Recent band-structure calculations predicted that the ruthenium-based ternary silicides are three-dimensional Kramers nodal-line semimetals. Among them, NbRuSi and TaRuSi show bulk superconductivity (SC) below $T_c\sim 3\mathrm{K}$ and 4 K, as well as spontaneous magnetic fields. The latter indicate the breaking of time-reversal symmetry and, thus, unconventional SC in both compounds. Previous temperature-dependent muon-spin spectroscopy studies failed to distinguish whether such compounds exhibit single-gap or multigap SC. Here we report on systematic measurements of the field-dependent muon-spin relaxation rates in the superconducting state and on temperature-dependent electrical resistivity and specific heat under applied magnetic fields. Both the upper critical field and the field-dependent superconducting relaxation are well described by a two-band model. By combining our experimental results with numerical band-structure calculations, we provide solid evidence for multiband SC in NbRuSi and TaRuSi, and thus offer further insight into the unconventional and topological nature of their superconductivity.

Rare-earth perovskites $\left(R^{3+}{\mathrm{M}}^{3+}{\mathrm{O}}_3\right)$, with $e_g^1$ electronic occupation of the M $d$ states, display different types of metal-insulator transition. For manganites (M = Mn), the metal-insulator transition is usually induced by Jahn-Teller distortions, which stabilize orbital orderings (OO) at Mn sites. Among them, ${\mathrm{LaMnO}}_3$ shows a $C$-type OO and crystallizes with $Pbnm$ structure. Instead, ${\mathrm{TlMnO}}_3$ shows a very distinct $G$-type OO with an unusual $P\overline{1}$ structure. Employing first-principles calculations and symmetry-mode analysis, we rationalize structural and electronic origin of $G$-type OO in ${\mathrm{TlMnO}}_3$. Going further, we also consider ${\mathrm{TlNiO}}_3$, showing a metal-insulator transition driven by a breathing distortion, which stabilizes charge ordering (CO) at Ni sites. Interestingly, distinct Jahn-Teller and breathing distortions appearing in these compounds are very similar distortions of ${\mathrm{MO}}_6$ octahedra and stem from high-frequency phonon modes of their reference $Pm\overline{3}m$ structure. Our comparative study of ${\mathrm{TlMnO}}_3$, ${\mathrm{LaMnO}}_3$, and ${\mathrm{TlNiO}}_3$ highlights that, in spite of their distinct ground states, these compounds show a generic triggering of Jahn-Teller and breathing distortions by oxygen octahedra rotations, according to a mechanism previously reported in rare-earth nickelates.

In this work, we propose dual mechanical metamaterial designs, which exhibit both non-Abelian wave packet dynamics and non-Abelian band topology. We show that the band structure of self-dual metamaterials possesses a global twofold degeneracy and three tilted Dirac cones. Theoretical derivations demonstrate that non-Abelian wave packet propagation occurs when the Dirac cones are broken by perturbing the lattice masses. Breaking the twofold degeneracy by altering the lattice angle away self-duality, we also observe non-Abelian nodal braiding, which we theoretically characterize by introducing the Euler class and frame charge. We validate the duality of band structures in our design with both numerical calculations and experiments. Our metamaterial may provide a useful platform for quantumlike computation in mechanical systems with elastic wave propagation.

High-entropy materials (HEMs) enable essential technologies, and their properties are determined by multiple principal elements and their positions. Deciphering the atomic structure of HEMs is an essential prerequisite to elucidate their structure-property relationships. Although efficient heuristics has been developed to identify atomic structure, its implementation seems powerless to the near-infinite configuration space of HEMs. Here we propose a configuration decomposition strategy that allows an incredibly efficient search of an optimal special quasirandom structure (SQS) for random multicomponent alloys. Taking body-centered-cubic and face-centered-cubic ternary/quaternary alloys as examples, we demonstrate that the search efficiency for an optimal SQS by our strategy estimates to be more than ${10}^4\text{−}/{10}^7$-fold higher than the traditional exhaustive method; furthermore, the searched SQSs are far superior to those generated by a Monte Carlo simulated annealing technique. The proposed strategy is universal, and when combined with the Monte Carlo simulated annealing technique, it is possible to significantly further accelerate the search speed of a SQS. Our approach can thus identify the SQS of HEMs, a challenge currently considered impractical, and establishes the base for exploring the structure-property relationships of multicomponent materials.

The magnetic response of the Tsai-type 1/1 Au-Al-Gd approximant crystals (ACs) was quantitatively investigated in terms of the magnetic entropy change ($\mathrm{\Delta }{S}_M$) for different magnetic ground states. A comprehensive $\mathrm{\Delta }{S}_M$ map over a wide electron concentration range has been established, demonstrating the detailed variation of $\mathrm{\Delta }{S}_M$ across the entire magnetic phase diagram in the Tsai-type 1/1 ACs. Near the boundaries of the ferromagnetic (FM) phase, a clear deviation from the mean-field theory (MFT) was observed in both the Curie temperature ($T_{\mathrm{C}}$) and magnetic field ($H$) dependencies of the maximum magnetic entropy change ($\mathrm{\Delta }{S}_M^{\max }$). Contrary to general expectations, a high $\mathrm{\Delta }{S}_M^{\max }$ (7.2 J/(K mol Gd) under a 5-T field variation), even comparable to those of candidate materials for low-temperature magnetic refrigeration, was obtained within the antiferromagnetic (AFM) region near the FM/AFM phase boundary. The unexpected enhancement of $\mathrm{\Delta }{S}_M^{\max }$ toward the AFM region under high magnetic fields indicates an anomalous magnetic response in the present Tsai-type 1/1 AC, which is presumably associated with the breakdown of the MFT. The present finding suggests that tuning the magnetic ground state across the phase boundary is an effective strategy to enhance $\mathrm{\Delta }{S}_M$, even in general rare-earth intermetallic compounds.

The U(1) nonlinear sigma model (NLSM) with a one-dimensional (1D) Berry phase is studied by a renormalization group theory. Order-disorder transition in U(1) NLSMs in $D(\ge 2)$-dimensional space [($d+1$)-dimensional spacetime, $d\ge 1]$ is instigated by the proliferation of vortex excitations, where the 1D Berry phase term confers finite phase factors upon those vortex excitations that have finite projection in a subspace complementary to a topological direction with the 1D Berry phase. Due to a destructive interference effect caused by the phase factors, a partition function near the order-disorder transition point can be dominated by vortex excitations polarized along the topological direction with the Berry phase. The proliferation of the polarized vortex excitations helps to develop an extremely anisotropic correlation of the order parameter, which has a divergent correlation length along the topological direction with the Berry phase and a finite correlation length along the other directions. In order to explore such a possibility in $D=3$, we develop a perturbative renormalization group theory of a 3D model of vortex loops, in which loop segments interact via a $1/r$ Coulomb interaction, and the 1D Berry phase confers the phase factor upon each vortex loop. We derive renormalization group (RG) equations among vortex-loop fugacity, Berry phase term, and the Coulomb potential. The RG equations analyzed with approximations show that a characteristic size of the vortex loop along the topological direction becomes anomalously large near an order-disorder transition point, while the characteristic loop size within the other directions remains finite. Utilizing a duality mapping to a lattice model of a type-II superconductor under a magnetic field, we also argue that a global phase diagram of the 3D U(1) sigma model with 1D Berry phase should have an intermediate quasidisordered phase between ordered and disordered phases.

Kagome metals have emerged as pivotal materials in condensed matter physics due to their unique geometric arrangement and intriguing electronic properties. Understanding the origin of magnetism in these materials, particularly in iron-rich Fe-Sn binary compounds such as ${\mathrm{Fe}}_3\mathrm{Sn}$, holds a significant importance, as they represent potential candidates for permanent magnets with a high Curie temperature and a strong magnetic anisotropy. In the present study, we employ density functional theory and dynamical mean-field theory to analyze the electronic structure and magnetic properties of ${\mathrm{Fe}}_3\mathrm{Sn}$. Our investigation reveals the presence of several nearly flat bands and Weyl nodes at low excitation energies. The inclusion of local correlation effects is shown to push these features even closer to the Fermi energy, which may be important for their manipulation via external stimuli. Regarding magnetism, the Hubbard-like interaction leads to an increase of orbital polarization at the expenses of a minor reduction of the spin moment. The magnetic anisotropy energy exhibits a strong dependence on the particular choice of the Coulomb interaction parameters. Additionally, our detailed analysis of the interatomic exchange interactions indicates a significant contribution from the antisymmetric exchange, i.e., the Dzyaloshinskii-Moriya interaction, which showcases the existence of magnetic chirality in the system. Overall, our investigation highlights a strong interplay between the flat bands near the Fermi level, the local Coulomb interaction, and the triangular geometry of the lattice, which plays a crucial role in driving the magnetic properties of this material.

Two-dimensional (2D) materials with giant nonlinear optical (NLO) responses are essential for the development of advanced on-chip NLO devices. Using first-principles calculations, we predict a remarkable strain-induced enhancement of second-harmonic generation (SHG) in the high-performance 2D semiconductors ${\mathrm{Bi}}_2{\mathrm{O}}_{2}X$ ($X$ = S, Se, Te). The SHG susceptibilities of ${\mathrm{Bi}}_2{\mathrm{O}}_{2}X$ under strain are on the order of 1 nm/V, rivaling the highest values reported among 2D materials. This giant SHG response originates from gauge-invariant geometric quantities, including the quantum metric, the shift vector, and the triple phase product. The strain also induces a band-gap variation in ${\mathrm{Bi}}_2{\mathrm{O}}_{2}X$. Intriguingly, in ${\mathrm{Bi}}_2{\mathrm{O}}_2\mathrm{Te}$, strain-induced band-gap tuning drives a transition from a semiconductor to a half-metal, and ultimately to a polar metal. Our findings present a unique platform that combines strain-tunable band-gap engineering with exceptional NLO properties, while also highlighting the crucial role of quantum geometry in enhancing SHG.

Tight-binding models can accurately replicate the band structure and topology of crystalline systems. They have been widely used in solid-state physics due to their versatility and low computational cost. It is straightforward to build an accurate tight-binding model of any crystalline system using the crystal's maximally localized Wannier functions as a basis. Unfortunately, in three-dimensional (3D) photonic crystals, the transversality condition of Maxwell's equations precludes the construction of a basis of maximally localized Wannier functions via usual techniques. As a result, building reliable tight-binding models of 3D Photonic Crystals has not been straightforward up to now. In this work, we show how to overcome this problem using topological quantum chemistry, allowing us to express the band structure of the photonic crystal as a difference of band representations. This can be achieved by introducing a set of auxiliary modes, as recently proposed in Christensen et al. [Phys. Rev. X 12, 021066 (2022)], which regularizes the $\mathrm{\Gamma }$-point obstruction arising from the transversality constraint of Maxwell's equations. The decomposition into elementary band representations allows us to isolate a set of pseudo-orbitals that permit us to construct an accurate transversality-enforced tight-binding model that matches the dispersion, symmetry content, and topology of the 3D photonic crystal under study. Moreover, we show how to introduce the effects of a gyrotropic bias in the framework, modeled via nonminimal coupling to a static magnetic field. Our work provides the first systematic method to analytically model the photonic bands of the lowest transverse modes over the entire Brillouin zone via a transversality-enforced tight-binding model.

Leveraging the higher harmonics content of the Josephson potential in a superconducting circuit offers a promising route in the search for new qubits with increased protection against decoherence. In this work, we demonstrate how the flux tunability of a hybrid semiconductor-superconductor Josephson junction based on a single full-shell nanowire enables this possibility. Near one flux quantum, $\mathrm{\Phi }\approx {\mathrm{\Phi }}_0=h/2e$, we find that the qubit system can be tuned from a gatemon regime to a parity-protected regime with qubit eigenstates localized in phase space in the ${\phi }_0=0$ and $\pi$ minima of the Josephson potential $(cos2{\phi }_0)$. Estimates of qubit coherence and relaxation times due to different noise sources are presented.

A magnetic impurity with a larger $S=1$ spin remains partially screened by the Kondo effect when embedded in a metal. However, when placed within an $s$-wave superconductor, the interplay between the superconducting energy gap $\mathrm{\Delta }$ and the Kondo temperature $T_K$ induces a quantum phase transition from an underscreened doublet Kondo to an unscreened triplet phase, typically occurring when $\mathrm{\Delta }/T_K\approx 1$. We investigate the Kondo compensation of the impurity spin resulting from this partial screening across the quantum phase transition, which together with the spin-spin correlation function serves as a measure of the Kondo cloud's integrity. Deep within the unscreened triplet phase, $\mathrm{\Delta }/T_K\gg 1$, the compensation vanishes, signifying complete decoupling of the impurity spin from the environment, while in the partially screened doublet phase, $\mathrm{\Delta }/T_K\ll 1$, it asymptotically approaches $1/2$, indicating that half of the spin is screened. Notably, there is a universal jump in the compensation precisely at the phase transition, which we accurately calculate. The spin-spin correlation function exhibits an oscillatory pattern with an envelope function decaying as $\approx 1/x$ at short distances. At larger distances, the superconducting gap induces an exponentially decaying behavior $\approx exp(-x/{\xi }_{\mathrm{\Delta }})$ governed by the superconducting correlation length ${\xi }_{\mathrm{\Delta }}$, irrespective of the phase, without any distinctive features across the transition. Furthermore, the spectral functions of some relevant operators are evaluated and discussed. In terms of the methods used, a consistent description is provided through the application of multiplicative, numerical, and density-matrix renormalization group techniques.

The nonlinear anomalous Hall effect can reveal various aspects of the quantum geometry of Bloch electrons and disorder scattering that are not accessible in its linear counterpart, such as Berry curvature multipole and Berry connection polarizability. Here we study the nonlinear transport in a unique heterodimensional superlattice of ${\mathrm{V}}_5{\mathrm{S}}_8$. Strong third-order nonlinear Hall and longitudinal resistances persisting up to room temperature are observed. Moreover, the nonlinear resistances exhibit a marked magnetic field dependence. By using a special measurement method and a transformation formula to avoid issues largely overlooked in nonlinear transport experiments, we obtain nonlinear conductivity coefficients and their temperature and magnetic field dependences. First-principles calculations suggest that disorder-induced extrinsic contributions dominate the nonlinear transport at zero magnetic field, while the Berry connection polarizability can contribute a giant magnetic field dependence. The exceptionally strong nonlinear effects may stimulate further theoretical development in the nonlinear anomalous transport.

Manipulating orbital angular momentum (OAM) offers significant opportunities for advancing orbitronics in quantum device applications. In this study, we investigate topological phase transitions in two-dimensional ferromagnetic higher-order topological insulators driven by electronic correlations. We reveal that these transitions are intrinsically linked to the orbital Hall effect (OHE) through valley degrees. During the phase transitions, the OAM remains valley locked, giving rise to distinct orbital valley Hall effects, which reflect the inherent connection between topological properties and orbital transport. Using first-principles calculations and tight-binding models, we identify ${\mathrm{FeBr}}_2$ as a representative system to illustrate the intrinsic correlation between the OHE and higher-order topology. Notably, the OHE exhibits unique signatures across different topological phases, highlighting the interplay of electronic correlations and valley physics. This work provides a robust framework for understanding the interplay between topological phases and orbital transport phenomena, paving the way for different applications in topological materials and orbitronics.

Two-dimensional chromium chalcogenides $\mathrm{C}{\mathrm{r}}_{1-\delta }\mathrm{Se}$ have garnered significant interest owing to their intrinsic magnetic orders. In this study, we present the molecular beam epitaxy growth of $\mathrm{C}{\mathrm{r}}_{0.68}\mathrm{Se}$ thin films on $\mathrm{SrTi}{\mathrm{O}}_3$(111) substrates through precise control of Cr/Se flux ratio. A semiconducting-to-metallic transition has been realized by annealing of the $\mathrm{C}{\mathrm{r}}_{0.68}\mathrm{Se}$ films, and the mechanism of the phase transition is elucidated by scanning tunneling microscopy. Magnetic measurements reveal that the metallic $\mathrm{C}{\mathrm{r}}_{0.68}\mathrm{Se}$ films exhibit spin-glass-like behavior and perpendicular magnetic anisotropy at low temperatures. We also observe the anomalous Hall effect in $\mathrm{C}{\mathrm{r}}_{0.68}\mathrm{Se}$ thin films, which possibly originates from the skew-scattering mechanism. Our findings not only provide valuable insights into the controversial magnetic and electrical properties of $\mathrm{C}{\mathrm{r}}_{1-\delta }\mathrm{Se}$, but also advance their potential applications for spintronic device.

We report new results on classical nonrelativistic dipole conserving particles—fractons. These have been previously shown to exhibit “Machian” dynamics where the motion of one particle requires the presence of others in its proximity, such that dynamics produces ergodicity breaking steady states characterized by clusters. In this work, we show that although the global state breaks ergodicity, a limited version of ergodic behavior is retained within the clusters which may or may not be chaotic, depending on the nature of the microscopic Hamiltonian. In certain cases, we show that the dynamics can be mapped to that of a billiards particle in various stadiums. We also show that the many-fracton trajectories characteristically exhibit a central time or “Janus point” and thus a generic nonequilibrium bidirectional arrow of time.

We study the spectral properties and local topology of the Kane-Mele-Rashba model on a Sierpinski carpet fractal, constructed from a rectangular flake with an underlying honeycomb arrangement and open boundary conditions. When the system parameters correspond to a topologically trivial phase, the energy spectrum is characterized solely by bulk states that are not significantly modified by the system's fractality. For parameters corresponding to the quantum spin Hall insulator (QSHI) phase, in addition to bulk states, the energy spectrum exhibits in-gap topological states that are strongly influenced by the fractal geometry. As the fractal generation increases, the energy spectrum of the in-gap topological states develops a staircaselike profile, resulting in sharp peaks in the density of states. We also show that both the QSHI and the trivial phase exhibit a large gap in the valence-projected spin spectrum, allowing the use of the local spin Chern marker (LSCM) to index the local topology of the system. Fractality does not affect this gap, allowing the application of LSCM to higher fractal generations. Our results explore the LSCM versatility, showing its potential to access local topology in complex geometries such as fractal systems.

We report here on the successful growth by molecular beam epitaxy of high crystalline quality ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Se}:\mathrm{Bi}/{\mathrm{Pb}}_{1-y}{\mathrm{Eu}}_y\mathrm{Se}$ quantum wells (QWs) with $x=0.25$ and $y=0.1$, and on their magnetotransport characterization as a function of the QW thickness between 10 and 50 nm, temperatures down to 300 mK, perpendicular and tilted magnetic fields up to 36 T. The character of weak antilocalization magnetoresistance and universal conductance fluctuations points to a notably long phase-coherence length. It is argued that a relatively large magnitude of the dielectric constant of IV-VI compounds suppresses the decoherence by electron-electron scattering. The observation of Shubnikov–de Haas oscillations and the quantum Hall effect, together with multiband $k·p$ modeling, have enabled us to assess valley degeneracies, the magnitude of strain, subbands effective masses, and the topological phase diagram as a function of the QW thickness. Our results demonstrate that further progress in controlling Sn content, carrier densities, and magnetism in ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Se}/{\mathrm{Pb}}_{1-y}{\mathrm{Eu}}_y\mathrm{Se}$ QWs will allow for the exploration of the topologically protected quantized edge transport even in the absence of an external magnetic field.

The vibrational properties of semiconducting graphene buffer layer epitaxially grown on hexagonal silicon carbide are determined using first-principles calculations on a realistic structural model. Despite the important chemical and structural disorder associated with the partial covalent bonding with the substrate, the buffer-layer carbon atoms still display quasidispersive phonons mimicking those of graphene. The related frequency softening and broadening provide a natural interpretation of the measured Raman signal. The vibrations determining thermal conduction are found to delocalize completely on the SiC substrate, leading to an effective spatial separation between material components determining, respectively, electronic and thermal transport properties. This situation opens perspectives for thermoelectric applications.

The Dzyaloshinskii-Moriya interaction (DMI) creates spin spirals and supports chiral magnetic structures, making it highly desirable for low-power spin-based memory, logic, and signal transmission. However, achieving nonvolatile control of the DMI remains a big challenge, especially at ferromagnetic interfaces under ambient temperatures. Here, we demonstrate ferroelectricity-controlled modulation of the DMI at $\mathrm{Fe}/\mathrm{Pb}{\left(\mathrm{M}{\mathrm{g}}_{1/3}\mathrm{N}{\mathrm{b}}_{2/3}\right)}_{0.7}\mathrm{T}{\mathrm{i}}_{0.3}{\mathrm{O}}_3$ interfaces using Brillouin light scattering (BLS). We observed a variation of more than 65% in DMI strength upon applying a strong electric field. This modulation is attributed to the interfacial Rashba spin-orbit coupling induced solely by ferroelectricity, which exhibits hysteresis-loop-like behavior in response to electric fields. The capability to modulate the DMI with external electric fields at room temperature positions vortexlike structures as promising candidates for chiral spintronics.

Time-resolved pump-probe soft x-ray ptychography and scanning transmission x-ray microscopy were employed to study the magnetic domain-wall dynamics in microstructures of permalloy $({\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}; \mathrm{Py})$ with a weak growth-induced perpendicular magnetic anisotropy. The x-ray magnetic circular dichroism images of a micrometer-sized Py square (160 nm thickness) and an elliptical disk (80 nm thickness) show flux-closure patterns with domain walls that fall into alternating out-of-plane (OOP) magnetization states precipitated by the perpendicular anisotropy, which is a precursor of the nucleation of stripe domains at higher thicknesses. An oscillating magnetic field at frequencies from tens of MHz to GHz and up to 4 mT magnitude excited dynamic modes in the domain walls along with the vortex core gyration. The domain-wall dynamics include the translation of inversion points of the OOP magnetization and nucleation of one-dimensional spin waves.