From studies of exotic quantum many-body phenomena to applications in spintronics and quantum information processing, topological materials are poised to revolutionize the condensed-matter frontier and the landscape of modern materials science. Accordingly, there is a broad effort to realize topologically nontrivial electronic and photonic materials for fundamental science as well as practical applications. In this work, we demonstrate the first simultaneous site- and time-resolved measurements of a time-reversal-invariant topological band structure, which we realize in a radio-frequency photonic circuit. We control band-structure topology via local permutation of a traveling-wave capacitor-inductor network, increasing robustness by going beyond the tight-binding limit. We observe a gapped density of states consistent with a modified Hofstadter spectrum at a flux per plaquette of $\varphi =\pi /2$. In situ probes of the band gaps reveal spatially localized bulk states and delocalized edge states. Time-resolved measurements reveal dynamical separation of localized edge excitations into spin-polarized currents. The radio-frequency circuit paradigm is naturally compatible with nonlocal coupling schemes, allowing us to implement a Möbius strip topology inaccessible in conventional systems. This room-temperature experiment illuminates the origins of topology in band structure, and when combined with circuit quantum electrodynamics techniques, it provides a direct path to topologically ordered quantum matter.

In 2009, Briane and Milton proved mathematically the existence of three-dimensional isotropic metamaterials with a classical Hall coefficient that is negative with respect to that of all of the metamaterial constituents. Here, we significantly simplify their blueprint towards an architecture composed of only a single-constituent material in vacuum or air, which can be seen as a special type of porosity. We show numerically that the sign of the Hall voltage is determined by a separation parameter between adjacent tori. This qualitative behavior is robust even for only a small number of metamaterial unit cells. The combination of simplification and robustness brings experimental verification of this striking sign inversion into reach. Furthermore, we provide a simple intuitive explanation of the underlying physical mechanism.

Bosonic topological insulators (BTIs) in three dimensions are symmetry-protected topological phases protected by time-reversal and boson number conservation symmetries. BTIs in three dimensions were first proposed and classified by the group cohomology theory, which suggests two distinct root states, each carrying a ${\mathbb{Z}}_2$ index. Soon after, surface anomalous topological orders were proposed to identify different root states of BTIs, which even leads to a new BTI root state beyond the group cohomology classification. In this paper, we propose a universal physical mechanism via vortex-line condensation from a 3D superfluid to achieve all three root states. It naturally produces a bulk topological quantum field theory description for each root state. Topologically ordered states on the surface are rigorously derived by placing topological quantum field theory on an open manifold, which allows us to explicitly demonstrate the bulk-boundary correspondence. Finally, we generalize the mechanism to $Z_N$ symmetries and discuss potential symmetry-protected topological phases beyond the group cohomology classification.

A major goal of neuroscience, statistical physics, and nonlinear dynamics is to understand how brain function arises from the collective dynamics of networks of spiking neurons. This challenge has been chiefly addressed through large-scale numerical simulations. Alternatively, researchers have formulated mean-field theories to gain insight into macroscopic states of large neuronal networks in terms of the collective firing activity of the neurons, or the firing rate. However, these theories have not succeeded in establishing an exact correspondence between the firing rate of the network and the underlying microscopic state of the spiking neurons. This has largely constrained the range of applicability of such macroscopic descriptions, particularly when trying to describe neuronal synchronization. Here, we provide the derivation of a set of exact macroscopic equations for a network of spiking neurons. Our results reveal that the spike generation mechanism of individual neurons introduces an effective coupling between two biophysically relevant macroscopic quantities, the firing rate and the mean membrane potential, which together govern the evolution of the neuronal network. The resulting equations exactly describe all possible macroscopic dynamical states of the network, including states of synchronous spiking activity. Finally, we show that the firing-rate description is related, via a conformal map, to a low-dimensional description in terms of the Kuramoto order parameter, called Ott-Antonsen theory. We anticipate that our results will be an important tool in investigating how large networks of spiking neurons self-organize in time to process and encode information in the brain.

Systems of interacting quantum spins show a rich spectrum of quantum phases and display interesting many-body dynamics. Computing characteristics of even small systems on conventional computers poses significant challenges. A quantum simulator has the potential to outperform standard computers in calculating the evolution of complex quantum systems. Here, we perform a digital quantum simulation of the paradigmatic Heisenberg and Ising interacting spin models using a two transmon-qubit circuit quantum electrodynamics setup. We make use of the exchange interaction naturally present in the simulator to construct a digital decomposition of the model-specific evolution and extract its full dynamics. This approach is universal and efficient, employing only resources that are polynomial in the number of spins, and indicates a path towards the controlled simulation of general spin dynamics in superconducting qubit platforms.

The physics of interacting integer-spin chains has been a topic of intense theoretical interest, particularly in the context of symmetry-protected topological phases. However, there has not been a controllable model system to study this physics experimentally. We demonstrate how spin-dependent forces on trapped ions can be used to engineer an effective system of interacting spin-1 particles. Our system evolves coherently under an applied spin-1 $XY$ Hamiltonian with tunable, long-range couplings, and all three quantum levels at each site participate in the dynamics. We observe the time evolution of the system and verify its coherence by entangling a pair of effective three-level particles (“qutrits”) with 86% fidelity. By adiabatically ramping a global field, we produce ground states of the $XY$ model, and we demonstrate an instance where the ground state cannot be created without breaking the same symmetries that protect the topological Haldane phase. This experimental platform enables future studies of symmetry-protected order in spin-1 systems and their use in quantum applications.

We discuss a general method for constructing nonreciprocal, cavity-based photonic devices, based on matching a given coherent interaction with its corresponding dissipative counterpart; our method generalizes the basic structure used in the theory of cascaded quantum systems and can render an extremely wide class of interactions directional. In contrast to standard interference-based schemes, our approach allows directional behavior over a wide bandwidth. We show how it can be used to devise isolators and directional, quantum-limited amplifiers. We discuss in detail how this general method allows the construction of a directional, noise-free phase-sensitive amplifier that is not limited by any fundamental gain-bandwidth constraint. Our approach is particularly well suited to implementations using superconducting microwave circuits and optomechanical systems.

We report experimental results validating the concept that plasma confinement is enhanced in a magnetic cusp configuration when $\beta$ (plasma pressure/magnetic field pressure) is of order unity. This enhancement is required for a fusion power reactor based on cusp confinement to be feasible. The magnetic cusp configuration possesses a critical advantage: the plasma is stable to large scale perturbations. However, early work indicated that plasma loss rates in a reactor based on a cusp configuration were too large for net power production. Grad and others theorized that at high $\beta$ a sharp boundary would form between the plasma and the magnetic field, leading to substantially smaller loss rates. While not able to confirm the details of Grad’s work, the current experiment does validate, for the first time, the conjecture that confinement is substantially improved at high $\beta$. This represents critical progress toward an understanding of the plasma dynamics in a high-$\beta$ cusp system. We hope that these results will stimulate a renewed interest in the cusp configuration as a fusion confinement candidate. In addition, the enhanced high-energy electron confinement resolves a key impediment to progress of the Polywell fusion concept, which combines a high-$\beta$ cusp configuration with electrostatic fusion for a compact, power-producing nuclear fusion reactor.

Macroscopic quantum tunneling is a fundamental phenomenon of quantum mechanics related to the actively debated topic of quantum-to-classical transition. The ability to realize macroscopic quantum tunneling affects implementation of qubit-based quantum computing schemes and their protection against decoherence. Decoherence in qubits can be reduced by means of topological protection, e.g., by exploiting various parity effects. In particular, paired phase slips can provide such protection for superconducting qubits. Here, we report on the direct observation of quantum paired phase slips in thin-wire superconducting loops. We show that in addition to conventional single phase slips that change the superconducting order parameter phase by $2\pi$, there are quantum transitions that change the phase by $4\pi$. Quantum paired phase slips represent a synchronized occurrence of two macroscopic quantum tunneling events, i.e., cotunneling. We demonstrate the existence of a remarkable regime in which paired phase slips are exponentially more probable than single ones.

We present an extensive study of angle-dependent transverse magnetoresistance in bismuth, with a magnetic field perpendicular to the applied electric current and rotating in three distinct crystallographic planes. The observed angular oscillations are confronted with the expectations of semiclassic transport theory for a multivalley system with anisotropic mobility and the agreement allows us to quantify the components of the mobility tensor for both electrons and holes. A quadratic temperature dependence is resolved. As Hartman argued long ago, this indicates that inelastic resistivity in bismuth is dominated by carrier-carrier scattering. At low temperature and high magnetic field, the threefold symmetry of the lattice is suddenly lost. Specifically, a $2\pi /3$ rotation of magnetic field around the trigonal axis modifies the amplitude of the magnetoresistance below a field-dependent temperature. By following the evolution of this anomaly as a function of temperature and magnetic field, we map the boundary in the (field, temperature) plane separating two electronic states. In the less symmetric state, confined to low temperature and high magnetic field, the three Dirac valleys cease to be rotationally invariant. We discuss the possible origins of this spontaneous valley polarization, including a valley-nematic scenario.

In contrast to strong plasmonic scattering from metal particles or structures in metal films, we show that patterns of arbitrary shape fabricated out of multilayer hyperbolic metamaterials become invisible within a chosen band of optical frequencies. This is due to anomalously weak scattering when the in-plane permittivity of the multilayer hyperbolic metamaterials is tuned to match with the surrounding medium. This new phenomenon is described theoretically and demonstrated experimentally by optical characterization of various patterns in Au-Si multilayer hyperbolic metamaterials. This anomalously weak scattering is insensitive to pattern sizes, shapes, and incident angles, and has potential applications in scattering cross-section engineering, optical encryption, low-observable conductive probes, and optoelectric devices.

It has been shown numerically that systems of particles interacting with isotropic “stealthy” bounded long-ranged pair potentials (similar to Friedel oscillations) have classical ground states that are (counterintuitively) disordered, hyperuniform, and highly degenerate. Disordered hyperuniform systems have received attention recently because they are distinguishable exotic states of matter poised between a crystal and liquid that are endowed with novel thermodynamic and physical properties. The task of formulating an ensemble theory that yields analytical predictions for the structural characteristics and other properties of stealthy degenerate ground states in $d$-dimensional Euclidean space ${\mathbb{R}}^d$ is highly nontrivial because the dimensionality of the configuration space depends on the number density $\rho$ and there is a multitude of ways of sampling the ground-state manifold, each with its own probability measure for finding a particular ground-state configuration. The purpose of this paper is to take some initial steps in this direction. Specifically, we derive general exact relations for thermodynamic properties (energy, pressure, and isothermal compressibility) that apply to any ground-state ensemble as a function of $\rho$ in any $d$, and we show how disordered degenerate ground states arise as part of the ground-state manifold. We also derive exact integral conditions that both the pair correlation function $g_2(r)$ and structure factor $S(k)$ must obey for any $d$. We then specialize our results to the canonical ensemble (in the zero-temperature limit) by exploiting an ansatz that stealthy states behave remarkably like “pseudo”-equilibrium hard-sphere systems in Fourier space. Our theoretical predictions for $g_2(r)$ and $S(k)$ are in excellent agreement with computer simulations across the first three space dimensions. These results are used to obtain order metrics, local number variance, and nearest-neighbor functions across dimensions. We also derive accurate analytical formulas for the structure factor and thermal expansion coefficient for the excited states at sufficiently small temperatures for any $d$. The development of this theory provides new insights regarding our fundamental understanding of the nature and formation of low-temperature states of amorphous matter. Our work also offers challenges to experimentalists to synthesize stealthy ground states at the molecular level.

Combining superconductors ($S$) and ferromagnets ($F$) offers the opportunity to create a new class of superconducting spintronic devices. In particular, the $S/F$ interface can be specifically engineered to convert singlet Cooper pairs to spin-polarized triplet Cooper pairs. The efficiency of this process can be studied using a so-called triplet spin valve (TSV), which is composed of two $F$ layers and a $S$ layer. When the magnetizations in the two $F$ layers are not collinear, singlet pairs are drained from the $S$ layer, and triplet generation is signaled by a decrease of the critical temperature $T_c$. Here, we build highly efficient TSVs using a 100% spin-polarized half-metallic ferromagnet, ${\mathrm{CrO}}_2$. The application of out-of-plane magnetic fields results in an extremely strong suppression of $T_c$, by well over a Kelvin. The observed effect is an order of magnitude larger than previous studies on TSVs with standard ferromagnets. Furthermore, we clearly demonstrate that this triplet proximity effect is strongly dependent on the transparency and spin activity of the interface. Our results are particularly important in view of the growing interest in generating long-range triplet supercurrents for dissipationless spintronics.

We derive a scheme for systematically characterizing the responses of gapped as well as gapless systems of free fermions to electromagnetic and strain fields starting from a common parent theory. Using the fact that position operators in the lowest Landau level of a quantum Hall state are canonically conjugate, we consider a massive Dirac fermion in $2n$ spatial dimensions under $n$ mutually orthogonal magnetic fields and reinterpret physical space in the resulting zeroth Landau level as phase space in $n$ spatial dimensions. The bulk topological responses of the parent Dirac fermion, given by a Chern-Simons theory, translate into quantized insulator responses, while its edge anomalies characterize the response of gapless systems. Moreover, various physically different responses are seen to be related by the interchange of position and momentum variables. We derive many well-known responses and demonstrate the utility of our theory by predicting spectral flow along dislocations in Weyl semimetals.

Topological Kondo insulators are strongly correlated materials where itinerant electrons hybridize with localized spins, giving rise to a topologically nontrivial band structure. Here, we use nonperturbative bosonization and renormalization-group techniques to study theoretically a one-dimensional topological Kondo insulator, described as a Kondo-Heisenberg model, where the Heisenberg spin-$1/2$ chain is coupled to a Hubbard chain through a Kondo exchange interaction in the $p$-wave channel (i.e., a strongly correlated version of the prototypical Tamm-Schockley model). We derive and solve renormalization-group equations at two-loop order in the Kondo parameter, and find that, at half filling, the charge degrees of freedom in the Hubbard chain acquire a Mott gap, even in the case of a noninteracting conduction band (Hubbard parameter $U=0$). Furthermore, at low enough temperatures, the system maps onto a spin-$1/2$ ladder with local ferromagnetic interactions along the rungs, effectively locking the spin degrees of freedom into a spin-1 chain with frozen charge degrees of freedom. This structure behaves as a spin-1 Haldane chain, a prototypical interacting topological spin model, and features two magnetic spin-$1/2$ end states for chains with open boundary conditions. Our analysis allows us to derive an insightful connection between topological Kondo insulators in one spatial dimension and the well-known physics of the Haldane chain, showing that the ground state of the former is qualitatively different from the predictions of the naive mean-field theory.

Transition metal oxides play important roles as contact and electrode materials, but their use as active layers in solar energy conversion requires achieving semiconducting properties akin to those of conventional semiconductors like Si or GaAs. In particular, efficient bipolar carrier transport is a challenge in these materials. Based on the prediction that a tetrahedral polymorph of MnO should have such desirable semiconducting properties, and the possibility to overcome thermodynamic solubility limits by nonequilibrium thin-film growth, we exploit both structure-property and composition-structure relationships to design and realize novel wurtzite-structure ${\mathrm{Mn}}_{1-x}{\mathrm{Zn}}_x\mathrm{O}$ alloys. At Zn compositions above $x\approx 0.3$, thin films of these alloys assume the tetrahedral wurtzite structure instead of the octahedral rocksalt structure of MnO, thereby enabling semiconductor properties that are unique among transition metal oxides, i.e., a band gap within the visible spectrum, a band-transport mechanism for both electron and hole carriers, electron doping, and a band lineup suitable for solar hydrogen generation. A proof of principle is provided by initial photo-electrocatalytic device measurements, corroborating, in particular, the predicted favorable hole-transport properties of these alloys.

We study the dynamic after a smooth quench across a continuous transition from the disordered phase to the ordered phase. Based on scaling ideas, linear response, and the spectrum of unstable modes, we develop a theoretical framework, valid for any second-order phase transition, for the early-time evolution of the condensate in the broken phase. Our analysis unveils a novel period of nonadiabatic evolution after the system passes through the phase transition, where a parametrically large amount of coarsening occurs before a well-defined condensate forms. Our formalism predicts a rate of defect formation parametrically smaller than the Kibble-Zurek prediction and yields a criterion for the breakdown of Kibble-Zurek scaling for sufficiently fast quenches. We numerically test our formalism for a thermal quench in a ($2+1$)-dimensional holographic superfluid. These findings, of direct relevance in a broad range of fields including cold atom, condensed matter, statistical mechanics, and cosmology, are an important step toward a more quantitative understanding of dynamical phase transitions.

The best reported resolution in optical failure analysis of silicon chips is 120-nm half pitch demonstrated by Semicaps Private Limited, whereas the current and future industry requirement for 10-nm node technology is 100-nm half pitch. We show the first experimental evidence for resolution of features with 100-nm half pitch buried in silicon ($\lambda /10.6$), thus fulfilling the industry requirement. These results are obtained using near-infrared reflection-mode imaging using a solid immersion lens. The key novel feature of our approach is the choice of an appropriately sized collection pinhole. Although it is usually understood that, in general, resolution is improved by using the smallest pinhole consistent with an adequate signal level, it is found that in practice for silicon chips there is an optimum pinhole size, determined by the generation of induced currents in the sample. In failure analysis of silicon chips, nondestructive imaging is important to avoid disturbing the functionality of integrated circuits. High-resolution imaging techniques like SEM or TEM require the transistors to be exposed destructively. Optical microscopy techniques may be used, but silicon is opaque in the visible spectrum, mandating the use of near-infrared light and thus poor resolution in conventional optical microscopy. We expect our result to change the way semiconductor failure analysis is performed.

One of the major puzzles regarding unconventional superconductivity is how some of the most interesting superconductors are related to an insulating phase that lies in close proximity. Here, we report scanning tunneling microscopy studies of the local electronic structure of Cu-doped NaFeAs across the superconductor-to-insulator transition. We find that in the highly insulating regime, the electronic spectrum develops an energy gap with diminishing density of states at the Fermi level. The overall line shape and strong spatial variations of the spectra are strikingly similar to those of lightly doped cuprates close to the parent Mott insulator. We propose that the suppression of the itinerant electron states and the strong impurity potential induced by Cu dopants lead to this insulating iron pnictide.