall effect of Pt and the drift-diffusion model of spin angular momentum. These findings suggest little generation of orbital current from the Pt/${\mathrm{CuO}}_x$ interface.

We propose a generalized composite fermion (CF) theory for fractional Chern insulators (FCIs) by adapting the quantum mechanics approach of CFs. The theoretical framework naturally produces an effective CF Hamiltonian and a wave-function ansatz, and the Bloch band characteristics of FCIs determine effective scalar and vector potentials experienced by CFs. Our analysis clarifies the construction of CF wave functions and state counting in CF phase space, which is subject to a density-of-states correction. We apply the theory to study the $\nu =-2/3$ FCI state of the twisted bilayer ${\mathrm{MoTe}}_2$ system, modeling it as either a $1/3$-filled electron band or a $2/3$-filled hole band. While both CF models exhibit trends and features consistent with exact diagonalization results, the electron-based model shows better agreement. Furthermore, we find that the FCI phase transition coincides with a gap closure in unoccupied CF $\mathrm{\Lambda }$ bands. This coincidence suggests that changes in CF excitons, such as CF-roton softening, may drive the transition.

The acoustic surface plasmon (ASP) with a low and linear dispersion relation is usually attributed to the strong Coulomb screening of surface states by bulk electrons, offering a promising avenue for studying fundamental quantum phenomena such as pairing glue for unconventional superconductivity and practical plasmonic applications. However, whether ASPs can persist in systems with reduced electronic screening remains unclear. Topological semimetals feature linear band touching, where the low density of states near the nodes leads to insufficient screening of the long-range Coulomb interactions and give rise to intriguing physical properties, providing a natural platform for exploring ASPs under weak-screening conditions. Here, using high-resolution electron energy loss spectroscopy with precise beam energy tuning, we unambiguously observe an ASP mode over a wide energy-momentum range on prototypical nodal-line semimetals, ZrSiS and ZrSiSe. We further find the ASP mode originates from the interplay between the floating surface states and substantially lower bulk charge carrier densities than conventional metals. Our results establish the physical foundation for the realization and application of ASPs on the surface of nodal-line semimetals.

The integration of hexagonal boron nitride (hBN) into next-generation 2D heterostructures requires a precise mapping of how structural defects modulate its exceptional thermal and mechanical properties. In this work, we utilize a machine-learned Atomic Cluster Expansion (ACE) potential to systematically investigate the structure–property relationships of monolayer hBN resulting from eight distinct defect types. Our simulations reveal a clear hierarchy of the impact of defects on thermal conductivity, where square-octagon ($4|8$) triplets and vacancies act as “super-scatterers” of phonons because of their massive local strain fields and disruption of planar continuity. Mechanically, we discover a strain-induced self-healing mechanism unique to Stone-Wales (SW) defect pairs; specifically, under uniaxial strain along the armchair direction, the work of tensile deformation drives the reorientation of all the homonuclear bonds back into the pristine hexagonal framework. This restoration, combined with the unfolding of initial lattice corrugations (“decrumpling”), results in an anomalous increase in fracture strain compared to the pristine limit. In contrast, all other defects lack this restorative capacity and trigger a “weakest-link” catastrophic failure. We also discover a new “hole” defect (H defect) that emerges when antisite nitrogen defects are strained along the armchair direction. These defects provide additional stability, increasing the fracture stress by $\approx 10\%$ compared with that under straining along the zigzag direction. These H defects remain stable after the strain is released. By bridging the gap between local atomic topology, lattice corrugation, and global failure limits, this study provides a framework to facilitate the functional design of defect-engineered hBN in high-performance flexible electronics and thermal management systems.

CeAlGe, a noncentrosymmetric tetragonal type-II Weyl semimetal, exhibits unique topological and magnetic properties, making it an excellent candidate for exploring novel magnetotransport phenomena. In this paper, we investigate the planar Hall effect (PHE) in single-crystalline CeAlGe, focusing on its intrinsic anisotropic features. We identify distinct angular singularities in the PHE, which correlate with longitudinal magnetoresistance. The angular singularities observed in both longitudinal and transverse resistivities in the planar geometry share a common origin associated with the noncollinear metamagnetic spin-canted regime.

We present a general theoretical approach for the quantitative description of parametric excitation of spin-wave modes in confined micromagnetic systems. This type of problem belongs to a broader class of nonlinear modal dynamics that arise across many areas of physics and engineering. The ferromagnetic sample is driven by parallel pumping with an external applied magnetic field having two tones at different frequencies, which are able to trigger parametric instability of two resonant modes. The two excited spin-wave modes interact in a strongly nonlinear fashion giving rise to quasiperiodicity, hysteresis and noncommutativity of steady-state oscillation regimes. To disentangle such a complex variety of dynamics, we develop a reduced-order model based on magnetization normal modes that is amenable of appropriate analytical treatment, leading to quantitative description of parametric instability thresholds, postinstability steady-state amplitude saturation and complete determination of phase diagrams for steady-state oscillation regimes. We have performed validation of the theory using numerical simulations. The phase diagrams allow to predict and explain all the features of the nonlinear interaction between the parametrically excited spin-wave modes and can be directly compared with experimental results.

The harmonic Hall measurements are commonly used to quantify the spin-orbit torque in ferromagnet/normal metal bilayers. The contribution from ordinary Nernst effect to the second harmonic voltages is usually assumed to be negligible and omitted in the data analysis. We show that in Cr/Co bilayers the ordinary Nernst effect cannot be neglected and can lead to largely exaggerated values of spin-orbit torque efficiency. Conducting additional experiments, we estimate the Nernst coefficient of Cr and find it comparable to the values reported for other metals. Consequently, the ordinary Nernst effect should be carefully considered when employing the harmonic Hall technique to quantify spin-orbit torque in metals, while the results of some previous works might need to be reexamined.

We present an extensive x-ray and neutron scattering study of the structure and magnetic excitations of ${\mathrm{Nd}}_2{\mathrm{PdSi}}_3$, a sister compound of ${\mathrm{Gd}}_2{\mathrm{PdSi}}_3$ that was recently found to host a skyrmion lattice phase despite its centrosymmetric crystal structure. Dispersive magnetic excitations were measured throughout the Brillouin zone and modeled to determine the magnetic interactions between Nd ions. Our analysis reveals that the magnetic interactions in this system extend over large distances and are significantly affected by a crystallographic superstructure formed by ordering of the Pd and Si atoms. The results suggest that the mechanism for the skyrmion phase formation in this family of materials, specifically ${\mathrm{Gd}}_2{\mathrm{PdSi}}_3$, is through the long-range Ruderman-Kittel-Kasuya-Yosida interactions rather than short-range triangular-lattice frustration.

Geometric phases play a fundamental role in understanding the geometric structure of quantum states, yet extending the Uhlmann phase to non-Hermitian systems poses significant challenges due to parameter-dependent inner product structures. In this work, we develop a comprehensive theory of the Uhlmann phase for quasi-Hermitian systems, where the physical Hilbert space metric varies with external parameters. By constructing a generalized purification that respects the quasi-Hermitian inner product, we derive the corresponding parallel transport condition and Uhlmann connection. Our analysis reveals that the parameter-dependent metric modifies the Uhlmann connection and leads to a finite-temperature distribution of Uhlmann-phase regions that differs from the standard Hermitian case. Applying this formalism to solvable two-level models, we uncover tunable finite-temperature Uhlmann-phase diagrams, where the parameter-dependent metric shifts and deforms the zeros of the Uhlmann amplitude, thereby reshaping the temperature intervals in which nontrivial Uhlmann phases occur. Furthermore, by extending established interferometric protocols originally developed for Hermitian systems, the geometric amplitude can be recast as a measurable Loschmidt amplitude between purified states, providing a practical and experimentally accessible pathway to investigate quasi-Hermitian mixed-state geometric phases and their finite-temperature transitions. This work establishes a unified framework for understanding mixed-state geometric phases in quasi-Hermitian quantum systems and, through its natural relation to the mixed-state quantum geometric tensor, opens new avenues for exploring local geometry in quasi-Hermitian thermal states.

We propose an approach to engineer the quantum Mpemba effect (QME)—wherein an initial state farther from equilibrium relaxes faster than a closer one—using the Liouvillian skin effect (LSE) in open quantum systems. In an open quantum chain with LSE, we show that the QME can be readily achieved simply by tailoring the spatial profile of the initial state, taking advantage of the distinct relaxation dynamics, algebraic, or exponential decay, exhibited by states localized on the left or right edges. This approach circumvents the need for delicate initial-state design or control parameter fine-tuning. Furthermore, when the initial single-particle correlation matrix contains off-diagonal elements, we reveal a multiple QME characterized by two distinct crossings in the Hilbert–Schmidt distance at different times, caused by distinct relaxation dynamics. Our work uncovers the deep connection between QME and LSE, offers an intuitive physical picture for the QME, and provides a straightforward protocol for initial state preparation, facilitating future experimental realizations.

The influence of hyperfine coupling to nuclear spins and of their quadrupolar splitting on the induced moment order in singlet ground state magnets is investigated. The latter are found among non-Kramers $f$ electron compounds. Without coupling to the nuclear spins, these magnets have a quantum critical point (QCP) separating the paramagnetic and induced moment regimes. The hyperfine interaction suppresses the QCP and leads to a gradual crossover between induced electronic and nuclear hyperfine coupling dominated magnetic order. It is shown how the critical temperature depends on the electronic and nuclear control parameters, including the nuclear spin size and its possible nuclear quadrupole splitting. In particular, the dependence of the specific heat on the control parameters and applied field is investigated for ferro- and antiferromagnetic order. It is shown that the three-peak structure in the electronic-induced moment regime gradually changes to a two-peak structure in the hyperfine coupling dominated nuclear moment order regime or for increasing field strength. Most importantly, the possibility of a reentrance behavior of magnetic order or likewise nonmonotonic critical fields due to hyperfine coupling influence is demonstrated. Finally, the systematic evolution of the phase diagram under the influence of nuclear quadrupole coupling is clarified.

Ultrafast spin relaxation in two-dimensional (2D) magnets is a cutting-edge topic in next-generation spintronics. Among existing 2D magnets, $\mathrm{F}{\mathrm{e}}_{3\text{−}x}{\mathrm{GaTe}}_2$ (FGT) is one of the few systems exhibiting room-temperature ferromagnetism and strong perpendicular magnetic anisotropy. However, the role of Fe-deficient non-stoichiometric nature in FGT remains poorly understood. In this work, we investigate the effect of nonstoichiometry (i.e., $\mathrm{F}{\mathrm{e}}_{\mathrm{I}}$ vacancies, $\mathrm{F}{\mathrm{e}}_{\mathrm{II}}$ vacancies, and $\mathrm{F}{\mathrm{e}}_{\mathrm{I}}-\mathrm{F}{\mathrm{e}}_{\mathrm{II}}$ covacancies) on the ultrafast spin dynamics of FGT by combining first-principles-based nonadiabatic molecular dynamics (NAMD) with phonon spectrum analysis. We identify two distinct spin relaxation pathways arising by the competition between spin orbit coupling (SOC) and electron phonon coupling (EPC): (1) a two-step process mediated by SOC and SOC-EPC occurring within and between Fe sites (path1), and (2) a direct EPC-driven $\mathrm{F}{\mathrm{e}}_{\mathrm{I}}\text{−}3d$ spin-up to $\mathrm{F}{\mathrm{e}}_{\mathrm{II}}\text{−}3d$ spin-up transition (path2). The latter pathway dominates the ultrafast relaxation, yielding a characteristic relaxation time of $\sim 100$ fs in $\mathrm{F}{\mathrm{e}}_{\mathrm{II}}$-deficient systems. Different Fe-vacancy configurations can modify the SOC- and EPC-assisted relaxation pathways: $\mathrm{F}{\mathrm{e}}_{\mathrm{II}}$ vacancies enhance EPC and accelerate spin decay; $\mathrm{F}{\mathrm{e}}_{\mathrm{I}}$ vacancies suppress EPC and prolong spin lifetimes, while $\mathrm{F}{\mathrm{e}}_{\mathrm{I}}\text{−}\mathrm{F}{\mathrm{e}}_{\mathrm{II}}$ co-vacancies provide a balanced modulation. These results indicate that Fe vacancies can modify the ultrafast spin-relaxation timescale and the associated electronic relaxation pathways in two-dimensional FGT.

Based on first-principles calculations and atomistic simulations, this work reveals the underlying mechanism of interlayer polarization coupling in governing topological spin states. We demonstrated polarization-guided Dzyaloshinskii-Moriya interaction sign reversal in the predicted multiferroic material ${\mathrm{Cr}}_2{\mathrm{Sn}}_2{\mathrm{Te}}_6$, interlayer polarization coupling mediated the multiple modulation of spin textures in the ${\mathrm{Cr}}_2{\mathrm{Sn}}_2{\mathrm{Te}}_6/{\mathrm{In}}_2{\mathrm{Se}}_2$ heterostructure, and the layer-dependent topological Hall effect in the ${\mathrm{Cr}}_2{\mathrm{Sn}}_2{\mathrm{Te}}_6/{\mathrm{In}}_2{\mathrm{Se}}_3/{\mathrm{Cr}}_2{\mathrm{Sn}}_2{\mathrm{Te}}_6$ sandwich structure. Combined with magnetic field control and ferroelectric polarization, the stable and flexible switching between various types of skyrmions can be achieved in ${\mathrm{Cr}}_2{\mathrm{Sn}}_2{\mathrm{Te}}_6$. In the ${\mathrm{Cr}}_2{\mathrm{Sn}}_2{\mathrm{Te}}_6/{\mathrm{In}}_2{\mathrm{Se}}_3$ heterostructure, the synergistic interaction between interlayer polarization coupling and strain effectively modulates the Dzyaloshinskii-Moriya interaction strength and magnetic anisotropy, enabling continuous and reversible transitions between multiple spin textures, including skyrmions, bimerons, in-plane ferromagnetic states, and out-of-plane ferromagnetic states. The ${\mathrm{Cr}}_2{\mathrm{Sn}}_2{\mathrm{Te}}_6/{\mathrm{In}}_2{\mathrm{Se}}_3/{\mathrm{Cr}}_2{\mathrm{Sn}}_2{\mathrm{Te}}_6$ integrates two polarization coupling modes within a single system, establishing a multitopological coupling platform in the vertical dimension. By regulating ferroelectric polarization reversal, directional transfer of spin textures and their topological Hall signals between different layers is achievable, enabling nonvolatile electrical control of the layer-dependent topological Hall effect.

Defect engineering offers a powerful route for tuning lattice thermal conductivity, yet a systematic comparison of the relative impact of distinct point defects and their extended counterparts in materials remains underexplored. In this work, we employ equilibrium molecular dynamics simulations to quantify the effects of vacancy, interstitial, substitutional, and void (extended) defects on lattice thermal conductivity in crystalline Si and Ge. Across all concentrations studied, vacancy and interstitial defects produce the greatest suppression of lattice thermal conductivity, whereas substitutional and void defects yield comparatively weaker scattering. The reduction in lattice thermal conductivity is strongly concentration dependent, with deviations between defect classes diminishing at low defect fractions. To elucidate the microscopic origins of these trends, we analyze changes in phonon transport through mass-weighted phonon density of states, revealing that defects which introduce large local strain fields or strong mass perturbations induce the most significant modifications in vibrational spectra. Our results provide a unified, comparative framework for understanding how different classes of defects in Si and Ge affect phonon scattering and thermal transport, enabling more rational design at the defect level for tuning thermal conductivity and thermal management applications.