Antiferromagnetic (AFM) materials are considered as promising building blocks of novel data storage devices, however, detecting and manipulating AFM domains remains challenging. Here, we demonstrate that the two antiphase domains of the magnetoelectric antiferromagnet ${\mathrm{LiCoPO}}_4$ can be distinguished by their light absorption difference. Using visible and infrared spectroscopy, we observed spontaneous nonreciprocal absorption, also referred to as directional dichroism, at the crystal-field excitations of ${\mathrm{Co}}^{2+}$ ions coordinated by distorted oxygen octahedra. This absorption contrast is particularly pronounced near the telecommunication wavelength of 1550 nm. These findings allowed us to image the AFM domains in ${\mathrm{LiCoPO}}_4$ using a simple transmission light microscopy setup. Our findings suggest that optical magnetoelectric effects offer promising routes for probing the AFM order parameter in noncentrosymmetric transition metal compounds.

The transport of spin currents across interfaces is relatively well studied, while the transport properties of orbital currents are just starting to be examined. In Cr/Ni bilayers, the spin-orbit torque (SOT) due to the orbital current generated in the Cr layer is believed to dominate over torques of other origins. In this work, we study SOT in Cr/$X$/Ni trilayers, where $X$ is an ultrathin spacer of a different material. Using the SOT as a proxy for the orbital current transferred from the Cr to the Ni layer, we compare Cr/$X$/Ni results to Pt/$X$/Ni, the system in which spin current generated in the Pt layer plays a dominant role. We find that across 12 different spacers the apparent interface transparency to the orbital current is comparable to or larger than the spin current.

Solving ill-posed problems is central to a variety of scientific investigations. We focus here on the analytic continuation of imaginary-time data obtained from quantum Monte Carlo (QMC) simulations to the real frequency axis, which involves the numerical inversion of a Laplace transform, a well-known ill-posed problem. We propose an unsupervised autoencoder-type neural network to address this problem, and we show that our encoder-decoder approach can extract high-quality real frequency spectral functions from imaginary-time Green's functions $G\left(\tau \right)$. With a deeply tunable architecture we demonstrate, for artificial test data with noise added, that the autoencoder neural network can locate sharp features of spectral functions, which may be lost using maximum entropy (MaxEnt) methods currently in use. We demonstrate the strength of the autoencoder approach by applying it to QMC results for a single-band Hubbard model as a function of density, and we show that it is more robust against noise in the input $G\left(\tau \right)$ compared to MaxEnt. The proposed method is general and can also be applied to other ill-posed inverse problems.

Detecting symmetry-breaking hidden orders with conventional probes has been a long-standing challenge in the field of magnetism. Higher-rank multipolar ordering—anisotropic charge and magnetization distributions arising from a combination of spin-orbit coupling and crystalline environments—is a quintessential example of such hidden orders, where new protocols of direct detection remain highly desirable. In this paper, we propose nonlinear Hall effects as a probe for multipolar ordering in metallic systems. Taking inspiration from the family of Pr-based heavy-fermion compounds, Pr(Ti,${\mathrm{V})}_2{\mathrm{Al}}_{20}$, we formulate a minimal cubic-lattice model of conduction electrons coupled to a ferro-octupolar order parameter. The time-reversal-breaking order leads to a band structure that supports strong quadrupolar moments of Berry curvature (BC). Using a semiclassical Boltzmann formalism in conjunction with a symmetry analysis, we demonstrate that the BC quadrupoles produce a third harmonic generation of the Hall voltage $\left[V_H\left(3\omega \right)\right]$ measurable in an AC Hall experiment. Properties of the Hall response such as its anisotropy, its dissipationlessness, and its dependence on the order parameter are also examined. Our paper encourages an alternative realm of investigation of multipolar ordering from nonlinear transport experiments.

Current complementary metal-oxide semiconductor (CMOS) quantum processors employ dense gate arrays to define quantum dots, making them susceptible to crosstalk from capacitive coupling between the dots and the neighboring gates. Small but sizable spin-orbit interactions can transfer this electrostatic crosstalk to the spin $g$ factors, creating a dependence of the Larmor frequency on the electric field generated by gate electrodes positioned tens of nanometers apart. We study the Stark shift from tens of CMOS spin qubits measured in nine devices and develop a theoretical framework that explains how electric fields couple to the spin of the electrons in increasingly complex arrays. This includes electric fluctuations that limit qubit coherence times $T_2^{*}$. The results will aid in the design of robust strategies to scale CMOS quantum technology.

The electron-phonon interaction is in many ways a solid state equivalent of quantum electrodynamics. Being always present, the e-p coupling is responsible for the intrinsic resistance of metals at finite temperatures, making it one of the most fundamental interactions present in solids. In typical metals, different regimes of e-p scattering are separated by a characteristic phonon energy scale—the Debye temperature. However, in metals harboring very small Fermi surfaces a new scale emerges—the Bloch-Grüneisen temperature. This is a temperature at which the average phonon momentum becomes comparable to the Fermi momentum of the electrons. Here we report sub-Kelvin transport and sound propagation experiments on the Dirac semimetal ${\mathrm{ZrTe}}_5$. The combination of the simple band structure with only a single small Fermi surface sheet allowed us to directly observe the Bloch-Grüneisen temperature and its consequences on electronic transport of a 3D metal in the limit where the small size of the Fermi surface leads to effective restoration of translational invariance of free space. Our results indicate that on entering this hydrodynamic transport regime, the viscosity of the Dirac electronic liquid undergoes an anomalous increase beyond the theoretically predicted $T^5$ temperature dependence. Extension of our measurements to strong magnetic fields reveal that, despite the dimensional reduction of the electronic band structure, the electronic liquid retains characteristics of the zero-field hydrodynamic regime up to the quantum limit. This is vividly reflected by an anomalous suppression of the amplitude of quantum oscillations seen in the Shubnikov-de Haas effect.

Entanglement entropy characterizes the correlation of multiparticles and unveils the crucial features of open quantum systems. However, the experimental realization of exploring entanglement in non-Hermitian systems remains a challenge. In parallel, quantum walks have offered the possibility of studying the underlying mechanisms of non-Hermitian physics, which includes exceptional points, the non-Hermitian skin effect, and non-Bloch phase transitions. Unfortunately, these studies have only involved and prevailingly focused on the behavior of a single particle. Here, we propose and experimentally realize quantum walks of two indistinguishable photons in engineered non-Hermitian photonic lattices. We have successfully observed the unidirectional behavior of quantum walks in the bulk far from the edges induced by the skin effect. Moreover, we experimentally reveal the suppression of entanglement that is caused by the skin effect in non-Hermitian systems. Our study may facilitate a deep understanding of entanglement in open quantum many-body systems that are far from thermal equilibrium.

We investigated the magnetic and magnetoelastic properties of ${\mathrm{MnSc}}_2{\mathrm{Se}}_4$ single crystals at low temperature under a magnetic field directed along the crystallographic [111] axis. The magnetization data at low temperature show a linear increase with magnetic field, until saturation is reached above 15 T. In ultrasound, a longitudinal acoustic mode shows a softening in field, which is absent for a transverse acoustic mode. We discuss these results using a microscopic model based on the framework of linear spin-wave theory. The magnetic and magnetoelastic data are qualitatively reproduced by considering magnon-phonon interactions arising from exchange-striction coupling between the crystal lattice and spin-wave fluctuations in the zero-temperature limit.

Inelastic neutron scattering (INS) has traditionally been one of the primary methods for investigating quantum magnets, particularly in identifying a continuum of excitations as a hallmark of spin fractionalization in quantum spin liquids (QSLs). However, INS faces severe limitations due to its inability to distinguish between such QSL signatures and similar excitation continua arising from highly frustrated magnetic orders with large unit cells or classical spin liquids. In contrast, two-dimensional coherent spectroscopy (2DCS) has emerged as a powerful tool to probe nonlinear excitation dynamics, offering insights into the underlying mechanisms behind these broad spectral features. In this paper, we utilize classical molecular dynamics techniques to explore the 2DCS responses of frustrated magnets with dominant Kitaev interactions. Comparing the classical and quantum versions of the pure Kitaev model, our results indicate both clear similarities, in the form of sharp line features, and clear distinctions, in the locations of these features and in selection rules. Moreover, in the extended $K\mathrm{\Gamma }{\mathrm{\Gamma }}^{\prime }$ model, we show that the 2DCS response of the Kitaev spin liquid is completely distinct from that of large unit cell magnetic orders, despite both generating a broad continuum in INS. Additionally, we demonstrate the extreme sensitivity of classical 2DCS to thermal fluctuations and discuss the potential significance of quantum coherence in experimental settings. Overall, our paper illustrates the potential of 2DCS in resolving the complex physics underlying ambiguous spin excitation continua, thereby enhancing our understanding of the dynamics in these frustrated systems.

We study the topological bands in twisted bilayer transition metal dichalcogenides in an external magnetic field. We first focus on a paradigmatic model of ${\mathrm{WSe}}_2$, which can be described in an adiabatic approximation as particles moving in a periodic potential and an emergent periodic magnetic field with nonzero average. We understand the magnetic-field-dependent spectra of ${\mathrm{WSe}}_2$ based on the point net zero flux, at which the external field cancels the average emergent field. At this point, the band structure interpolates between the tightly bound and nearly free (weak periodic potential) paradigms as the twist angle increases. For small twist angles, the energy levels in a magnetic field mirror the Hofstadter butterfly of the Haldane model. For larger twist angles, the isolated Chern band at zero flux evolves from nearly free bands at the point of net zero flux. We also apply our framework to a realistic model of twisted bilayer ${\mathrm{MoTe}}_2$, which has recently been suggested to feature higher Landau-level analogs. We show that at negative unit flux per unit cell, the bands exhibit remarkable similarity to a backfolded parabolic dispersion, even though the adiabatic approximation is inapplicable. This backfolded parabolic dispersion naturally explains the similarity of the Chern bands at zero applied flux to the two lowest Landau levels, offering a simple picture supporting the emergence of non-Abelian states in twisted bilayer ${\mathrm{MoTe}}_2$. We propose the study of magnetic-field-dependent band structures as a versatile method to investigate the nature of topological bands and identify Landau-level analogs.

Point defects in wide-band-gap semiconductors have emerged as leading qubit candidates for realizing quantum information processing. Due to the strong spatial localization of the wave functions, these defects can be described as artificial atoms or molecules in a solid-state matrix. Here we propose the positively charged scandium–nitrogen-vacancy defect ${\left({\mathrm{Sc}}_{\mathrm{Al}}{V}_{\mathrm{N}}\right)}^{+}$ in AlN as a potential quantum memory, similar to the ST1 center in diamond, based on hybrid density functional theory calculations. ${\mathrm{Sc}}_{\mathrm{Al}}{V}_{\mathrm{N}}$ is stable in the positive charge state over a wide range of Fermi-level positions, where it possesses a singlet ground state and triplet shelving state. By comparing with $V_{\mathrm{N}}^{+}$, we elucidate the role of Sc in redshifting the emission energy and enhancing the intersystem crossing via increased spin-orbit coupling. Nuclear spins in the vicinity of ${\left({\mathrm{Sc}}_{\mathrm{Al}}{V}_{\mathrm{N}}\right)}^{+}$ may be used as a resource to store the quantum information. We outline an optical spin manipulation protocol for ${\left({\mathrm{Sc}}_{\mathrm{Al}}{V}_{\mathrm{N}}\right)}^{+}$ and discuss its utility as a solid-state qubit.

Unusual time-delayed changes in the x-ray diffraction parameters of ${\mathrm{LiNbO}}_3$ and ${\mathrm{LiNbO}}_3:\text{Fe}$ crystals were observed under nanosecond laser impact. Subnanosecond time resolution in the registration of diffraction rocking curve (DRC) dynamics was achieved through the synchronization of a 4 ns laser pulse with the circulation phase of electron bunches within a synchrotron storage ring. The response of the crystals to optical impact resulted in a reversible center-of-mass shift and integral intensity decrease of the DRC recovering in $\sim 35$ ns. The dynamics of lattice deformation indicates the process of formation and subsequent decay of an electrical charged layer near the surface due to directed migration of photoelectrons as a result of the bulk photovoltaic effect. The drop in the integral intensity of the DRCs is apparently caused by a running wave generated by a sharp change in the deformation of the crystal lattice. In the case of the nominally undoped crystal, the time-delayed processes occur within the same time interval but with significantly smaller amplitudes.

We prove the Lieb-Schultz-Mattis theorem in $d$-dimensional spin systems exhibiting $SO\left(3\right)$ spin rotation and lattice translation symmetries in the presence of $k$-local interactions decaying as $\sim 1/r^{\alpha }$ with distance $r$. Two types of Hamiltonians are considered: Type I comprises long-range spin-spin couplings, while type II features long-range couplings between $SO\left(3\right)$ symmetric local operators. For spin-$\frac{1}{2}$ systems, it is shown that type I cannot have a unique symmetric ground state with a nonzero excitation gap when the interaction decays sufficiently fast, i.e., when $\alpha >max(3d,4d-2)$. For type II, the condition becomes $\alpha >max(3d-1,4d-3)$. In $1d$, this ingappability condition is improved to $\alpha >2$ for type I and $\alpha >0$ for type II by examining the energy of a state with a uniform $2\pi$ twist. Notably, in $2d$, a type II Hamiltonian with van der Waals interaction is subject to the constraint of the theorem.

Steady illumination of a noncentrosymmetric semiconductor results in a bulk photovoltaic current, which is contributed by real-space displacements (“shifts”) of charged quasiparticles as they transit between Bloch states. The shift induced by interband excitation via absorption of photons has received the prevailing attention. However, this excitation-induced shift can be far outweighed ($\ll$) by the shift induced by intraband relaxation, or by the shift induced by radiative recombination of electron-hole pairs. This outweighing ($\ll$) is attributed to (i) time-reversal-symmetric, intraband Berry curvature, which results in an anomalous shift of quasiparticles as they scatter with phonons, as well as to (ii) topological singularities in the interband Berry phase (“optical vortices”), which makes the photovoltaic current extraordinarily sensitive to the linear polarization vector of the light source. Both (i) and (ii) potentially lead to nonlinear conductivities of order $\text{mA}{\text{V}}^{-2}$, without fine-tuning of the incident radiation frequency, band gap, or joint density of states. A case study of BiTeI showcases the anomalous shift and optical vorticity in a realistic material.

Due to technological needs, nanoscale heat management, energy conversion, and quantum thermodynamics have become key areas of research, putting heat pumps and nanomotors center stage. The treatment of these particular systems often requires the use of adiabatic expansions in terms of the frequency of the external driving or the velocity of some classical degree of freedom. However, due to the difficulty of getting the expressions, most works have only explored first-order terms. Despite this, adiabatic expansions have allowed the study of intriguing phenomena such as adiabatic quantum pumps and motors, or electronic friction. Here, we use nonequilibrium Green's functions, within a Schwinger-Keldysh approach, to develop second-order expressions for the energy, heat, and charge currents. We illustrate, through two simple models, how the obtained formulas produce physically consistent results, and allow for the thermodynamic study of unexplored phenomena, such as second-order monoparametric pumping.

Circularly polarized lattice vibrations carry angular momentum and lead to magnetic responses in applied magnetic fields or when resonantly driven with ultrashort laser pulses. Recent measurements have found responses that are orders of magnitude larger than those calculated in prior theoretical studies. Here, we present a microscopic model for the effective magnetic moments of chiral phonons in magnetic materials that can reproduce the experimentally measured magnitudes and that allows us to make quantitative predictions for materials with giant magnetic responses using microscopic parameters. Our model is based on orbit-lattice couplings that hybridize optical phonons with orbital electronic transitions. First, we test our model by applying it to $4f$ rare-earth halide paramagnets, which are known to exhibit a giant phonon Zeeman effect. Next, we predict that this effect can also occur for optical phonons in $3d$ transition-metal oxide magnets. We show that the nature of low-energy excitations involved in phonon hybridization is remarkably different than that of rare-earth systems. The temperature trend of phonon magnetic moment in $d$-orbital magnets also reveals valuable insights about the magnetic ground state and the unique interplay of spin, orbital, and lattice degree of freedom. In both cases, we find that chiral phonons can carry giant effective magnetic moments of the order of a Bohr magneton, orders of magnitude larger than previous predictions.

We fabricated a twisted trilayer graphene device with consecutive twist angles of 1.33 ° and 1.64 °, in which we electrostatically tuned the electronic states from each of the two coexisting moiré superlattices and the interactions between them. When both moiré superlattices contribute equally to the electrical transport, we report a type of inter-moiré Hofstadter butterfly. Its Brown-Zak oscillation corresponds to one of the intermediate quasicrystal length scales of the reconstructed moiré-of-moiré superlattice, shedding light on emergent physics from competing atomic orders.

We report an investigation of the phonon thermal Hall effect in single crystal samples of ${\mathrm{Y}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, and ${\mathrm{DyYTi}}_2{\mathrm{O}}_7$. We measured the field-linear thermal Hall effect in all three samples. The temperature dependence of thermal Hall conductivities shows a peak around 15 K, which coincides with the peak positions of the longitudinal thermal conductivities. The temperature-dependent longitudinal thermal conductivities indicates that phonons dominate thermal transport in all three samples. However, the presence of ${\mathrm{Dy}}^{3+}$ magnetic ions introduces significant effects on the field dependence of the longitudinal thermal conductivities. The thermal Hall ratio is sizable in all three samples and consistent with the values reported for other insulating materials exhibiting a phononic thermal Hall effect, though their exact underlying mechanism remains yet to be identified. The thermal Hall ratio is nearly the same for ${\mathrm{Y}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ and ${\mathrm{DyYTi}}_2{\mathrm{O}}_7$, and slightly larger for ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, suggesting that magnetic impurities are less significant in generating the phononic thermal Hall effect. Our observations of the phononic thermal Hall effect support an intrinsic origin in ${\mathrm{Y}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ and suggest a combination of intrinsic and extrinsic effects in ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ and ${\mathrm{DyYTi}}_2{\mathrm{O}}_7$.

Strongly coupling materials to cavity fields can affect their electronic properties altering the phases of matter. We study monolayer graphene whose electrons are coupled to both left and right circularly polarized vacuum fluctuations, and time-reversal symmetry is broken due to a phase shift between the two polarizations. We develop a many-body perturbative theory, and derive cavity-mediated electronic interactions. This theory leads to a gap equation which predicts a topological band gap at Dirac nodes in vacuum and when the cavity is prepared in an excited Fock state. Remarkably, topological band gaps also open in light-matter hybridization points away from the Dirac nodes giving rise to photoelectron bands with high Chern numbers. We reveal that the physical mechanism behind this phenomenon is generic and due to the exchange of photons with electronic matter at the hybridization points. Specifically, the number and polarization of exchanged photons directly determine the band topology of graphene subject to enhanced chiral vacuum fluctuations. Hence, our theory shows that graphene-based materials could host Chern insulator phases in engineered electromagnetic environments, bridging cavity quantum electrodynamics to Floquet engineering of materials while protected from the ensuing heating effects.

Recent scanning tunneling microscopy experiments in twisted bilayer [K. P. Nuckolls et al., Nature (London) 620, 525 (2023)] and trilayer [H. Kim et al., Nature (London) 623, 942 (2023)] graphene have revealed the ubiquity of Kekulé charge-density wave order in magic-angle graphene. Most samples are moderately strained and show “incommensurate Kekulé spiral” (IKS) order involving a graphene-scale charge density distortion uniaxially modulated on the scale of the moiré superlattice, in accord with theoretical predictions. However, ultralow strain bilayer samples instead show graphene-scale Kekulé charge order that is uniform on the moiré scale. This order, especially prominent near filling factor $\nu =-2$, is unanticipated by theory which predicts a time-reversal breaking Kekulé current order at low strain. We show that including the coupling of moiré electrons to graphene-scale optical zone-corner (ZC) phonons stabilizes a uniform Kekulé charge ordered state at $\left|\nu \right|=2$ with a quantized topological (spin or anomalous Hall) response. Our work clarifies how this phonon-driven selection of electronic order emerges in the strong-coupling regime of moiré graphene.