Nagaoka ferromagnetism (NF) is a long-predicted example of itinerant ferromagnetism (IF) in the Hubbard model that has been studied theoretically for many years. The condition for NF, an infinite on-site Coulomb repulsion and a single hole in a half-filled band, does not arise naturally in materials. NF was only realized recently for the first time in experiments on a $2\times 2$ array of gated quantum dots. Dopant arrays and gated quantum dots in Si allow for engineering controllable systems with complex geometries. This makes dopant and quantum dot arrays good candidates to study NF in different array geometries through analog quantum simulation. Here we present theoretical simulations done for $3\times 3$ arrays and larger $N\times N$ arrays and predict the emergence of different forms of ferromagnetism in different geometries. We find NF in perfect $3\times 3$ arrays, as well as in $N\times N$ arrays for one hole doping of a half-filled band. The ratio of the hopping $t$ to Hubbard on-site repulsion $U$ that defines the onset of NF scales as $1/N^4$ as $N$ increases, approaching the bulk limit of infinite $U$ for large $N$. Additional simulations are done for geometries made by removing sites from $N\times N$ arrays. Different forms of ferromagnetism are found for different geometries. Loops show ferromagnetism, but only for three electrons. For loops, the critical $t/U$ for the onset of ferromagnetism scales as $N$ as the loop length increases. We show that the different dependencies on size for loops and $N\times N$ arrays can be understood by scaling arguments that highlight the different energy contributions to each different form of ferromagnetism. Our results show how analog quantum simulation with small arrays can elucidate the role of effects including wave-function connectivity; system geometry, size, and symmetry; bulk and edge sites; and kinetic energy in determining quantum magnetism of small systems.

Due to the quantum confinement effect, electrons in low-dimensional systems often display pronounced correlated effects, giving rise to various exotic electronic states such as charge density waves, Luttinger liquid states, and superconductivity. However, the electronic behavior in insulating quasi-one-dimensional materials is rarely explored. Here we report the pressure-driven Lifshitz insulator-metal transition and superconductivity in ${\mathrm{Bi}}_2{\mathrm{S}}_3$, which was reported to be a quasi-one-dimensional material, different from the two-dimensional sister compounds ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. Synchrotron x-ray diffraction and Raman spectroscopy confirm the stability of the original structure up to approximately 51 GPa. Notably, at around 21.8 GPa, ${\mathrm{Bi}}_2{\mathrm{S}}_3$ begins to exhibit metallic behavior across a broad temperature range due to the enhanced interchain interaction, evolving into a good metal by approximately 30.5 GPa. Above this critical pressure, we observe clear features of superconductivity, with the superconducting transition temperature ($T_c$) rising to approximately 3.7 K at 51.4 GPa. Ab initio calculations suggest that superconductivity in ${\mathrm{Bi}}_2{\mathrm{S}}_3$ arises from enhanced electron-phonon coupling, facilitated by a two-step bonding change following the Lifshitz insulator-metal transition around 30 GPa. While the compound shows an enhanced interchain interaction after the metallization, the electron density distribution shows a highly anisotropic behavior with a stronger conductive channel along a axis. This investigation provides a comprehensive understanding of the structural evolution and the underlying mechanisms of electron-phonon coupling induced superconductivity in ${\mathrm{Bi}}_2{\mathrm{S}}_3$. Our work provides a more intrinsic and clear phase diagram that perfectly explains the mechanism and greatly excludes the influence of nonhydrostatic conditions on the results. These insights are pivotal for advancing our understanding of topological phase transitions and superconductivity in analogous low-dimensional materials.

Regular nonlinear metasurfaces can relax the phase matching condition in conventional nonlinear optics, but unfortunately they still suffer from unsatisfactory nonlinear conversion efficiency due to the weak interaction between light and matter occurring within individual meta-atoms. In this work, we demonstrate that the interactions can be enhanced further in nonlocal metasurfaces by harnessing the quasiguided modes (QGMs). This enhancement arises mainly from an extended interaction length within the plane of nonlocal metasurfaces, together with the large local electric field enhancement provided by QGMs. Upon excitation, the incident light will couple into the QGM and propagate laterally within the metasurface plane. The distributed nonlinear signals generated at different positions of the nonlocal metasurface will be directed towards certain directions determined by the momentum matching. Thanks to the steep dispersion of QGM and the high robustness of the Q factor against wave vector, one can spectrally tune the QGM by simply changing the incident angle. Using a static nonlocal metasurface in the form of dimerized grating on a silicon slab incorporating a period-doubling perturbation, we report the experimental demonstration of third-harmonic generation enhanced by a general factor of 5 × ${10}^3$ with the operation wavelength easily tuned over a broad bandwidth.

Elasto-optic effects characterize the dependency of optical birefringence on strain. Thus, by changing the strain, one can control the optical properties of the sample. Large elasto-optic effects are desirable to improve the sensitivity of elasto-optic devices, their performances, and lower their energy consumption. Yet, the microscopic mechanisms underlying elasto-optic conversion effects are not well understood. For example, the temperature dependencies of the elasto-optic effect as well as the effect of the concentration in solid solutions have not been investigated from first principles. Here, we develop a coupled density functional theory and effective Hamiltonian numerical method to compute and understand the elasto-optic response of ferroelectric materials at finite temperature. In particular, we apply such scheme to calculate the elasto-optic response of ${\mathrm{BaTiO}}_3$ and ${\mathrm{Ba}}_{1-\mathrm{x}}{\mathrm{Sr}}_{\mathrm{x}}{\mathrm{TiO}}_3$ compounds in their tetragonal phase near room temperature, and report how elasto-optic coefficients can be significantly enhanced in the visible range. We also demonstrate that, and explain why, this effect can be enlarged in the THz-frequency range.

Flatband systems form a new class of materials that challenge the conventional wisdom of transport. The intrinsically strong electronic correlations combined with the vanishing kinetic energy scale suggest a sensitive dependence of transport properties on the flat band states and make interacting flat bands promising candidates for exotic quantum transport. Utilizing the Drude weight, we investigate the low-frequency spectral properties of the electrical conductivity within a controlled analytic treatment of the many-body response at temperatures above the bandwidth and the interaction strength and below the band gap. Focusing on this new transport regime, we demonstrate the potential of a quantum geometric approach for interacting systems and intermediate temperatures. The derived spectral weight yields unexplored four-point geometric contributions unrelated to the quantum metric, which questions the previously proposed projection methods. For long-ranged interactions, we show that the low-frequency spectral weight reduces to the variance of the Berry curvature.

Fractal lattices, featuring the self-similarity symmetry, are often geometric descents of parent crystals, possessing all their discrete symmetries (such as rotations and reflections) except the translational ones. Here, we formulate three different general approaches to construct real space Hamiltonian on a fractal lattice starting from the Bloch Hamiltonian on the parent crystal, fostering for example strong and crystalline topological insulators resulting from the interplay between the nontrivial geometry of the underlying electronic wave functions and the crystal symmetries. As a demonstrative example, we consider a generalized square lattice Chern insulator model and within the framework of all three methods we successfully showcase incarnations of strong and crystalline Chern insulators on the Sierpiński carpet fractal lattices. The proposed theoretical framework thus lays a generic foundation to build a tower of topological phases on the landscape of fractal lattices.

The plastic behavior of solids is crucial to their mechanical properties, and solid helium offers a unique perspective due to its quantum nature. Unlike typical materials, the defects in solid helium—such as dislocations and grain boundaries—are profoundly affected by atomic zero-point motion. This paper explores the mechanisms of helium's unusual plasticity by examining the dislocation dynamics during deformation. Measurements of shear moduli reveal that helium undergoes strain hardening due to dislocation interactions below $400\mathrm{mK}$, and an unexpected softening driven by dislocation alignment and grain boundary evolutions during subsequent warm-up. Notably, this softening is linked to dislocation “superclimb,” a quantum phenomenon involving superfluidity along specific dislocation cores. These findings shed light on the distinctive mechanical properties of solid helium and hint at a connection to macroscopic superfluidlike mass flow.

Rare earth ion doped crystals are state-of-the-art platforms for processing quantum information, particularly thanks to their excellent optical and spin coherence properties at cryogenic temperatures. Experimental observations have shown that the application of a static magnetic bias field significantly improves the coherence times in the rare earth ions ensemble, but only a few studies have focused on its dependency as a function of both magnetic field direction and amplitude. This is especially true for magnetic field amplitudes under the mT, and for low magnetic dipole moment ions. In this paper, we investigate the relationship between the magnetic field parameters and the decoherence caused by magnetic dipole-dipole coupling with the nearest-neighbor nuclear spins in the crystal. The primary non-Kramers rare earth ions investigated here are europium and praseodymium, but we also extend our study to the ytterbium Kramers ion due to its low magnetic dipole in the mT range. We perform theoretical investigations and simulations of the energy structure and coherence time evolution and identify good correspondences between experimental and simulated spin echo data. This work allows us to pinpoint the most relevant decoherence mechanisms in the considered magnetic field regime, and to predict favorable magnetic configurations.

For a Hamiltonian $\widehat{H}$ containing a position-dependent (disordered) potential, we introduce a sequence of landscape functions $u_n\left(\mathbf{r}\right)$ obeying $\widehat{H}{u}_n\left(\mathbf{r}\right)=u_{n-1}\left(\mathbf{r}\right)$ with $u_0\left(\mathbf{r}\right)=1$. For $n\to \infty ,1/v_n\left(\mathbf{r}\right)=u_{n-1}\left(\mathbf{r}\right)/u_n\left(\mathbf{r}\right)$ converges to the lowest eigenenergy $E_1$ of $\widehat{H}$ whereas $u_{\infty }\left(\mathbf{r}\right)$ yields the corresponding wave function ${\psi }_1\left(\mathbf{r}\right)$. For large but finite $n,v_n\left(\mathbf{r}\right)$ can be approximated by a piecewise constant function $v_n\left(\mathbf{r}\right)\simeq v_n^{\left(m\right)}$ for $\mathbf{r}\in {\mathrm{\Omega }}_m$ and yields progressively improving estimations of eigenenergies $E_m=1/v_n^{\left(m\right)}$ of locally fundamental eigenstates ${\psi }_m\left(\mathbf{r}\right)\propto u_n\left(\mathbf{r}\right)$ in spatial domains ${\mathrm{\Omega }}_m$. These general results are illustrated by a number of examples in one dimension: box potential, sequence of randomly placed infinite potential barriers, smooth and spatially uncorrelated random potentials, quasiperodic potential, as well as for the uncorrelated random potential in two dimensions.

The ytterbium-based delafossite ${\mathrm{NaYbSe}}_2$ is discussed as a prototype for a spin-orbit entangled, effective spin-1/2 triangular spin lattice with emerging antiferromagnetic correlations and a quantum spin liquid (QSL) ground state. We report on a comprehensive study of the static and dynamic anisotropic magnetism in single-crystalline samples of ${\mathrm{NaYbSe}}_2$ using NMR spectroscopy as a local-probe technique. We performed ${}^{23}\mathrm{Na}$ and ${}^{77}\mathrm{Se}$ NMR measurements in magnetic fields up to 16 T, applied along the in-plane and out-of-plane crystallographic directions and at temperatures from 300 down to 0.3 K. We could determine the anisotropic hyperfine contributions from the angular dependence of the ${}^{23}\mathrm{Na}$ and ${}^{77}\mathrm{Se}$ NMR spectra. In the paramagnetic regime, we probed the temperature dependence of the ${}^{23}\mathrm{Na}$ and ${}^{77}\mathrm{Se}$ spectral shift and the hyperfine coupling constants for fields applied along the principal crystal axes. The spin-lattice relaxation-rate data indicate critical spin fluctuations and the absence of long-range magnetic order at low magnetic fields and temperatures down to 0.3 K, evidenced by a monotonic increase of $1/T_1$ and associated spectral broadening. This is clear proof of the evolution of a critical QSL ground state with residual fluctuations down to lowest temperatures. At elevated fields, we observe the emergence of long-range order as the temperature-dependent $1/T_1$ rate passes through a pronounced maximum at $T_{\text{N}}$ at a given field, followed by a decrease at lower temperatures. Further, we find an inhomogeneous broadening of the ${}^{23}\mathrm{Na}$ spectra below $T_{\text{N}}$, probing the histogram of the local-field distribution in the presence of the field-induced order.

We report on a muon spin relaxation ($\mu \mathrm{SR}$) study on the polycrystalline noncentrosymmetric superconductor ${\mathrm{NbGe}}_2$ with superconducting transition temperature $T_c=2.0–2.1$ K. The zero-field $\mu \mathrm{SR}$ experiment indicates the absence of a spontaneous magnetic field in the superconducting state, showing the preservation of time-reversal symmetry in the superconducting state. The transverse-field $\mu \mathrm{SR}$ experiment is performed to map the phase diagram of ${\mathrm{NbGe}}_2$, from which clear evidence of both type-I and type-II superconductivities is obtained. More importantly, we clearly delineate the region in the phase diagram where type-I and type-II superconductivities coexist.

We study the phase diagram of spin-triplet superconductors, considering the effect of the external magnetic field on the electrons' spins. For a given symmetry of the order parameter and a generic orientation of the field, the paramagnetic limit for superconductivity diverges at low temperatures. For specific directions of the field, we identify a range of temperatures where the transition between normal and superconducting phases becomes of the first order. When two tricritical points exist along the transition line, a first-order phase transition between two superconducting phases may develop in vicinity of the tricritical point with lower temperature. We discuss the implications of our findings for the anisotropy of the upper critical field in ${\mathrm{UPt}}_3$, a candidate material for triplet superconductivity, when both the paramagnetic and orbital effects are taken into account.

Quench dynamics of topological phases has been studied in the past few years and dynamical topological invariants are formulated in different ways. Yet, most of these invariants are limited to minimal systems in which Hamiltonians are expanded by Gamma matrices. Here, we generalize the dynamical three-winding number in two-band systems into the one in generic multiband Chern insulators and prove that its value is equal to the difference of Chern numbers between postquench and prequench Hamiltonians. Moreover, we obtain an expression of this dynamical three-winding number represented by gapless fermions in phase bands depending only on the phase and its projectors, so it is generic for the quench of all multiband Chern insulators. Besides, we obtain a multifold fermion in the phase band in $(\mathbf{k},t)$ space by quenching a three-band model, which cannot happen for two-band models.

We theoretically investigate the thermally induced backaction effects in absorption-sensitive micro- and nanomechanical resonators. We propose a unified approach, enabling to simultaneously address both the effective dynamics and nonequilibrium phononic state, depending on the position of a punctual sensing (and heating) probe at the surface of the mechanical device. We present an analytical solution in terms of green functions for a unidimensional resonator whose thermomechanical deformation profile generally follows that of the mechanical losses. In particular, we find that both the dynamics and the mechanical fluctuations strongly depend on the loss distribution. The effect of the quantum fluctuations of the heat source is also discussed. Our approach provides the first steps towards a thorough, general platform for analyzing thermal backaction effects and their consequences, which may be of significance for future development in ultrasensitive nanomechanical research.

We investigate a specific limit of the one-dimensional non-Hermitian Hubbard Hamiltonian with complex interactions. In this framework, fermions with different spin quantum numbers are mapped onto two distinct spin species, resulting in two $XY$ spin chains that are coupled through Ising $ZZ$ interaction. The spin ladder model is then examined within the semiclassical limit using a spin-coherent state basis, where the dynamics is governed by a set of coupled Landau-Lifshitz-Gilbert equations. The non-Hermitian interactions in this model generate a spin-transfer torque term. We analyze the system's evolution toward several potential steady states, including a state of decoupled chains that is accessible when each chain has uniform initial conditions. Other possible steady states involve dimerized configurations with decoupled rungs, where the rung spins are either ferromagnetically or antiferromagnetically coupled, depending on the sign of the imaginary interactions. The spin dynamics is then studied in the infinite-temperature limit, which favors dimerized steady states. Despite the decoupled rungs, we observe the formation of ferromagnetic domains along each chain in the steady state. Additionally, we investigate the spin correlation functions and identify signatures of anomalous spin dynamics.

Here, by conducting a site-selective nuclear magnetic resonance (NMR) study on ${}^{75}\mathrm{As}, {}^{133}\mathrm{Cs}$, and ${}^{19}\mathrm{F}$ nuclei, we reveal the characteristic dynamics of two-dimensional (2D) pancake vortices in the highly anisotropic iron-based superconductor ${\mathrm{CsCa}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ (12442). First, the temperature-dependent nuclear spin-lattice relaxation rate divided by temperature ${\left(1/T_{1}T\right)}_{\mathrm{B}\parallel c}$ shows a typical crossover behavior below the superconducting temperature $T_{\mathrm{c}}$, which can be attributed to the dynamic freezing of 2D pancake vortices within the bilayer FeAs structure separated by the ${\mathrm{Ca}}_2{\mathrm{F}}_2$ block. Second, by analyzing the site-dependent $1/T_{1}T$, we confirm the spatial distribution of 2D pancake vortices with bent flux lines. Additionally, ${\left(1/T_{1}T\right)}_{\mathrm{B}\parallel ab}$ shows a stepwise decrease below $T_{\mathrm{c}}$, consistent with multiple superconducting gaps in iron-pnictide superconductors. More interestingly, $1/T_{1}T$ and $1/T_2$ display significant differences at the As1 and As2 sites, which cannot be explained by a simple flux motion model. Finally, our results offer a potential methodology based on the site-selective NMR technique to study the spatial structure of flux lines in highly anisotropic superconductors.

Using spectroscopic ellipsometry, we studied the optical conductivity of ${\mathrm{LaCoO}}_3$ with various degrees of strain. The optical response of the compressively strained ${\mathrm{LaCoO}}_3$ film is qualitatively similar to the one of the unstrained ${\mathrm{LaCoO}}_3$ polycrystalline sample and exhibits a redistribution of the spectral weight between $\sim 0.2$ and 6 eV, which is most likely related to the thermal excitation of the high-spin (HS) states. The optical response of the ferromagnetic (FM) tensile strained film exhibits clear signatures of the FM state. Below the Curie temperature $T_c=82$ K, a spectral weight transfer sets on from high energies (between 3.3 and 5.6 eV) to low energies (between 0.2 and 3.3 eV). The temperature dependence of the low-energy spectral weight can be understood in the framework of the HS biexciton model of Sotnikov et al. [SciPost Phys. 8, 082 (2020)] as corresponding to the increase of the concentration of the HS states that are stabilized below $T_c$. The magnitude of the redistribution of the spectral weight due to the formation of the FM state is sizable and corresponds to 0.009 $e$ per Co ion. We discuss it in terms of the effective kinetic energy of Co $3d$ bands.