The chiral Luttinger liquid develops quantum chaos as soon as a—however slight—nonlinear dispersion is introduced for the microscopic electronic degrees of freedom. For this nonlinear version of the model, we identify an infinite family of translation-invariant interaction potentials with corresponding modulated symmetries. These symmetries are highly unconventional: they are modulated in momentum space (and do not seem to have an easy physical interpretation). We develop a systematic understanding of these symmetries and study the resulting blocks in the Hamiltonian. In particular, this approach allows us to predict the analytic Hamiltonian block sizes and derive asymptotic scaling laws in the limit of large total momentum. These blocks are reminiscent of Hilbert space fragmentation in that, even though they are labeled by a symmetry, this symmetry is highly nonlocal and does not have a simple interpretation. We corroborate this result by studying entanglement entropy and level statistics.

The divacancies in 4$H$-SiC attract significant attention for use as qubits owing to their spin and photoluminescence (PL) properties and near telecom PL emission. Nevertheless, there exist some ambiguities in the interpretation of their optically detected magnetic resonance (ODMR) spectra, especially at elevated temperatures. In this study, we investigate the divacancy configurations PL1–PL7 using PL and ODMR. We record the full temperature dependence between liquid-helium temperature (3.8 K) and room temperature (295 K), obtained with two different laser energies and different laser polarizations. We also present PL data recorded simultaneously with the ODMR. Our study allows us to continuously follow the evolution of all divacancy configurations in ODMR with temperature, even though their signature is not distinguishable in PL at elevated temperatures. We identify all lines in the room-temperature ODMR spectrum and show that a hypothetical defect PL7, assumed in earlier work to stem from another divacancy configuration, does not exist and its ODMR signal at room temperature is fully explained with PL4. We also provide direct PL evidence on the spatial distribution of PL5, PL6, and a new PL3a defect, showing their presence only close to the surface of the sample, thus corroborating their association with divacancies near stacking faults. We address also the role of the upconversion of the photoluminescence in the ODMR spectra observed at higher temperatures.

Amorphous CoFeB, a soft ferromagnetic material with low magnetic damping, high saturation magnetization, and high spin polarization, has gained significant attention for spintronic applications. However, the increasing demand for higher-speed and higher-capacity data storage devices has led to growing energy consumption concerns. The anomalous Nernst effect (ANE), a transverse thermoelectric phenomenon, offers a promising solution to address this energy challenge in spintronic devices, however, the origin of ANE in amorphous CoFeB is not well understood yet. While previous studies have independently explored the anomalous Hall effect (AHE) and ANE in amorphous CoFeB, a comprehensive investigation combining both effects which can provide deeper insights into the underlying mechanisms is missing. By studying the temperature dependence of AHE and ANE, we have been able to evaluate critical parameters such as longitudinal and transverse electrical and thermoelectric conductivities, as well as Hall and Nernst angles. Our findings suggest a significant contribution from intrinsic mechanism, i.e., from local Berry curvature, to the anomalous transverse electrical and thermoelectric effects in amorphous CoFeB thin films. The observed intrinsic contribution is particularly notable given the challenges associated with studying the electronic structure of amorphous materials.

In the past decade, photoemission orbital tomography (POT) has evolved into a powerful tool to investigate the electronic structure of organic molecules adsorbed on surfaces. Here we show that POT allows for the comprehensive experimental identification of all molecular orbitals in a substantial binding energy range of more than 10 eV. Making use of the angular distribution of photoelectrons as a function of binding-energy, we exemplify this by extracting an orbital-resolved projected density of states for 15 $\pi$ and 23 $\sigma$ orbitals from the experimental data of the prototypical organic molecule bisanthene (${\mathrm{C}}_{28}{\mathrm{H}}_{14}$) on a Cu(110) surface. These experimental results for an essentially complete set of orbitals within the given binding-energy range serve as stringent benchmarks for electronic structure methods, which we illustrate by performing density functional calculations employing four frequently used exchange-correlation functionals. By computing the respective molecular-orbital-projected densities of states, a one-to-one comparison with experimental data for an unprecedented number of 38 orbital energies became possible. The quantitative analysis of our data reveals that the range-separated hybrid functional HSE performs best for the investigated organic/metal interface. At a more fundamental level, the remarkable agreement between the experimental and the Kohn-Sham orbital energies over a binding-energy range larger than 10 eV suggests that—perhaps unexpectedly—Kohn-Sham orbitals approximate Dyson orbitals, which would rigorously account for the electron extraction process in photoemission spectroscopy but are notoriously difficult to compute, in a much better way than previously thought.

Superior to ferromagnetic (FM) valleytronics, antiferromagnetic (AFM) counterparts exhibit ultradense and ultrafast potential due to their intrinsic advantages of zero stray field, terahertz dynamics, and compensated moments of antiferromagnets. However, the physics of spontaneous valley polarization is mainly rooted in FM hexagonal lattices and is rarely used to explore the simultaneous spin and valley polarizations in AFM materials. Here, we propose a general stacking method to achieve valley polarization in AFM bilayer systems. The hexagonal ferrovalley material is used as the basic building unit, and then the space-inversion centrosymmetric bilayer system with interlayer AFM ordering is constructed by horizontal mirror and twofold rotational operations, which can exhibit spontaneous valley polarization. In this construction process, the rarely explored layer-locked hidden valley polarization, hidden Berry curvature, and layer Hall effect are involved, and an out-of-plane electric field can be used to detect hidden valley polarization and to realize layer-locked anomalous valley Hall effect. We use three examples to illustrate our proposal. First, the Janus GdBrI is used to illustrate concepts and effects involved in our design process. Second, the ${\mathrm{RuBr}}_2$ is used to demonstrate other phenomena, including valley polarization transition and near-ideal quantum spin Hall insulators. Finally, we use our design principles to understand the valley polarization of experimentally synthesized MnSe from a new perspective. Our works establish a robust general scheme to achieve valley polarization in AFM bilayer systems, thereby opening up new avenues for AFM valleytronics.

We use our developed AI search engine (InvDesFlow) to perform extensive investigations regarding ambient stable superconducting hydrides. A cubic structure ${\mathrm{Li}}_2{\mathrm{AuH}}_6$ with Au-H octahedral motifs is identified to be a candidate. After performing thermodynamical analysis, we provide a feasible route to experimentally synthesize this material via the known LiAu and LiH compounds under ambient pressure. The further first-principles calculations suggest that ${\mathrm{Li}}_2{\mathrm{AuH}}_6$ shows a high superconducting transition temperature ($T_c$) $\sim$ 140 K under ambient pressure. The H-$1s$ electrons strongly couple with phonon modes of vibrations of Au-H octahedrons as well as vibrations of Li atoms, where the latter is not taken seriously in other previously similar cases. Hence, different from previous claims of searching metallic covalent bonds to find high-$T_c$ superconductors, we emphasize here the importance of those phonon modes with strong electron-phonon coupling (EPC). And we suggest that one can intercalate atoms into binary or ternary hydrides to introduce more potential phonon modes with strong EPC, which is an effective approach to find high-$T_c$ superconductors within multicomponent compounds.

We demonstrate that the kinematically constrained model of Rydberg atoms on a two-leg ladder with staggered detuning, $\mathrm{\Delta }\in [0,1]$, has quantum many-body scars (QMBSs) in its spectrum and represents a nonperturbative generalization of the paradigmatic PXP model defined on a chain. We show that these QMBSs result in coherent many-body revivals and site-dependent magnetization dynamics for both Néel and Rydberg vacuum initial states around $\mathrm{\Delta }=1$. The latter feature leads to eigenstate thermalization hypothesis (ETH)-violating finite imbalance at long times in a disorder-free system. This is further demonstrated by constructing appropriate local imbalance operators that display nonzero long-time averages for Néel and vacuum initial states. We also study the fidelity and Shannon entropy for such dynamics which, along with the presence of long-time finite imbalance, brings out the qualitatively different nature of QMBSs in PXP ladders with $\mathrm{\Delta }\sim 1$ from those in the PXP chain. Finally, we identify additional exact midspectrum zero modes that stay unchanged as a function of $\mathrm{\Delta }$ and violate ETH.

We propose a theoretical framework for the realization of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing in a helical Shiba chain subjected to an out-of-plane Zeeman field, analyzed through a self-consistent Bogoliubov–de Gennes mean-field formalism approach. A chain of magnetic adatoms with helical spin texture deposited on the surface of a common $s$-wave superconductor has emerged as a pivotal platform for realizing topological Majorana zero modes (MZMs). Our study reveals the crucial role of finite momentum pairing of Cooper pairs in the form of a FFLO state which also supports topological MZMs at the ends of the chain. Interestingly, we demonstrate that FFLO pairing facilitates nonreciprocal charge transport, giving rise to a superconducting diode effect in our system where both time-reversal and inversion symmetries are broken. Such a diode effect stems directly from the presence of finite Cooper pair momentum of the FFLO ground state. Our comprehensive analysis highlights the intricate interplay between the richness of the helical Shiba chain, out-of-plane Zeeman field, and FFLO pairing in the emergence of MZMs and driving the superconducting diode effect. These findings offer valuable insights into the design and realization of topological superconducting devices with diode-like properties, potentially advancing technological applications in quantum computing and superconducting electronics.

Vanadium undergoes a solid-solid phase transformation from a body-centered cubic (bcc) to a rhombohedral (rh) structure under high pressure, significantly affecting its physical and mechanical properties, including strength and transport properties. In this paper, we investigated the electrical resistivity of vanadium subjected to shock compression. Using a four-probe technique in conjunction with one- and two-stage light gas guns, in situ measurements of the electrical resistivity of vanadium foil were performed at pressures reaching $\sim 50$ GPa and temperatures nearing 750 K. The findings reveal a distinct discontinuity in electrical resistivity at shock pressures between 32 and 36 GPa. These results align with prior shock compression experiments involving sound velocity measurements, suggesting that the bcc-to-rh phase transformation in vanadium happens at 32–36 GPa under shock loading—substantially lower than the transition pressure reported under hydrostatic conditions (62–69 GPa at room temperature). In this paper, we confirm that the bcc-to-rh phase transformation in vanadium, driven by shear softening, is strongly dependent on hydrostatic stress, where the nonhydrostatic and shock compression could significantly facilitate the transformation.

We present a comprehensive study of the high-pressure behavior of ${\mathrm{ReO}}_3$ using x-ray and neutron diffraction, Raman scattering, and first-principles calculations. We show that the ambient pressure $Pm\overline{3}m$ structure converts at 0.7 GPa in a continuous phase transition directly to a cubic phase with space group $Im\overline{3}$, which is then stable up to at least 15 GPa. We show that previous reports of monoclinic $C2/c$ and rhombohedral $R\overline{3}c$ structures in this pressure range are an artifact due to an alteration of the sample by high-flux synchrotron x-ray radiation. The structural pressure dependence of the $Im\overline{3}$ phase is reported as well as the precise equation of state. Raman scattering data of both natural and isotopically enriched ${}^{18}\mathrm{O}$ samples are presented. The data shed light on the unusual transition and densification mechanism due to progressive tilting of essentially rigid ${\mathrm{ReO}}_6$ octahedra.

Chemical substitution is an effective route to manipulate the magnetic exchange couplings and modify the magnetic properties. However, replacement between ${\mathrm{Cd}}^{2+}$ and ${\mathrm{Hg}}^{2+}$ cations, both belonging to IIB group in the periodic table but having quite close ionic radii, is rarely studied. In this work, the chemical-pressure effect in $A{\mathrm{Co}}_2\left({\mathrm{Te}}_3{\mathrm{O}}_8\right)\left({\mathrm{SO}}_4\right)(A=\mathrm{Hg},\mathrm{Cd})$ is reported, which is an $S=1/2$ structural screw-chain antiferromagnetic series with two unique Co positions. Magnetic susceptibility, specific heat, and high-field magnetization measurements on both polycrystal samples suggest that Hg compound experiences two successive antiferromagnetic transitions at $T_{\mathrm{N}1}=25.5\mathrm{K}$ and $T_{\mathrm{N}2}=21.5\mathrm{K}$ in zero field, and multiple field-induced transitions at $B_1=10.5\mathrm{T}, B_2=13\mathrm{T}$, and $B_3=19.5\mathrm{T}$ at 1.6 K. By contrast, a single magnetic transition takes place at $T_{\mathrm{N}}=20$ K and $B_{\mathrm{c}}=10.7\mathrm{T}$ in Cd compound. Different twists of ${\mathrm{CoO}}_6$ octahedra are discussed to be responsible for the distinct magnetic behaviors. To further understand the influence of the chemical pressure, additional anisotropic characterizations are performed on Hg single crystal and subsequently the magnetic field $\mathrm{versus}$ temperature phase diagrams are established. Large magnetic anisotropy is observed with the moments lying within the $bc$ plane. Besides, a possible field-induced order-disorder transition is uncovered under the application of a magnetic field along the $b$ axis. The opposite features of the anisotropic magnetic susceptibility in Hg compound might demonstrate separate antiferromagnetic orders of the two Co sublattices, the discrepancy of which is reduced due to the weakened twist of ${\mathrm{CoO}}_6$ octahedra in Cd compound, leading to a simultaneous occurrence of these transitions instead.

The behavior of strongly interacting electrons in bands with Berry curvature is a problem of wide interest. In this paper, we study this problem by numerically studying a fluxed Hubbard-type model on a square lattice. Using this model, we demonstrate that a metallic ferromagnet in electron bands equipped with Berry curvature can develop noncoplanar spin order in which spin-polarization axes at different positions span finite solid angles. We find that spin chirality can emerge in this setting by doping or adding gauge flux on top of a collinear ferromagnet. This result supports the prediction of spin chirality occurring through an emergent spin-orbital interaction. Meanwhile, our result shows that on top a ferromagnetic background, the spin chirality emerges at a finite threshold value of orbital magnetization, resembling the predicted behavior in theory.

A common feature of both single- and multiband superconductors is the presence of a crossover between conventional type I and type II superconductivity through an intertype (IT) domain in the phase diagram of the magnetic response. In diffusive single-band superconductors, this domain is known to be very narrow due to scattering by nonmagnetic impurities. Recently, it has been shown that in multiband superconductors the IT domain can significantly expand when the band diffusion coefficients differ substantially. In this paper, we demonstrate that this expansion is a general feature of diffusive multiband superconductors and is accompanied by a qualitative change in vortex-vortex interaction. This interaction shifts from the combination of short-range attraction and long-range repulsion, typical of diffusive single-band IT superconductors, to the inverse configuration of short-range repulsion and long-range attraction. Strikingly, this latter behavior resembles the vortex interaction in clean IT superconductors. Consequently, one can expect a corresponding rearrangement of vortex configurations—from the mixtures of Abrikosov and giant vortices, expected in diffusive single-band IT superconductors, to vortex chains, labyrinths, and clusters, which are characteristic of vortex matter in clean IT superconducting materials.

Flat-band systems are of great interest due to their strong electron correlations and unique band geometry. In this paper, we investigate quantum geometric effects on a collective mode of the order parameter, the Higgs mode. We derive the Higgs-mode correlation length and further answer two key questions: whether the third-harmonic generation (THG) of the Higgs mode persists in a flat-band system and the relative contributions of quantum-metric-mediated quasiparticle fluctuations and Higgs fluctuations to THG. We numerically calculated the correlation length and THG in the Lieb lattice. In contrast to traditional single-band results, we find that the correlation length determined by the quantum metric plays the role of the effective mass to determine the dispersion of the Higgs mode, and Higgs fluctuations contribute almost entirely to THG, with the quasiparticle contribution being negligible. This finding provides valuable guidance for detecting Higgs modes in flat-band systems through optical methods and reveals the profound influence of quantum geometry in flat-band systems.

The structural response to high pressures as well as to high temperatures of $(1\text{−}x){\mathrm{PbTiO}}_3\text{−}x\mathrm{Bi}\left({\mathrm{Zn}}_{0.5}{\mathrm{Ti}}_{0.5}\right){\mathrm{O}}_3$ with $x=0.08$, $(1\text{−}x){\mathrm{PbTiO}}_3\text{−}x\mathrm{Bi}\left({\mathrm{Mg}}_{0.5}{\mathrm{Ti}}_{0.5}\right){\mathrm{O}}_3$ with $x=0.17$, and ${\mathrm{PbTiO}}_3$ single crystals was studied by in situ pressure-/temperature-dependent polarized Raman spectroscopy, complemented by synchrotron x-ray diffraction analysis at ambient pressure and different temperatures. The compositional and pressure dependencies of phonon anomalies indicate the existence of local-scale antiferrodistortive structural entities inside the perovskite $\left({\mathrm{ABO}}_3\right)$ polar tetragonal matrix, the fraction of which is enhanced by the substitution of ${\mathrm{Bi}Me\mathrm{O}}_3$ for ${\mathrm{PbTiO}}_3$. The type of cation (${\mathrm{Zn}}^{2+}$ versus ${\mathrm{Mg}}^{2+}$) replacing ${\mathrm{Ti}}^{4+}$ at the B site affects the coherence within the dominant single-perovskite polar tetragonal matrix and the coupling between the “defect” double-perovskite antiferrodistortive entities. As a result, on increasing pressure, the partial substitution of $\mathrm{Bi}\left({\mathrm{Mg}}_{0.5}{\mathrm{Ti}}_{0.5}\right){\mathrm{O}}_3$ triggers a structural instability at lower pressure values as compared to pure ${\mathrm{PbTiO}}_3$, whereas that of $\mathrm{Bi}\left({\mathrm{Zn}}_{0.5}{\mathrm{Ti}}_{0.5}\right){\mathrm{O}}_3$ preserves the polar tetragonal phase over a wider pressure range. Furthermore, at ambient pressure B-site ${\mathrm{Zn}}^{2+}$ favors the coherence between local ${\mathrm{BO}}_6$ tetragonal distortions already above the Curie temperature $T_C$, causing a larger unit-cell tetragonality below $T_C$; in contrast, B-site ${\mathrm{Mg}}^{2+}$ reduces the local ${\mathrm{BO}}_6$ anisotropy and disturbs the correlation between polar ${\mathrm{AO}}_{12}$ tetragonal distortions below $T_C$, which results in a considerable reduction of both the unit-cell tetragonality and accumulated volume strain on cooling between $T_C$ and room temperature.

Out-of-time-ordered correlators (OTOCs) are widely used to investigate information scrambling in quantum systems. However, directly computing OTOCs with classical computers is an expensive procedure. This is due to the need to classically simulate the dynamics of quantum many-body systems, which entails computational costs that scale rapidly with system size. Similarly, exact simulation of the dynamics with a quantum computer (QC) will either only be possible for short times with noisy intermediate-scale quantum devices or require a fault-tolerant QC which is currently beyond technological capabilities. This motivates a search for alternative approaches to determine OTOCs and related quantities. In this paper, we explore four parameterized sets of Hamiltonians describing local one-dimensional quantum systems of interest in condensed matter physics. For each set, we investigate whether classical kernel methods can accurately learn the $\mathit{XZ}$-OTOC and a particular sum of OTOCs as functions of the Hamiltonian parameters. We frame the problem as a regression task, generating small batches of labeled data with classical tensor network methods for quantum many-body systems with up to 40 qubits. Using this data, we train a variety of standard kernel machines and observe that the Laplacian and radial basis function kernels perform best, achieving a coefficient of determination ($R^2$) on testing sets of at least 0.7167, with averages between 0.8112 and 0.9822 for the various sets of Hamiltonians, together with small root mean squared error and mean absolute error. Hence, after training, the models can replace further uses of tensor networks for calculating an OTOC function of a system within the parameterized sets. Accordingly, the proposed method can assist with extensive evaluations of an OTOC function.

The topological crystalline insulator SnTe exhibits surface-dependent Dirac cones, which are located at non-time-reversal-invariant momenta on the (001) and (110) surfaces, but at time-reversal-invariant momenta on the (111) surface. Motivated by the recent experimental evidence of Majorana vortex end modes (MVEMs) and their hybridization on the (001) surface [Liu et al., Nature (London) 633, 71 (2024)], we present a comprehensive investigation of Majorana vortex phases in SnTe with proximity-induced superconductivity, including topological classification, surface-state Hamiltonians analysis, and lattice model calculations. By utilizing rotational and magnetic mirror symmetries, we present two equivalent methods to reveal the topology of Majorana phases on different surfaces. We find that the MVEMs on the (001) and (110) surfaces are protected by both magnetic group and rotational symmetries. In contrast, the MVEMs on the (111) surface are protected by magnetic group or particle-hole symmetry. Due to the different properties of Dirac fermions in the $\overline{\mathrm{\Gamma }}$ and $\overline{M}$ valleys on the (111) surfaces, including Fermi velocities and energy levels, we find that abundant vortex phase transitions can occur for the [111]-direction vortex. As the chemical potential shifts from the surface to bulk states, the number of robust MVEMs can change from $2\to 1\to 0$. These vortex transitions are characterized by both $Z$ winding number and $Z_2$ pfaffian topological invariants.

Electronic ordering is prevalent in correlated systems, which commonly exhibit competing interactions. Here, we use x-ray diffraction to demonstrate a cascade of pressure-induced order-disorder transformations, with propagation vectors ${\mathbf{q}}_{\mathrm{CDW}}=\left(\frac{1}{2}0\frac{1}{2}\right), {\mathbf{q}}^{*}=\left(\frac{1}{3}\frac{1}{3}\frac{1}{2}\right)$, and ${\mathbf{q}}^{†}=\left(\frac{1}{3}\frac{1}{3}\frac{1}{3}\right)$, in the kagome metal FeGe. In the pressure interval between $4<p<10$ GPa, ${\mathbf{q}}_{\mathrm{CDW}}$ and ${\mathbf{q}}^{*}$ coexist and the spatial extent of the $\sqrt{3}\times \sqrt{3}$ order is nearly long range at $\sim 15$ GPa, $\sim 30$ unit cells. Above $\sim 25$ GPa, the periodic lattice distortion has a propagation wave vector of ${\mathbf{q}}^{†}=\left(\frac{1}{3}\frac{1}{3}\frac{1}{3}\right)$ at room temperature. The cascade of phase transitions is captured by the Ising model of frustrated triangular lattices and modeled by Monte Carlo simulations based on the dimerization of trigonal ${\mathrm{Ge}}_1$. The pressure dependence of the integrated intensities and correlation lengths of ${\mathbf{q}}_{\mathrm{CDW}}, {\mathbf{q}}^{*}$, and ${\mathbf{q}}^{†}$ demonstrating a competition between the $2\times 2$ and $\sqrt{3}\times \sqrt{3}$ phases prove the tunability of order-disorder phase transitions under pressure and the rich landscape of metastable/fragile phases of FeGe.

We report the synthesis of single crystals of the $R_3{\mathrm{Ni}}_{30}{\mathrm{B}}_{10}$ $(R=\mathrm{La},\mathrm{Ce})$ system which realizes the tetragonal $P4/nmm$ (No. 129) space group. We performed single crystal, transmission x-ray diffraction measurements to determine the crystal structure. Additionally, we characterized the samples through magnetization, resistivity, and heat capacity measurements. The $R=\mathrm{Ce}$ system exhibits mixed-valence states and we observe maxima in the heat capacity at $T_1^{*}=6\text{K}$ and $T_2^{*}=2\text{K}$ (both absent for $R=\mathrm{La}$) with no corresponding features in the resistivity or magnetization. We discuss the potential roles of multipolar and short-ranged/partial order in connection to the $T_1^{*}$ anomalous order.