The authors present a method for characterizing the hyperuniformity (the suppression of density fluctuations at long wavelengths) for quasicrystals (and other structures whose diffraction pattern includes a dense set of Bragg peaks) based on determining the behavior of the integrated spectral intensity $Z$($k$) for small wavenumber $k$. Surprisingly, we find that quasicrystals with peaks at the same wavenumbers $k$ can have different behavior for $Z$($k$) and, hence, qualitatively different degrees of hyperuniformity. This effect has never been explored in the laboratory. The figure shows a one-dimensional example: two “sidewalks” with different widths (pitched at an incommensurate angle) built on a lawn with a square crystal pattern of spots. The construction rule is that, every time the sidewalk crosses a spot, the sidewalk slab is cut and a new one begins. This rule guarantees both sidewalks are quasicrystalline. But the upper one (a Fibonacci sidewalk) has a different degree of hyperuniformity than the lower one.

The time evolution of a quantum system after a sudden change of one of its parameters may show characteristic nonanalyticities, provided that this quench crosses a quantum phase transition. The authors investigate the relation between such dynamical quantum phase transitions and the universal properties of the corresponding quantum critical point.

It has been argued that the itinerant magnetism in the simplest of all iron arsenide systems, the monoarsenide FeAs, may be related to the magnetic ground states of iron-based superconductors. Here, the authors provide new insight into the magnetism of FeAs through a combination of resonant x-ray scattering measurements and electronic structure calculations. They report measurements of the magnetic anisotropy of the spin helices by using polarized x-rays tuned to the resonant absorption edge of iron. They elucidate details of the magnetic structure, showing that the ratio of ellipticity of the spin helix is significantly larger than previously thought, and discover both a right-handed chirality and an out-of-plane component of the magnetic moments in the spin helix. The electronic structure calculations demonstrate how the origin of this spin canting effect may be accounted for by considering the spin-orbit coupling at work in the system.

Understanding the spread of quantum entanglement and scrambling of information across a quantum many-body system is a fundamental problem in quantum dynamics. A necessary part of the spread of the entanglement is the growth in time of Heisenberg operators of initially localized operators. This operator growth can be diagnosed by studying the space-time structure of commutators of well-separated operators. Previous studies in this area focused on translation invariant models, but the effects of disorder, which can radically alter the motion of heat and charge, had not been studied. Here, the authors study the growth of operators in interacting systems with quenched disorder. In the localized phase, they find that operator sizes grow logarithmically in time similar to other measures of entanglement spreading. In the disordered metal, they find that operator sizes grow linearly with time, i.e., ballistically, in contrast to the diffusive motion of charge and heat. The ballistic growth of operators is quantified by the butterfly velocity which the authors relate to the charge diffusion constant and the interaction-induced inelastic scattering rate. When the diffusion of charge is slow, the resulting butterfly velocity is much smaller than the maximum speed allowed by microscopic causality constraints.

Recently, there have been extensive efforts to extend the physics of the two-dimensional (2D) graphene to three-dimensional (3D) semimetals with point/line nodes. Although it has been known that certain crystalline symmetries play an important role in protecting band degeneracy, a general recipe for stabilizing the degeneracy, especially in the presence of spin-orbit coupling, is still lacking. Here, the authors show that a class of novel topological semimetals with point/line nodes can emerge in the presence of an off-centered rotation/mirror symmetry whose symmetry line/plane is displaced from the center of other symmorphic symmetries in nonsymmorphic crystals. Due to the partial translation perpendicular to the rotation axis/mirror plane, an off-centered rotation/mirror symmetry always forces two energy bands to stick together and form a doublet pair in the relevant invariant line/plane in momentum space. Such a doublet pair provides a basic building block for emerging topological semimetals with point/line nodes in systems with strong spin-orbit coupling. When an external magnetic field is applied to these semimetals, a Dirac-type point/line node with four-fold degeneracy splits into two Weyl-type point/line nodes with two-fold degeneracy, with emergent surface states connecting the split nodes.

In recent years, physicists have made great strides toward better understanding isolated many-body quantum systems. Already, two distinct phases are well known: systems that are ergodic and thermalize completely, and, by contrast, systems that exhibit many-body localization (MBL) due to a strong disorder potential, which prevents thermalization. It is tempting to wonder whether a phase of matter could exist between the extremes of full thermalization and MBL in a generic, i.e., nonintegrable, isolated many-body quantum system. Here, the authors provide evidence that such a nonergodic phase can be realized in a translationally invariant itinerant electron model, with both charge and spin degrees of freedom. Exact diagonalization calculations on finite system sizes reveal that there exists a “spin band” of nonthermal eigenstates. These states have entanglement entropy that scales as an overall “volume law,” but after a partial measurement of the spin on each site the scaling is modified to an “area law,” thus suggesting the states are not ergodic. These properties and others suggest that this model realizes a new nonthermal phase of matter, known as a quantum disentangled liquid (QDL). The putative existence of this phase has striking implications for the foundations of quantum statistical mechanics.

Laser beams carrying orbital angular momentum (OAM), first proposed by Allen et al. in 1992, is one of hottest research subjects in modern optics. Such a beam, called an optical vortex, is used to realize superresolution microscopes, chiral optical ablation, optical tweezers, and so on. More recently, electron beams with nonzero OAM are also proposed and experimentally realized. In spite of the growing attention towards such “vortex beams”, their applications for condensed matter physics are almost untapped so far, especially for controlling microscopic electronic and magnetic degrees of freedom in solids. Here, the authors show theoretically that vortex beams can be useful for controlling magnetic properties of solids. In particular, they focus on chiral ferromagnets and antiferromagnets where topologically stable magnetic defects (skyrmions) appear. On the basis of numerical simulations using the stochastic Landau-Lifshitz-Gilbert equation, they show that via the laser-beam-induced spatially nonuniform temperature changes, the characteristic donut-shaped spatial profile of vortex beams can be faithfully transferred to magnets as a family of magnetic defects (n$\pi$ vortices), which include skyrmions and skyrmioniums.

The rare-earth nickelate perovskites ($R$NiO${}_3$, $R$ = rare-earth element) are an archetypal class of correlated electron materials. They order antiferromagnetically at a composition-dependent “Néel” temperature. While it is known that the magnetic structure has a period of four Ni spins along each (pseudo)cubic crystal axis, the arrangement of these spins is still under debate, especially in view of the conjecture of ferroelectricity in the antiferromagnetic phase. Here, the authors report the experimental discovery of an unexpected second magnetic phase transition in TlNiO${}_3$, a material closely resembling the analogous rare-earth compounds. Results of nuclear magnetic resonance and muon spin rotation experiments reveal the presence of two distinct magnetic phase transitions. The new phase is suppressed by magnetic fields on the order of at most 1 T.

Helium nanodroplets are considered ideal model systems to explore quantum hydrodynamics in self-contained, isolated superfluids. Rotation of a superfluid droplet is manifested as a collection of quantum vortices. Here, the authors use single-shot femtosecond X-ray coherent diffractive imaging to investigate the shapes and vorticity of rotating superfluid ${}^4$He droplets. They find that most of the diffraction contours exhibit noticeable ellipticity. A smaller but still significant number of distorted diffraction contours are marked by regions of high intensity concentrated along the direction of the long axis in the diffraction image, indicating the presence of extremely deformed ${}^4$He droplets. Forward modeling of the diffraction images shows that the shapes of superfluid ${}^4$He droplets are very similar to their classical counterparts. In particular, the existence of both axially symmetric (oblate) and, for higher angular momenta, two-lobed (triaxial prolate) droplets is revealed. The latter shapes are strongly deformed compared to the spheroidal bodies that are expected for smaller rotational speeds. The observed shapes provide direct access to the droplet angular momenta, angular velocities, and estimated number of quantum vortices inside the droplets.

The simultaneous presence of sizable spin-orbit interactions and electron correlations in iridates has led to predictions of novel electronic ground states, including Dirac semimetals, Kitaev spin liquids, and superconductivity. Electron and hole-doping studies of Sr${}_2$IrO${}_4$ are one of the venues being pursued to attain such novel quantum states, driven in part by the extensive parallels with the La${}_2$CuO${}_4$ parent compound of high-$T_c$ cuprates. In particular, Rh doping has been intensively pursued but the mechanism of electronic doping and its impact on the evolution of magnetic and transport properties has been under scrutiny. Using x-ray absorption spectroscopy at the Rh $K$, $L$, and Ir $L$ edges, the authors reveal unusual charge partitioning between Rh and Ir sites. The resultant anomalous doping introduces holes into the $J_{\text{eff}}$=1/2 band at low Rh content only for these holes to be removed at higher Rh content. This anomalous doping provides a natural explanation for the reentrant insulating phase in the phase diagram of Rh-doped Sr${}_2$IrO${}_4$ and should be taken into account when searching for novel electronic phases in 5$d$ iridates doped with 4$d$ or 3$d$ elements where anomalous charge partitioning is expected.

Solitons are self-preserving traveling waves of great interest in nonlinear physics, offering many interesting application such as high-bandwidth optical fiber communication. Solitons can also appear in ultrafast acoustics, and several observations suggest acoustic solitons as short as 200 fs. Here, the authors designed an experimental setup to observe and characterize acoustic solitons traveling through a GaAs(001) substrate. The experimental signal is explained well with the help of the Korteweg–de Vries equation, demonstrating the particlelike nature and the unique properties of the solitons. Moreover, the temporal distribution of the solitons is also analyzed with the help of the inverse scattering method. Such investigations provide a new tool to probe transient properties of highly excited matter through the study of the solitons due to the acoustic pulse emitted after laser excitation.

The spin Hall effect is of great technological interest because it can produce efficient spin-transfer torques with the potential to advance magnetic memory technologies. Here, the authors demonstrate that the spin Hall effect can be enhanced by the presence of $f$-orbital states near the Fermi level. The authors compare measurements of spin Hall torques generated by the rare-earth metals Gd, Dy, Ho, and Lu with the results of first-principles calculations of intrinsic spin Hall conductivity with and without $f$-orbital participation. They find that contributions from the $f$-orbital states are required to explain the experimental trend in spin Hall conductivity as a function of $f$-orbital filling. The observed trend is consistent in both sign and magnitude with a simple Hund’s rules picture of $f$-orbital filling, similar to the trend observed in the 4$d$ and 5$d$ transition metals as a function of $d$-orbital filling. These results suggest that rare earths are a promising research direction for creating and tailoring materials with large spin-orbit torques.

The investigation of topological transitions in quantum systems is a thriving area of modern research. The authors recently predicted that multiterminal Josephson junctions realize a novel type of topological matter. Weyl singularities may appear in the Andreev bound-state spectrum of junctions with four superconducting terminals, giving rise to topological transitions as the superconducting phases are tuned. These transitions manifest themselves in a quantization of the transconductance between two voltage-biased terminals in fundamental units of 4$e^2$2/$h$, where $e$ is the electric charge and $h$ is the Planck constant. The present work addresses the observability of this effect. The quantized transconductance is associated with adiabatic transport at fixed occupations of the Andreev states. On the other hand, a bias voltage leads to multiple Andreev reflections, where a quasiparticle is dissipatively transferred from the occupied states below the superconducting gap to the empty states above the superconducting gap. By computing the currents in the presence of weak inelastic relaxation, the authors establish the voltage threshold below which the equilibrium occupations of the Andreev states are restored, and the transconductances reach their quantized values. The results are an important step towards experimental verification of the topological properties of multiterminal Josephson junctions.

The out-of-time-ordered (OTO) correlation is unconventional. It is a key quantity for quantifying quantum chaoticity and has been recently used in the investigation of quantum holography. On the other hand, it is difficult to reveal and understand the special features of many-body localization (MBL) by conventional quantities and methods. Here, the authors demonstrate that OTO correlation can provide a pertinent and comprehensive description for MBL. It readily reveals the special logarithmic dynamics of MBL, distinguishes MBL sharply from Anderson localization as well as ergodic states, and allows accurate extraction of localization lengths for MBL. The divergence of the localization length at a finite interaction predicts an ergodic-MBL transition. Furthermore, the infinite-time “thermal” fluctuation of the OTO correlation is zero (finite) in the ergodic (MBL) phase and thus can be considered as an order parameter for the ergodic-MBL transition, through which the transition can be identified and characterized. Specifically, the critical point and related critical exponents can be calculated.

Many semiconductor nanostructures are made from planar two-dimensional heterojunction systems. With a view to merging semiconductor physics, spintronics, and quantum computing, strongly spin-orbit coupled systems such as semiconductor holes have generated burgeoning research interest. While recent experiments in various low-dimensional hole systems have shown great promise in achieving electrical spin control, a thorough understanding of spin-orbit interactions in holes is lacking. Owing to the intricate interactions between holes and their environment, calculations on two-dimensional holes in semiconductor heterojunctions have hitherto always been numerical and material specific, and thus are not easily generalizable to other material systems. In this work, the authors exploit the variational method, k.p perturbation theory, and the theory of invariants to derive general, semianalytical expressions for the spin-orbit interaction in semiconductor heterojunctions. In particular, the authors systematically evaluate the dependence of the Rashba and Dresselhaus spin-orbit interactions on experimental parameters such as material, hole density, and background dopant type. The authors show that the semianalytical approach is easily generalizable to various materials, and present results for common semiconductors GaAs, Ge, InSb, InAs, and Si. Furthermore, the semianalytical results yield good agreement with existing numerical as well as experimental findings.

The dynamics in the vicinity of quantum phase transitions entails a variety of important and universal phenomena, such as critical slowing down or the Kibble-Zurek mechanism, which are associated with the low-energy and long-time properties at criticality. Here, the author reveals that the opposite regime of transient nonequilibrium time evolution at criticality can similarly host universal temporal behavior. By strongly perturbing a quantum critical state through quenching the associated order parameter, the system experiences a dynamical quantum phase transition with physical quantities becoming nonanalytic at critical times. These dynamical quantum phase transitions are caused by superextensive energy fluctuations induced by the particular protocol, which turn out to have profound consequences for quantum speed limits and potential restricted thermalization despite the nonintegrability of the system.

In the conventional theory of superconductivity the critical temperature Tc is determined by the electron-phonon coupling constant and the phonon cut-off frequency. The hallmark experiments of McMillan and Rowell demonstrated that bosons (phonons) responsible for pairing can be observed through the frequency dependence of the gap parameter. Determination of the electron-boson coupling strength in high-$T_c$ cuprates is, however, not an easy task. One of the promising ways is to measure the energy relaxation rate of photoexcited carriers by using femtosecond real-time techniques. Here, considering the electron relaxation process within the conduction band, it is commonly assumed that the underlying Eliashberg electron-boson coupling function is independent of electron excess energy. Conversely, studies of light-induced suppression of superconductivity in Pr${}_{1.85}$Ce${}_{0.15}$CuO${}_4$ reported here imply a strong variation of the electron-boson coupling function on electron energy. Considering the competing scenarios of superconductivity being mediated by either phonons or magnetic excitations, the results suggest that high-energy electrons strongly couple either to phonons or magnetic modes, while the situation is reversed when considering pairing of low-energy electrons.

Topological crystalline insulators are insulating in the bulk, but exhibit conducting surface states protected by crystal symmetries. Here, the authors show that the surface states of crystalline topological insulators come in two different varieties: (i) as standard Dirac cones with pointlike Fermi surfaces (type-I) and (ii) as tilted Dirac cones that appear at the contact of electron and hole pockets. They call these new tilted surface states “type-II Dirac states” in analogy to the three-dimensional type-II Weyl points that have been recently discovered in WTe${}_2$. These type-II Dirac states can exist only at the surface of topological crystalline insulators, but are absent in ordinary topological insulators, where they are forbidden by symmetry. The two types of Dirac surface states have very different physical properties, in particular with regards to their thermodynamics and magnetotransport. The authors predict that the antiperovskites $A_{3}E$O are an example of a crystalline topological insulator that hosts the type-II Dirac surface states.

Light waves propagating in optical fibers or other guides are usually vulnerable to defects or channel deformations, such as twisting and bending. These perturbations invariably generate undesired reflections and scattering and typically imply a power penalty. Here, building on an analogy with electronics and with the spin Hall effect, the author unveils a general theoretical solution for this dilemma. It is shown that there is a wide class of three-dimensional metamaterial platforms protected by a particular symmetry – a combination of a geometrical operation with other more subtle symmetries of the materials response – that guarantees bidirectional transport of light totally free of reflections, independent of the specific geometry of the propagation channel and other imperfections. Crucially, this scattering anomaly only requires the symmetry protection in the frequency range of interest, and hence relies on much weaker assumptions than topological theories.

Tamm resonators are an alternate type of cavities, in which the light-matter interaction may be significantly enhanced, as required for many applications in photonics or optoelectronics. A Tamm resonator comprises at least one metal layer as mirror, in the present case combined with a distributed Bragg reflector. The metal layer may turn out to be useful, for example, for injecting carriers or applying an electric field. Here, the authors use photon echoes in the exciton four-wave mixing signal to demonstrate that the studied Tamm resonator, which contains quantum dots as the optically active medium, allows one to perform coherent manipulations on quantum-dot excitons at power levels more than one order of magnitude lower than those required for bare quantum dots. This occurs despite the moderate quality factor of about 100. Moreover, it speeds up the radiative decay of the excitons by a factor of two (the so-called “Purcell effect”). On the other hand, the coherence of the quantum dot exciton, which may become compromised by plasmon excitations in the metal, is hardly shortened. These results demonstrate that Tamm resonators are indeed prospective candidates for performing coherent optical manipulations.