Materials with a kagome lattice structure display a wealth of intriguing magnetic properties due to their geometric frustration and intrinsically flat band structure. Recently, topological and superconducting states have also been observed in kagome systems. The kagome lattice may also host a “breathing” mode that leads to charge density wave (CDW) states, if there is strong electron-phonon coupling, electron-electron interaction, or external excitation of the material. This “breathing” mode can give rise to candidate distortions such as the star of David (SoD) or its inverse structure [trihexagonal (TrH)]. To date, in most materials, only a single type of distortion has been observed. Here, we present angle-resolved photoemission spectroscopy measurements on the kagome superconductor ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ at multiple temperatures and photon energies to reveal the nature of the CDW in this material. It is shown that ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ displays two intertwined CDW orders corresponding to the SoD and TrH distortions. These two distinct types of distortions are stacked along the $c$ direction to form a three-dimensional CDW order where the two 2-fold CDWs are phase shifted along the $c$ axis. The presented results provide not only key insights into the nature of the unconventional CDW order in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$, but also an important reference for further studies on the relationship between the CDW and superconducting order.

Local memory—the ability to extract information from a subsystem about its initial state—is a central feature of many-body localization. We introduce, investigate, and compare several information-theoretic quantifications of memory and discover a hierarchical relationship among them. We also find that while the Holevo quantity is the most complete quantifier of memory, vastly outperforming the imbalance, its decohered counterpart is significantly better at capturing the critical properties of the many-body localization transition at small system sizes. This motivates our suggestion that one can emulate the thermodynamic limit by artificially decohering otherwise quantum quantities. Applying this method to the von Neumann entropy results in critical exponents consistent with analytic predictions, a feature missing from similar small finite-size system treatments. In addition, the decohering process makes experiments significantly simpler by avoiding quantum state tomography.

Based on the first-principles calculations and model analysis, we propose that the isostructural compounds ${\mathrm{Cu}}_2{\mathrm{SnS}}_3$ and ${\mathrm{Cu}}_2{\mathrm{SnSe}}_3$ are both the simplest nodal-line semimetals with only one nodal line in their crystal momentum space when spin-orbit coupling (SOC) is ignored. The inclusion of SOC drives ${\mathrm{Cu}}_2{\mathrm{SnS}}_3$ into a Weyl semimetal (WSM) state with only two pairs of Weyl nodes, the minimum number required for a WSM with time-reversal symmetry. In contrast, SOC leads ${\mathrm{Cu}}_2{\mathrm{SnSe}}_3$ to a strong topological insulator (STI) state. This difference can be well understood as there is a topological phase transition (TPT). In it, the Weyl nodes are driven by tunable SOC and annihilate in a mirror plane, resulting in a STI. This TPT, together with the evolution of Weyl nodes, the changing of mirror Chern numbers of the mirror plane, and the $Z_2$ indices protected by time-reversal symmetry, has been demonstrated by the calculation of ${\mathrm{Cu}}_2\mathrm{Sn}{\left({\mathrm{S}}_{1-x}{\mathrm{Se}}_x\right)}_3$ within virtual crystal approximation and an effective $k·p$ model analysis. Though our first-principles calculations have overestimated the topological states in both compounds, we believe that the theoretical demonstration of controlling the TPT and the evolution of Weyl nodes will stimulate further efforts to explore them.

Recent measurements in several different laboratories report the observation of an approximately linear-in-temperature resistivity with a large twist-angle-dependent slope (or temperature coefficient) in moiré twisted bilayer graphene down to a few K and sometimes to much lower temperatures. In this paper, we theoretically discuss this “strange metal” linear-in-temperature transport behavior from the perspective of resistive scattering by acoustic phonons, emphasizing the aspects of the transport data, which are and which are not consistent with the phonon scattering mechanism. An extensive theoretical comparison with a recent experiment [A. Jaoui et al., Nat. Phys. 18, 633 (2022)] is the central new aspect of this work.

Rapid proliferation of hyperspectral imaging in scanning probe microscopy creates unique opportunities to systematically capture and categorize higher dimensional datasets, toward insights into electronic, mechanical, and chemical properties of materials with nano- and atomic-scale resolution. Effective hyperspectral imaging requires a consistent framework for data analysis that would be broadly applicable, reproducible, and transferrable, conceptually resembling the success of integral transforms in image analysis. Here, we demonstrate application of similarity learning for resolving the structure of tunneling spectroscopy data, characterizing a superconducting material with sparse density of defects. Popular methods for unsupervised learning and discrete representation of the data in terms of clusters of characteristic behaviors were found to produce inconsistencies with respect to capturing the location and tunneling characteristics of defect sites. The underlying reason for their ambiguity was traced to continuous variation of the electronic properties across the surface and therefore the absence of clear structural boundaries in the low-dimensional latent spaces of the data. We supported this hypothesis by direct analysis of the distributions of Euclidean distances within the dataset. We further proposed distance rescaling with probabilistic description as a possible approach to mitigate the detrimental effect of the long tails of the distributions on the performance of clustering methods. Subsequently, we applied a more general, nonlinear similarity learning, where dimension reduction was explicitly trained to amplify similarities and dissimilarities among individual spectra. This approach was found to outperform several widely used methods for dimensionality reduction and produce a clear categorization of tunneling spectra. Significant spectral weight transfer associated with the electronic reconstruction by the vacancy sites was systematically captured, as was the spatial extent of the vacancy region. Given that a great variety of electronic materials will exhibit similarly smooth variation of spectral response due to random or engineered inhomogeneities, we believe our approach will be useful for systematic analysis of hyperspectral imaging with minimal prior knowledge as well as prospective comparison of experimental measurements with theoretical calculations with explicit consideration of disorder.

We develop an analytical description of static ferrodark solitons, the ${\mathbb{Z}}_2$ topological defects in the magnetic order, in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates. We find that the type-I ferrodark soliton has a single width while the type-II ferrodark soliton exhibits two characteristic length scales. The proposed Ansätze show excellent agreement with numerical results. Spin-singlet amplitudes, nematic tensor densities, and nematic currents of ferrodark solitons are also discussed. The ${\mathbb{Z}}_2$ topological defects in the mass superfluid order, dark-dark-dark vector solitons, are obtained exactly in the parameter regime where exact ferrodark solitons exist. The dark-dark-dark vector soliton has higher excitation energy than ferrodark solitons.

Besides magnetic and charge order, regular arrangements of orbital occupation constitute a fundamental order parameter of condensed matter physics. Even though orbital order is difficult to identify directly in experiments, its presence was firmly established in a number of strongly correlated, three-dimensional Mott insulators. Here, reporting resonant x-ray-scattering experiments on the layered van der Waals compound $1T\text{−}{\mathrm{TiSe}}_2$, we establish that the known charge density wave in this weakly correlated, quasi-two-dimensional material corresponds to an orbital ordered phase. Our experimental scattering results are consistent with first-principles calculations that bring to the fore a generic mechanism of close interplay between charge redistribution, lattice displacements, and orbital order. It demonstrates the essential role that orbital degrees of freedom play in ${\mathrm{TiSe}}_2$, and their importance throughout the family of correlated van der Waals materials.

In spin qubit arrays the exchange coupling can be harnessed to implement two-qubit gates and to realize intermediate-range qubit connectivity along a spin bus. In this work, we propose a scheme to characterize the exchange coupling between electrons in adjacent quantum dots. We investigate theoretically the transmission of a microwave resonator coupled to a triple quantum dot occupied by two electrons. We assume that the right quantum dot (QD) is always occupied by one electron while the second electron can tunnel between the left and center QDs. If the two electrons are in adjacent dots they interact via the exchange coupling. By means of analytical calculations we show that the transmission profile of the resonator directly reveals the value of the exchange coupling strength between two electrons. From perturbation theory up to second order we conclude that the exchange can still be identified in the presence of magnetic gradients. A valley splitting comparable to the interdot tunnel coupling will lead to further modifications of the cavity transmission dips that also depend on the valley phases.

The on-site Coulomb potential, $U$, and the covalent state of electronic orbitals play key roles for the Cooper pair symmetry and exotic electromagnetic properties of high-$T_{\mathrm{c}}$ superconducting cuprates. In this paper, we demonstrate a way to determine the value of $U$ and present the whole picture of the covalent state of Cu spins in the mother system of the La-based high-$T_{\mathrm{c}}$ superconducting cuprate, ${\mathrm{La}}_2{\mathrm{CuO}}_4$, by combining the muon spin rotation $\left(\mu \mathrm{SR}\right)$ and the density functional theory (DFT) calculation. We reveal local deformations of the ${\mathrm{CuO}}_6$ octahedron followed by changes in Cu-spin distributions caused by the injected muon. Adjusting the DFT and $\mu \mathrm{SR}$ results, $U$ and the minimum charge-transfer energy between the upper Hubbard band and the O $2p$ band were optimized to be 4.87(4) and 1.24(1) eV, respectively.

We study unitary evolution of bipartite entanglement in a circuit with nearest-neighbor random gates. Deriving a compact nonunitary description of purity dynamics on qudits we find a sudden transition in the purity relaxation rate the origin of which is in the underlying boundary localized eigenmodes—the skin effect. We provide the full solution of the problem, being one of the simplest iterations of two-site matrices, namely, that each is a sum of only two projectors. This leads to rich dynamics influenced by the Jordan normal form of the kernel and, most importantly, a spectrum that is completely discontinuous in the thermodynamic limit. It provides a simple example of how a seemingly innocuous many-body unitary evolution can harbor interesting mathematical effects: an effective nonsymmetric Toeplitz transfer matrix description causes a phantom relaxation, such that the correct relaxation rate is not given by the matrix spectrum, but rather by its pseudospectrum.

Spin-orbit torque (SOT) characterizations on magnetic heterostructures with perpendicular anisotropy are demonstrated on a projected vector field magnet via hysteresis loop shift measurement and harmonic Hall measurement with planar Hall correction. Accurate magnetic field calibration of the vector magnet is realized with the help of deep learning models, which can capture the nonlinear behavior between the generated magnetic field and the currents applied to the magnet. The trained models can successfully predict the applied current combinations under the circumstances of magnetic field scans, angle scans, and hysteresis loop shift measurements. The validity of the models is further verified, complemented by the comparison of the SOT characterization results obtained from the deep-learning-trained vector magnet system with those obtained from a conventional setup comprised of two separated electromagnets. The dampinglike (DL) SOT efficiencies ($|{\xi }_{\mathrm{DL}}|$) extracted from the vector magnet and the traditional measurement configuration are consistent, where $|{\xi }_{\mathrm{DL}}|\approx$ 0.22 for amorphous W and $|{\xi }_{\mathrm{DL}}|\approx$ 0.02 for $\alpha$-W. In this paper, we provide an advanced method to meticulously control a vector magnet and to conveniently perform various SOT characterizations.

The orbital Hall effect provides an alternative means to the spin Hall effect to convert a charge current into a flow of angular momentum. Recently, compelling signatures of orbital Hall effects have been identified in $3d$ transition metals. Here, we report a systematic study of the generation, transmission, and conversion of orbital currents in heterostructures comprising $3d$, $5d$, and $4f$ metals. We show that the orbital Hall conductivity of Cr reaches giant values of the order of $5\times {10}^5$ $\left[\frac{\hslash }{2e}\right]$ ${\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-1}$ and that Pt presents a strong orbital Hall effect in addition to the spin Hall effect. Measurements performed as a function of thickness of nonmagnetic Cr, Mn, and Pt layers and ferromagnetic Co and Ni layers reveal how the orbital and spin currents compete or assist each other in determining the spin-orbit torques acting on the magnetic layer. We further show how this interplay can be drastically modulated by introducing $4f$ spacers between the nonmagnetic and magnetic layers. Gd and Tb act as very efficient orbital-to-spin current converters, boosting the spin-orbit torques generated by Cr by a factor of 4 and reversing the sign of the torques generated by Pt. To interpret our results, we present a generalized drift-diffusion model that includes both spin and orbital Hall effects and describes their interconversion mediated by spin-orbit coupling.

The study of high-harmonic generation in confined quantum systems is vital to establishing a complete physical picture of harmonic generation from atoms and molecules to bulk solids. Based on a multilevel approach, we demonstrate how intraband resonances significantly influence the harmonic spectra via charge pumping to the higher subbands and thus redefine the cutoff laws. As a proof of principle, we consider the interaction of graphene nanoribbons, with zigzag as well as armchair terminations, and resonant fields polarized along the cross-ribbon direction. Here, this effect is particularly prominent due to many nearly equiseparated energy levels. In such a scenario, a cascade resonance effect can take place in high-harmonic generation when the field strength is above a critical threshold, which is completely different from the harmonic generation mechanism of atoms, molecules, and bulk solids. We further discuss the implications not only for other systems in a nanoribbon geometry, but also systems where only a few subbands (energy levels) meet this frequency-matching condition by considering a generalized multilevel Hamiltonian. Our study highlights that cascade resonance has a fundamentally distinct influence on the laws of harmonic generation, specifically the cutoff laws based on laser duration, field strength, and wavelength, thus unraveling additional insights in solid-state high-harmonic generation.

The recently synthesized ${\mathrm{Ag}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$ has been proposed as a Kitaev magnet in proximity to the quantum spin liquid phase. We explore its microscopic Hamiltonian and magnetic ground state using many-body quantum chemistry methods and exact diagonalization techniques. Our calculations establish a dominant bond dependent ferromagnetic Kitaev exchange between Ir sites and find that the inclusion of Ag $4d$ orbitals in the configuration interaction calculations strikingly enhances the Kitaev exchange. Furthermore, using exact diagonalization of the nearest-neighbor fully anisotropic $J\text{−}K\text{−}\mathrm{\Gamma }$ Hamiltonian, we obtain the magnetic phase diagram as a function of further neighbor couplings. We find that the antiferromagnetic off-diagonal coupling stabilizes long range order, but the structure factor calculations suggest that the material is very close to the quantum spin liquid phase and the ordered state can easily collapse into a liquid by small perturbations such as structural distortion or bond disorder.

We present an inexpensive first-principles approach for describing quantum paraelectricity that combines density functional theory (DFT) treatment of the electronic subsystem with quantum mechanical treatment of the ions through solution of the single-particle Schrödinger equation with the DFT-calculated potential. Using ${\mathrm{BaTiO}}_3$, ${\mathrm{SrTiO}}_3$, and ${\mathrm{KTaO}}_3$ as model systems, we show that the approach can straightforwardly distinguish between ferroelectric, paraelectric, and quantum paraelectric materials, based on simple quantities extracted from standard density functional and density functional perturbation theories. We calculate the influence of isotope substitution and strain on quantum paraelectric behavior and find that, while complete replacement of oxygen-16 by oxygen-18 has a surprisingly small effect, experimentally accessible strains can induce large changes. Finally, we collect the various choices for the phonon mass that have been introduced in the literature. We identify those that are most physically meaningful by comparing them with our results that avoid such a choice through the use of mass-weighted coordinates.