Altermagnets break time-reversal symmetry, preserve crystal translation invariance, and have a spin density with $d$-wave, $g$-wave, etc. momentum dependencies, which do not contribute to magnetization. When an $s$-wave spin-density contribution cannot be excluded by symmetry, a small magnetization and an anomalous Hall effect (AHE) emerge. However, for so-called “pure” altermagnets, where the $s$-wave component is symmetry forbidden even in the presence of SOC, both the zero-field magnetization and the AHE vanish. We show that altermagnets generally exhibit a nonzero elasto-Hall conductivity, by which the application of strain leads to a nonzero AHE. For pure altermagnets, it is the only contribution to the AHE. This elasto-Hall conductivity is caused by strain coupling to the Berry curvature quadrupole that characterizes altermagnets and allows for the determination of the altermagnetic order using transport measurements that are linear in the electric field. We further show that the emergence of a nonzero magnetization in the presence of strain arises from a different response function: piezomagnetism. While this magnetization gives rise to an additional contribution to the elasto-Hall conductivity, the corresponding Berry curvature is qualitatively different from the distorted Berry curvature quadrupole originating from the altermagnetic order parameter. This insight also helps to disentangle AHE and weak ferromagnetism for systems with a symmetry-allowed $s$-wave contribution. Quantitatively, the elasto-Hall conductivity is particularly pronounced for systems with a Dirac spectrum in the altermagnetic state. The same mechanism gives rise to anomalous elasto-thermal Hall, Nernst, and Ettinghausen effects.

Ferro-/ferri- and antiferromagnetically ordered phases are typically exclusive in nature, thus, their coexistence in atomic-scale proximity is expected only in heterostructures. Breaking this paradigm and broadening the range of unconventional magnetic states, we report here on the observation of a new, atomic-scale hybrid spin state. This ordering is stabilized in three-dimensional crystals of the polar antiferromagnet ${\mathrm{Co}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$ by magnetic fields applied perpendicular to the Co honeycomb layers and possesses a spontaneous in-plane ferromagnetic moment. Our microscopic spin model, capturing the observed field dependence of the longitudinal and transverse magnetization as well as the magnetoelectric/elastic properties, reveals that this novel spin state is composed of an alternating stacking of antiferromagnetic and ferrimagnetic honeycomb layers. The strong intralayer and the weak interlayer exchange couplings together with competing anisotropies at octahedral and tetrahedral Co sites are identified as the key ingredients to stabilize antiferromagnetic and ferrimagnetic layers in such close proximity. We show that the proper balance of magnetic interactions can extend the stability range of this hybrid phase down to zero magnetic field. The possibility to realize a layer-by-layer stacking of such distinct spin orders via suitable combinations of microscopic interactions opens a new dimension toward the nanoscale engineering of magnetic states.

Dynamic nuclear polarization (DNP) using the boron vacancy $\left({\mathrm{V}}_{\mathrm{B}}^{-}\right)$ in hexagonal boron nitride (hBN) has gained increasing attention. Understanding this DNP requires systematically investigating the optically detected magnetic resonance (ODMR) spectra and developing a model that quantitatively describes its behavior. Here, we measure the ODMR spectra of ${\mathrm{V}}_{\mathrm{B}}^{-}$ in ${\mathrm{h}}^{10}{\mathrm{B}}^{15}\mathrm{N}$ over a wide magnetic field range, including the ground state level anticrossing (GSLAC), and compare them with the results of the Lindblad-based simulation that considers a single electron spin and three neighboring ${}^{15}\mathrm{N}$ nuclear spins. Our simulation successfully reproduces the experimental spectra, including the vicinity of GSLAC. It can explain the overall behavior of the magnetic field dependence of the nuclear spin polarization estimated using the Lorentzian fitting of the spectra. Despite such qualitative agreement, we also demonstrate that the fitting methods cannot give accurate polarizations. Finally, we discuss that symmetry-induced mechanisms of ${\mathrm{V}}_{\mathrm{B}}^{-}$ limit the maximum polarization. Our study is an essential step toward a quantitative understanding of DNP using defects in hBN and its quantum applications.

We show that in disordered $s$-wave superconductors, at sufficiently low frequencies $\omega$, the coupling of two-level systems (TLSs) to external ac electric fields increases dramatically in the presence of a dc supercurrent. This giant enhancement manifests in all ac linear and nonlinear phenomena. In particular, it leads to a parametric enhancement of the real part of the ac conductivity and, consequently, of the equilibrium current fluctuations. If the distribution of TLS relaxation times is broad, the conductivity is inversely proportional to $\omega$, and the spectrum of the equilibrium current fluctuations takes the form of $1/f$ noise.

Majorana modes can be engineered in arrays where quantum dots (QDs) are coupled via grounded superconductors, effectively realizing an artificial Kitaev chain. Minimal Kitaev chains, composed by two QDs, can host fully localized Majorana modes at discrete points in parameter space, known as Majorana sweet spots. Unlike grounded superconductors, where the superconducting phase is a conserved quantum number, floating islands have a well-defined number of charges. The coexistence of charging effects and Majorana physics allows us to explore novel phenomenology, including teleportation and topological Kondo effect. Here, we extend previous works by theoretically investigating a setup with two QDs coupled via a floating superconducting island. We study the effects of the charging energy of the island and the properties of the resulting minimal Kitaev chain. We initially employ a minimal perturbative model, valid in the weak QD-island coupling regime, to derive analytic expressions for the Majorana sweet spots and the splitting of the ground-state degeneracy as a function of tunable physical parameters. The conclusions from this perturbative approximation are then benchmarked using a microscopic model that explicitly describes the internal degrees of freedom of the island. Our work shows the existence of Majorana sweet spots, even when the island is not tuned at a charge-degeneracy point. In contrast to the Kitaev chains in grounded superconductors, these sweet spots involve a degeneracy between states with a well-defined number of particles and allow us to explore the interplay between Majorana states and charging effects.

We study topological transitions in one-dimensional superconductors that can harbor multiple edge Majorana bound states protected by chiral symmetry. The chiral symmetry arises from the structure of the internal spin degrees of freedom of the superconductor and can be guided by the coupling of the superconductor with sources of time-reversal symmetry breaking. We then consider distinct regions of the phase diagram in the parameter space that are marked by gapless excitations in the spectrum and evaluate the conditions for inducing a topological transition. We show that for gapless chiral symmetric superconductors one can identify a class of physical perturbations that enable a gap opening in the spectrum, without breaking chirality, and turn the system into a topological state. This type of superconductor is dubbed a marginal topological superconductor because an infinitesimally small perturbation is able to induce a transition into a topological nontrivial phase. To explicitly demonstrate and evaluate the character of the transitions from gapless to topological gapfull phases, we explore different physical cases including a $p$-wave superconductor in the presence of an applied magnetic field or proximity-coupled to a ferromagnet, and an $s$-wave superconductor in a noncollinear magnetic ordering.

Optical orientation of exciton and carrier spins by circularly polarized light is the basic phenomenon in the spin physics of semiconductors. Here, we investigate spin orientation in methylammonium lead iodide $\left({\mathrm{MAPbI}}_3\right)$ perovskite crystals at the cryogenic temperature of 1.6 K, where the material has an orthorhombic crystal structure. The recombination and spin dynamics of excitons and carriers are measured by time-resolved photoluminescence after circularly polarized excitation. The optical orientation of excitons reaches 85%, which persists within their lifetime of $15–80$ ps. This high orientation is maintained for excitation laser detunings from the exciton resonance to higher energies by up to 0.3 eV, then decreases and vanishes above 1.5 eV detuning. This indicates that the Dyakonov-Perel spin-relaxation mechanism based on inversion symmetry breaking is inactive in ${\mathrm{MAPbI}}_3$ crystals with orthorhombic symmetry. The optical orientation of localized and spatially separated electrons and holes results in 50% circular polarization of their emission. Their contributions can be identified from the complex spin beats dynamics in a transverse magnetic field. The dynamics analysis gives values of the Landé $g$ factors of $|g_{\text{V,e}}|=2.83$ for electrons and $|g_{\text{V,h}}|=0.54$ for holes. Also, the magnetic-field-induced polarization of excitons and carriers is analyzed in magnetic fields up to 6 T, showing that their spin-relaxation times are longer than their lifetimes. Namely, for the excitons, the spin-relaxation time exceeds the lifetime by a factor of 6. We model the dynamics of optical orientation degree for cumulative contributions of excitons and carriers and show that the exciton recombination dynamics can control these dynamics. The polarized emission of excitons and localized carriers, produced by their polarization on Zeeman-split levels in magnetic fields, is modeled. Their dependence on the magnetic field is identical for very short spin-relaxation times, but becomes qualitatively different as the spin-relaxation time approaches the carrier lifetime.

Nodal-line semimetals are characterized by one-dimensional lines or loops of topologically protected band-touching nodes. For two recent nodal-line semimetal candidates, CaCdGe and CaCdSn, band structure calculations show nontopological and topological valence bands with the nodal band crossings above the Fermi level. Here, we present our investigation of the Fermi surfaces of CaCdGe and CaCdSn by use of de Haas–van Alphen measurements and band structure calculations. Our measurements reveal many quantum oscillation frequencies that are not predicted by calculations. This discrepancy casts doubt on the calculated band structures and, thus, on the precise nature of the topology of these systems.

The ability to control absorption by modifying the polarization of light presents an exciting opportunity to experimentally determine the orbital alignment of absorption features. Here, attosecond extreme ultraviolet (XUV) transient absorption spectroscopy is used to investigate the polarization dependence of core exciton dynamics in LiF thin films at the ${\mathrm{Li}}^{+}\mathrm{K}$ edge. XUV pulses excite electrons from the Li 1s core level into the conduction band, allowing for the formation of a p-orbital-like core exciton, aligned along the XUV light polarization axis. A sub-5 fs near-infrared (NIR) probe pulse then arrives at variable time delays, perturbing the XUV-excited states and allowing the coherence decay of the core exciton to be mapped. The coherence lifetimes are found to be $\approx 2.4\pm 0.4\mathrm{fs}$, which is attributed to a phonon-mediated dephasing mechanism as in previous core exciton studies. The differential absorption features are also shown to be sensitive to the relative polarization of the XUV and NIR fields. The parallel NIR probe induces couplings between the initial XUV-excited p-like bright exciton and s-like dark excitons. When crossed pump and probe polarizations are used, the coupling between the bright and dark states is no longer dipole-allowed, and the transient absorption signal associated with the coupling is suppressed by approximately 90%. This interpretation is supported by simulations of a few-level model system, as well as analysis of the calculated band structure. The results indicate that laser polarization can serve as a powerful experimental tool for exploring the orbital alignment of core excitonic states in solid-state materials.

Recently, band-off-diagonal superconductivity has been proposed [Nat. Commun. 14, 7134 (2023)] as a candidate pairing state for twisted graphene systems. Based on mean-field theory, it was shown that it not only naturally emerges from both intervalley electron-phonon coupling and fluctuations of the nearby correlated insulator, but also exhibits nodal and gapped regimes as indicated by scanning tunneling microscopy experiments. Here, we study band-off-diagonal pairing within Eliashberg theory. We show that despite the additional frequency dependence, the leading-order description of both intervalley coherent fluctuations and intervalley phonons exhibits a symmetry prohibiting the admixture of an intraband component to the interband pairing state. It is found that even- and odd-frequency pairing mix, which originates from the reduced number of flavor degrees of freedom in the normal state, and that the thermal phase transition into the superconductor can become a first-order transition. From analytic continuation, we obtain the electronic spectral function, showing that, also within Eliashberg theory, the interband nature leads to an enhanced spectral weight below the order-parameter energy compared to band-diagonal pairing. Finally, we also study the superfluid stiffness of band-off-diagonal pairing, taking into account multiband and quantum geometry effects. It is shown that for $s$-wave and chiral momentum dependencies, conventionally leading to fully gapped phases, an interband structure reduces the temperature scale below which the stiffness saturates. Depending on parameters, for the chiral state, this scale can even be suppressed all the way to zero temperature, leading to a complex competition of multiple dispersive and geometrical contributions. Our results show that interband pairing might also be able to explain more recent stiffness measurements in the superconducting state of twisted multilayer graphene.

We develop a numerical scheme for the calculation of tunneling current $I$ and differential conductance $\mathsf{d}I/\mathsf{d}V$ of metal- and CO-terminated STM tips on the topological insulators ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$ as well as ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, and find excellent agreement with experiment. The calculation is an application of Chen's derivative rule, whereby the Bloch functions are obtained from Wannier-interpolated tight-binding Hamiltonians and maximally localized Wannier functions from first-principle $\mathrm{DFT}+GW$ calculations. We observe signatures of the topological boundary modes, their hybridization with bulk bands, Van Hove singularities of the bulk bands, and characterize the orbital character of these electronic modes using the high spatial resolution of STM and AFM. Bare DFT calculations are insufficient to explain the experimental data, which are instead accurately reproduced by many-body-corrected $GW$ calculations.

The pressure evolution of ${\mathrm{RuO}}_2$ is studied using single-crystal x-ray diffraction in a diamond anvil cell, combined with ab initio band-structure calculations. The tetragonal rutile structure transforms into the orthorhombic ${\mathrm{CaCl}}_2$-type structure above 13 GPa under quasihydrostatic pressure conditions. This second-order transition is ferroelastic in nature and accompanied by tilts of the ${\mathrm{RuO}}_6$ octahedra. Orthorhombic ${\mathrm{RuO}}_2$ is expected to be a paramagnetic metal, similar to ambient-pressure ${\mathrm{RuO}}_2$. It shows the increased $t_{2g}\text{−}{e}_g$ crystal-field splitting that is responsible for the pressure-induced color change. It further features the Dirac nodal line that shifts across the Fermi level upon compression.

We calculate the magnetic phase diagram of the spin-$1/2$ nearest neighbor XXZ pyrochlore model using the pseudo-Majorana functional renormalization group in the temperature flow formalism. Our phase diagram as a function of temperature and coupling ratio, allowing both longitudinal and transverse couplings to be ferromagnetic and antiferromagnetic, reveals a large nonmagnetic regime at low temperatures, which includes the quantum spin ice phase near the antiferromagnetic Ising model, as well as the antiferromagnetic Heisenberg and XY models. We are able to detect magnetic phase transitions via critical finite size scaling down to temperatures two orders of magnitude smaller than the spin interactions, demonstrating the remarkably good performance of our method upon approaching the ground state. Specifically, the low-temperature transition from the zero-flux quantum spin ice phase into the transverse ferromagnetic phase shows very good agreement with previous quantum Monte Carlo results. Comparing our findings with classical results, we identify a quantum order-by-disorder effect near the antiferromagnetic XY model. In magnetically disordered regimes, we find characteristic patterns of broadened pinch points in the spin structure factor and investigate their evolution when approaching magnetically ordered phases. We also compute linear responses to lattice symmetry breaking perturbations and identify a possible lattice nematic ground state of the antiferromagnetic XY model.

Hilbert space fragmentation provides a mechanism to break ergodicity in closed many-body systems. Here, we propose a feasible scheme to explore this exotic paradigm on a Rydberg quantum simulator. We show that the Rydberg Ising model in the large detuning regime can be mapped to a generalized folded $XXZ$ model featuring a strongly fragmented Hilbert space. The emergent Hamiltonian, however, displays distinct timescales for the transport of a magnon and a hole excitation. This interesting property facilitates a continuous tuning of the Krylov-subspace ergodicity, from the integrable regime, to the Krylov-restricted thermal phase, and eventually to the statistical bubble localization region. By further introducing nonlocal interactions, we find that both the fragmentation behavior and the ergodicity of the Krylov subspace can be significantly enriched. We also examine the role of atomic position disorders, and we identify a symmetry-selective many-body localization transition. We demonstrate that these phenomena manifest themselves in quench dynamics, which can be readily probed in state-of-the-art Rydberg array setups.

The paradigmatic state of a 1D collective metal, the Tomonaga-Luttinger liquid (TLL), offers us an exact analytic solution for a strongly interacting quantum system not only for infinite systems at zero temperature but also at finite temperature and with a boundary. These results are potentially of significant relevance for technology, as they could lay the foundation for a many-body description of various nanostructures. For this to happen, we need expressions for local (i.e., spatially resolved) correlations as a function of frequency. In this paper, we find such expressions and study their outcome. Based on our analytic expressions, we are able to identify two distinct cases of TLL, which we call the Coulomb metal and Hund metal, respectively. We argue that these two cases span all the situations possible in nanotubes made out of $p$-block elements. From an applications viewpoint, it is crucial to capture the fact that the end of the 1D system can be coupled to the external environment and emit electrons into it. We discuss such coupling on two levels for both Coulomb and Hund metals: (i) in the zeroth-order approximation, the coupling modifies the 1D system's boundary conditions; (ii) for stronger coupling, when the environment can self-consistently modify the 1D system, we introduce spatially dependent TLL parameters. In case (ii), we are able to capture the presence of plasmon-polariton particles, thus building a link between TLL and the field of nano-optics.

The coexistence of electronic and phononic higher-order band topology has been largely unexplored. Based on first-principles calculations and symmetry arguments, we demonstrate that III-V monolayers $XY$ ($X$ = B, Al, Ga, In; $Y$ = N, P, As, Sb), with planar and low-buckled honeycomb structures, exhibit both electronic and phononic higher-order band topology. We show the explicit existence of hallmark corner states with quantized fractional charge, which are linked to nontrivial topological indices, i.e., rotation topological invariants associated with threefold rotation symmetry. Moreover, we further verify by first-principles calculations and effective model analysis that the variation of atomic masses in III-V monolayers can induce phonon band inversion, leading to different quantized fractional charges. Our work reveals the coexistence of electronic and phononic higher-order band topology in experimentally accessible monolayers, which has profound implications for advancing our fundamental understanding of the topological properties of matter and related experiments and applications.

The spectral form factor (SFF) is a powerful diagnostic of random matrix behavior in quantum many-body systems. We introduce a family of random circuit ensembles whose SFFs can be computed exactly. These ensembles describe the evolution of noninteracting fermions in the presence of correlated on-site potentials drawn from the eigenvalue distribution of a circular ensemble. For disorder parameters drawn from the circular unitary ensemble (CUE), we derive an exact closed form for the SFF, valid for any choice of system size $L$ and integer time $t$. When the disorder is drawn from the circular orthogonal or symplectic ensembles (COE and CSE, respectively), we carry out the disorder averages analytically and reduce the computation of the SFF at integer times to a combinatorial problem amenable to transfer matrix methods. In each of these cases, the SFF grows exponentially in time, which we argue is a signature of random matrix universality at the single-particle level. Finally, we develop matchgate circuit representations of our circuit ensembles, enabling their experimental realization in quantum simulators.

The use of powerful numerical methods to study the optical properties of metasurfaces has led to an obvious need for the development of analytical models that provide meaningful physical analysis of the numerical results. In this paper, we present a general analytical approach to the study of electromagnetic resonances in metasurfaces consisting of meta-atoms with anisotropic dipole polarizabilities and irradiated with light under arbitrary angle of incidence. The presented approach allows us to clearly trace and explain features of coupling between electric and magnetic dipole moments in metasurfaces as well as identify the role of such coupling. For these purposes, the dependence of the dipole lattice sums on the angle of light incidence is also presented. Expressions for the specular transmission and reflection coefficients are presented with explicit inclusion of the incidence angles and the dipole moments of the particles in the array, which allows a clearer analysis of purely numerical results. The developed analytical method is tested to characterize the spectral resonances, including the generalized Brewster effect, of dielectric metasurfaces composed of rectangular silicon nanoprisms. In addition, we discuss the relationship and similarity between the results of coupled dipole and coupled dipole-quadrupole methods. Our analytical representation is an insightful and fast method for the characterization of collective resonances in metasurfaces for irradiation at an arbitrary angle of incidence. It could be especially useful for designing planar nanophotonic devices consisting of building blocks with noncanonical and complex shapes when considering their operation under special irradiation conditions.

Doping a self-assembled InGaAs/GaAs quantum dot (QD) with a single Mn atom, a magnetic acceptor impurity, provides a quantum system with discrete energy levels and original spin-dependent optical selection rules, which thus has large potential in quantum photonics, notably as a source of multientangled photons. To investigate this potential further, we perform coherent optical spectroscopy under continuous wave excitation of the three-level V-like system formed in such a Mn-doped QD when charged by a single hole. In spite of a large inhomogeneous broadening of the optical transitions, we demonstrate Autler-Townes splitting both by resonant Raman scattering and by probe absorption spectroscopy for different saturation powers. Analyzing these data with a comprehensive model based on optical Bloch equations, we show evidence for quantum interference within the V-like system and assess the pure dephasing rate between the corresponding spin states.

We report a twisted triple bilayer graphene platform consisting of three units of Bernal bilayer graphene consecutively twisted at $1.{49}^{\circ }$ and $1.{68}^{\circ }$. We demonstrate the atomic reconstruction between the two competing moiré superlattices strongly enhances the Berry curvature of each moiré band insulator state, characterized by measured strong nonlocal valley Hall effect that sensitively depends on the intermoiré competition strength, tunable by manipulating the out-of-plane carrier distribution. Our study sheds light on the microscopic mechanism of atomic and electronic reconstruction in twisted multilayer systems, by systematically investigating transport signatures of moiré Berry curvature and its enhancement from moiré-of-moiré lattice reconstruction. We show that the reconstructed electronic band can be versatilely tuned by electrostatics, providing an approach toward engineering the band structure and its topology for a quantum material platform with designer electrical and optical properties.