We propose the ${\mathbb{Z}}_Q$ Berry phase as a topological invariant for higher-order symmetry-protected topological (HOSPT) phases for two- and three-dimensional systems. It is topologically stable for electron-electron interactions assuming the gap remains open. As a concrete example, we show that the Berry phase is quantized in ${\mathbb{Z}}_4$ and characterizes the HOSPT phase of the extended Benalcazar-Bernevig-Hughes (BBH) model, which contains the next-nearest-neighbor hopping and the intersite Coulomb interactions. In addition, we introduce the ${\mathbb{Z}}_4$ Berry phase for the spin-model analog of the BBH model. Furthermore, we demonstrate the Berry phase is quantized in ${\mathbb{Z}}_4$ for the three-dimensional version of the BBH model. We also confirm the bulk-corner correspondence between the ${\mathbb{Z}}_4$ Berry phase and the corner states in the HOSPT phases.

In the conventional spin noise spectroscopy, the probe laser light monitors fluctuations of the spin orientation of a paramagnet revealed as fluctuations of its gyrotropy, i.e., circular birefringence. For spins larger than $1/2$, there exists spin arrangement of a higher order—the spin alignment—which also exhibits spontaneous fluctuations. We show theoretically and experimentally that the alignment fluctuations manifest themselves as the noise of the linear birefringence. In a magnetic field, the spin-alignment fluctuations, in contrast to those of spin orientation, show up as the noise of the probe-beam ellipticity at the double Larmor frequency, with the most efficient geometry of its observation being the Faraday configuration with the light propagating along the magnetic field. We have detected the spin-alignment noise in a cesium-vapor cell probed at the wavelength of D2 line ($852.35\mathrm{nm}$). The magnetic-field and polarization dependencies of the ellipticity noise are in full agreement with the developed theory.

We generate unidirectional coherent radiations at 391 and 428 nm corresponding to the $B{}^2{{\mathrm{\Sigma }}_u}^{+}\text{−}X{}^2{{\mathrm{\Sigma }}_g}^{+}$ (0,0) and (0,1) emission of ${{\mathrm{N}}_2}^{+}$ by irradiating neutral ${\mathrm{N}}_2$ with an elliptically modulated near-IR ultrashort laser field generated using a quarter-wave plate (QWP) with the different orders, and reveal that the lasing intensity at 391 nm becomes maximum at a specific orientation of the fast axis of QWP with respect to the polarization direction of the input laser field. We reproduce this observation by numerical calculations and show that the lasing intensity can be optimized by adjusting the temporal separation between the two polarization components of the elliptically modulated laser pulse and their relative amplitudes so that the inverted population between the $B{}^2{{\mathrm{\Sigma }}_u}^{+}$ and $X{}^2{{\mathrm{\Sigma }}_g}^{+}$ states can be achieved efficiently and the population in the $X{}^2{{\mathrm{\Sigma }}_g}^{+}(v^{″}=0)$ level is further depleted in the latter part of the laser pulse by the $A{}^2{\mathrm{\Pi }}_u\text{−}X{}^2{{\mathrm{\Sigma }}_g}^{+}$ transition.

A global heat flux model based on a fractional derivative of plasma pressure is proposed for the heat transport in fusion plasmas. The degree of the fractional derivative of the heat flux, $\alpha$, is defined through the power balance analysis of the steady state. The model was used to obtain the experimental values of $\alpha$ for a large database of the Joint European Torus (JET) carbon-wall as well as ITER like-wall plasmas. The fractional degrees of the electron heat flux are found to be $\alpha <2$, for all the selected pulses in the database, suggesting a deviation from the diffusive paradigm. Moreover, the results show that as the volume integrated input power is increased, the fractional degree of the electron heat flux converges to $\alpha \sim 0.8$, indicating a global scaling between the net heating and the pressure profile in the high-power JET plasmas. The model is expected to provide insight into the proper kinetic description for the fusion plasmas and improve the accuracy of the heat transport predictions.

An external magnetic field is needed to drive a nanowire in proximity to an $s$-wave superconductor into a topological regime which supports Majorana end states. However, magnetic field generally suppresses the proximity superconducting gap induced on the nanowire. In recent experiments using InSb nanowires coupled to conventional superconductors such as Al and NbTiN, the induced proximity gap vanishes at magnetic fields $B\sim 1$ T. This results in a small superconducting gap on the wire and a narrow topological regime which is proportional to the strength of the magnetic field. In this work, we show that by placing nanowires in proximity to recently discovered Ising superconductors such as the atomically thin transition-metal dichalcogenide ${\mathrm{NbSe}}_2$, the topological superconducting gap on the wire can be maintained at a large magnetic field as strong as $B\sim 10$ T. This robust topological superconducting gap is induced by the unique equal-spin triplet Cooper pairs of the parent Ising superconductor. The strong magnetic field allows a topological regime ten times larger than those in InSb wires coupled to conventional superconductors. Our work establishes a realistic platform for building robust Majorana-based qubits.

We study the nonequilibrium steady states in a unidirectional or driven single file motion (DSFM) of a collection of particles with hard-core repulsion in a closed system. For driven propulsion that is spatially smoothly varying with a few discontinuities, we show that the steady states are broadly classified into two classes, independently of any system detail: (i) when the steady state current depends explicitly on the conserved number density $n$, and (ii) when it is independent of $n$. This manifests itself in the universal topology of the phase diagrams and fundamental diagrams (i.e., the current versus density curves) for DSFM, which are determined solely by the interplay between two control parameters $n$ and the minimum propulsion speed along the chain. Our theory can be tested in laboratory experiments on driven particles in a closed geometry.

We show analytically and numerically that time-delayed nonlocal response induces traveling localized states in bistable systems. These states result from the interaction of fronts between homogeneous steady states. We illustrate this mechanism by considering an experimentally relevant system—the fiber cavity with the noninstantaneous Raman response. Close to the nascent bistability, we performed a derivation of a generic bistable model with a nonlocal delayed response. Analytical expressions of the width and the speed of traveling localized states are derived. Without a time-delayed nonlocal response, traveling localized states are excluded. In addition, we propose realistic parameters and perform numerical simulations of the governing model equation.

Realization of an elemental solid-state quasicrystal has remained a distant dream so far in spite of extensive work in this direction for almost two decades. In the present work, we report the discovery of quasiperiodic ordering in a thick layer of elemental Sn grown on icosahedral $\left(i\right)$-Al-Pd-Mn. The scanning tunneling microscopy (STM) images and the low-energy electron diffraction patterns of the Sn layer show specific structural signatures that portray quasiperiodicity but are distinct from the substrate. Photoemission spectroscopy reveals the existence of the pseudogap around the Fermi energy up to the maximal Sn thickness. The structure of the Sn layer is modeled as a form of quasicrystalline clathrate on the basis of multiple supporting evidences: First, from ab initio total energy evaluation, the energy of bulk Sn clathrate quasicrystal is lower than the high-temperature metallic $\beta$-Sn phase, but higher than the low-temperature $\alpha$-Sn phase. A comparative study of the free slab energetics shows that surface energy favors clathrate over $\alpha$-Sn up to about 4-nm layer thickness and matches $\beta$-Sn for narrow window of slab thickness of 2–3 nm. Second, the bulk clathrate exhibits gap opening near Fermi energy, while the free slab form exhibits a pronounced pseudogap, which explains the pseudogap observed in photoemission. Third, the STM images exhibit good agreement with clathrate model. Finally, we establish the adlayer-substrate compatibility based on very similar (within 1%) the cage-cage separation in the Sn clathrate and the pseudo-Mackay cluster-cluster separation on the $i$-Al-Pd-Mn surface. Furthermore, the nucleation centers of the Sn adlayer on the substrate are identified and these are shown to be a valid part of the Sn clathrate structure. Thus, based on both experimental and ab initio density functional theory calculations, we propose that 4-nm-thick Sn adlayer deposited on fivefold surface of $i$-Al-Pd-Mn substrate is in fact a metastable realization of elemental, clathrate family quasicrystal.

Traditional approaches to controlling single spins in quantum dots require the generation of large electromagnetic fields to drive many Rabi oscillations within the spin coherence time. We demonstrate “flopping-mode” electric dipole spin resonance, where an electron is electrically driven in a Si/SiGe double quantum dot in the presence of a large magnetic field gradient. At zero detuning, charge delocalization across the double quantum dot enhances coupling to the drive field and enables low-power electric dipole spin resonance. Through dispersive measurements of the single-electron spin state, we demonstrate a nearly three order of magnitude improvement in driving efficiency using flopping-mode resonance, which should facilitate low-power spin control in quantum dot arrays.

We study the effect of local projective measurements on the quantum quench dynamics. As a concrete example, a one-dimensional Bose-Hubbard model is simulated by the matrix product state and time-evolving block decimation. We map out a global phase diagram in terms of the measurement rate in spatial space and time domain, which demonstrates a volume-to-area law entanglement phase transition. When the measurement rate reaches the critical value, we observe a logarithmic growth of entanglement entropy as the subsystem size or evolved time increases. Moreover, we find that the probability distribution of the single-site entanglement entropy distinguishes the volume and area law phases, similar to the case of disorder-induced many-body localization. We also investigate the scaling behavior of entanglement entropy and mutual information between two separated sites, which is indicative of a single universality class and thus suggests a possible unified description of this transition.

We demonstrate kinematically complete measurements on frustrated double ionization of argon atoms in strong laser fields with a reaction microscope. We found that the electron trapping probability after strong-field double ionization is much higher than that after strong-field single ionization, especially in the case of high laser intensity. The retrieved electron momentum distributions of frustrated double ionization show a clear transition from the nonsequential to the sequential regime, similar to those of strong-field double ionization. The dependence of electron momentum width on the laser intensity further indicates that the second released electron has a dominant contribution to frustrated double ionization in the sequential regime.

The electron-positron pair production in the collision of two intense gamma lasers is studied beyond the dipole approximation. The complete electron/positron momentum spectrum obtained by three-dimensional computation shows directly the multiphoton pair production channels and provides a sensitive test on the widely used concept of the effective mass. Nonperturbative features are identified in the dependence of the total yield on the field intensity. In particular, various breaks in the momentum rings are observed and prove to be a manifestation of a particle's energy gaps in the standing light wave induced by the Kapitza-Dirac scattering. A theoretical model of multilevel systems coupled by the Kapitza-Dirac scattering and pair production channels is established. Multichannel interference effects and pair production suppression are revealed in these systems.

Air pollution by nitrogen oxides $\left({\mathrm{NO}}_x\right)$ is a major concern in large cities as it has severe adverse health effects. However, the statistical properties of air pollutants are not fully understood. Here, we use methods borrowed from nonequilibrium statistical mechanics to construct suitable superstatistical models for air pollution statistics. In particular, we analyze time series of nitritic oxide (NO) and nitrogen dioxide $\left({\text{NO}}_2\right)$ concentrations recorded at several locations throughout Greater London. We find that the probability distributions of concentrations have heavy tails and that the dynamics is well described by ${\chi }^2$ superstatistics for NO and inverse-${\chi }^2$ superstatistics for ${\text{NO}}_2$. Our results can be used to give precise risk estimates of high-pollution situations and pave the way to mitigation strategies.

Multilayer nanostructures represent an important class of materials with tunable optical and thermal radiative properties that can be leveraged for a wide range of energy applications. We present a theoretical framework for optimizing the geometry of such structures that utilizes gradients of various objective functions that are enabled through analytic differentiation of the transfer-matrix equations. We demonstrate the usefulness of this method by applying it to the local optimization of many-degree-of-freedom structures for incandescent light sources, and the global optimization of few-degree-of-freedom structures that serve as solar cell coatings and optical cavities for enhancing the absorption of organic chromophores embedded in thin films.

We investigate two-body collisions occurring during the time-of-flight expansion of interacting three-dimensional lattice Bose superfluids. The number of collisions is extracted from the observed $s$-wave scattering halos located between the diffraction peaks of the superfluids. These faint halos can be monitored owing to the large dynamical range in densities associated with detecting individual metastable helium atoms. We monitor the number of collisions as a function of the total atom number and of the amplitude of the lattice, in a regime where the number of trapped atoms per lattice site is large. In addition, we introduce a classical model of collisions that quantitatively describes the experiment without adjustable parameters. Finally, the present work validates quantitatively the assumption of a ballistic expansion when investigating the Bose-Hubbard Hamiltonian with a unity occupation of the lattice.

For practical applications of quantum randomness generation, it is important to certify and further produce a fixed block of fresh random bits with as few trials as possible. Consequently, protocols with high finite-data efficiency are preferred. To yield such protocols with respect to quantum side information, we develop quantum probability estimation. Our approach is applicable to device-independent as well as device-dependent scenarios, and it generalizes techniques from previous works [Miller and Shi, SIAM J. Comput. 46, 1304 (2017); Arnon-Friedman et al., Nat. Commun. 9, 459 (2018)]. Quantum probability estimation can adapt to changing experimental conditions, allows stopping the experiment as soon as the prespecified randomness goal is achieved, and can tolerate imperfect knowledge of the input distribution. Moreover, the randomness rate achieved at constant error is asymptotically optimal. For the device-independent scenario, our approach certifies the amount of randomness available in experimental results without first searching for relations between randomness and violations of fixed Bell inequalities. We implement quantum probability estimation for device-independent randomness generation in the CHSH Bell-test configuration, and we show significant improvements in finite-data efficiency, particularly at small Bell violations which are typical in current photonic loophole-free Bell tests.

A hierarchy of timescales is ubiquitous in biological systems, where enzymatic reactions play an important role because they can hasten the relaxation to equilibrium. We introduced a statistical physics model of interacting spins that also incorporates enzymatic reactions to extend the classic model for allosteric regulation. Through Monte Carlo simulations, we found that the relaxation dynamics are much slower than the elementary reactions and are logarithmic in time with several plateaus, as is commonly observed for glasses. This is because of the kinetic constraints from the cooperativity via the competition for an enzyme, which has a different affinity for molecules with different structures. Our model showed symmetry breaking in the relaxation trajectories that led to inherently kinetic transitions without any correspondence to the equilibrium state. In this Rapid Communication, we discuss the relevance of these results for diverse responses in biology.

We consider the electronic spectrum near $M=(\pi ,\pi )$ in the nematic phase of FeSe $(T<T_{\mathrm{nem}})$ and make a detailed comparison with recent ARPES and STM experiments. Our main focus is the unexpected temperature dependence of the excitations at the $M$ point. These have been identified as having $xz$ and $yz$ orbital character well below $T_{\mathrm{nem}}$, but remain split at $T>T_{\mathrm{nem}}$, in apparent contradiction to the fact that in the tetragonal phase the $xz$ and $yz$ orbitals are degenerate. Here we present two scenarios which can describe the data. In both scenarios, hybridization terms present in the tetragonal phase leads to an orbital transmutation, a change in the dominant orbital character of some of the bands, between $T>T_{\mathrm{nem}}$ and $T\ll T_{\mathrm{nem}}$. The first scenario relies on the spin-orbit coupling at the $M$ point. We show that a finite spin-orbit coupling gives rise to orbital transmutation, in which one of the modes, identified as $xz$ ($yz)$ at $T\ll T_{\mathrm{nem}}$, becomes predominantly $xy$ at $T>T_{\mathrm{nem}}$ and hence does not merge with the predominantly $yz$ ($xz$) mode. The second scenario, complementary to the first, takes into consideration the fact that both ARPES and STM are surface probes. In the bulk, a direct hybridization between the $xz$ and $yz$ orbitals is not allowed at the $M$ point, however, it is permitted on the surface. In the presence of a direct $xz/yz$ hybridization, the orbital character of the $xz/yz$ modes changes from pure $xz$ and pure $yz$ at $T\ll T_{\mathrm{nem}}$ to $xz\pm yz$ at $T>T_{\mathrm{nem}}$, i.e., the two modes again have mono-orbital character at low $T$, but do not merge at $T_{\mathrm{nem}}$. We discuss how these scenarios can be distinguished in polarized ARPES experiments.

There has been a great interest in magnetic field induced quantum spin liquids in Kitaev magnets after the discovery of neutron scattering continuum and half-quantized thermal Hall conductivity in the material $\alpha \text{−}{\mathrm{RuCl}}_3$. In this work, we provide a semiclassical analysis of the relevant theoretical models, which enable us to treat large system sizes approximating the thermodynamic limit. We find a series of competing magnetic orders with fairly large unit cells at intermediate magnetic fields, which are mostly missed by previous studies. We show that quantum fluctuations are typically strong in these large unit cell orders, while the magnetic excitations, magnons, have a dispersion that resembles a scattering continuum. The huge quantity of magnon bands with finite Chern numbers also gives rise to an unusually large thermal Hall conductivity. Given the highly frustrated nature of the spin model, the large unit cell orders are likely to melt into the putative spin liquid in the quantum limit. Our work provides an important basis for a thorough investigation of emergent spin liquids and competing phases in Kitaev magnets.

Layered van der Waals ferromagnets are promising candidates for designing new spintronic devices. Here we investigated the critical properties and magnetocaloric effect connected with ferromagnetic transition in layered van der Waals ${\mathrm{VI}}_3$ single crystals. The critical exponents $\beta =0.244\left(5\right)$ with a critical temperature $T_c=50.10\left(2\right)\mathrm{K}$ and $\gamma =1.028\left(12\right)$ with $T_c=49.97\left(5\right)\mathrm{K}$ are obtained from the modified Arrott plot, whereas $\delta =5.24\left(2\right)$ is obtained from a critical isotherm analysis at $T_c=50\mathrm{K}$. The magnetic entropy change $-\mathrm{\Delta }{S}_M(T,H)$ features a maximum at $T_c$, i.e., $-\mathrm{\Delta }{S}_M^{\max }\sim 2.64\left(2.27\right)\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ with out-of-plane (in-plane) field change of 5 T. This is consistent with $-\mathrm{\Delta }{S}_M^{\max }\sim 2.80\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ deduced from heat capacity and the corresponding adiabatic temperature change $\mathrm{\Delta }{T}_{\mathrm{ad}}\sim 0.96\mathrm{K}$ with out-of-plane field change of 5 T. The critical analysis suggests that the ferromagnetic phase transition in ${\mathrm{VI}}_3$ is situated close to a three- to two-dimensional critical point. The rescaled $\mathrm{\Delta }{S}_M(T,H)$ curves collapse onto a universal curve, confirming a second-order type of the magnetic transition and reliability of the obtained critical exponents.