The nucleation of crystals from liquid melt is often characterized by a competition between different crystalline structures or polymorphs and can result in nuclei with heterogeneous compositions. These mixed-phase nuclei can display nontrivial spatial arrangements, such as layered and onionlike structures, whose composition varies according to the radial distance, and which so far have been explained on the basis of bulk and surface free-energy differences between the competing phases. Here we extend the generality of these nonclassical nucleation processes, showing that layered and onionlike structures can emerge solely based on structural fluctuations even in the absence of free-energy differences. We consider two examples of competing crystalline structures, hcp and fcc forming in hard spheres relevant for repulsive colloids and dense liquids, and the cubic and hexagonal diamond forming in water relevant also for other group 14 elements such as carbon and silicon. We introduce a novel structural order parameter that combined with a neural-network classification scheme allows us to study the properties of the growing nucleus from the early stages of nucleation. We find that small nuclei have distinct size fluctuations and compositions from the nuclei that emerge from the growth stage. The transition between these two regimes is characterized by the formation of onionlike structures, in which the composition changes with the distance from the center of the nucleus, similar to what is seen in the two-step nucleation process.

The physical realization of ${\mathbb{Z}}_2$ topological order as encountered in the paradigmatic toric code has proven to be an elusive goal. We predict that this phase of matter can be realized in a two-dimensional array of Rydberg atoms placed on the ruby lattice, at specific values of the Rydberg blockade radius. First, we show that the blockade model—also known as a “$PXP$” model—realizes a monomer-dimer model on the kagome lattice with a single-site kinetic term. This model can be interpreted as a ${\mathbb{Z}}_2$ gauge theory whose dynamics is generated by monomer fluctuations. We obtain its phase diagram using the numerical density matrix renormalization group method and find a topological quantum liquid (TQL) as evidenced by multiple measures including (i) a continuous transition between two featureless phases, (ii) a topological entanglement entropy of $\ln 2$ as measured in various geometries, (iii) degenerate topological ground states, and (iv) the expected modular matrix from ground state overlap. Next, we show that the TQL persists upon including realistic, algebraically decaying van der Waals interactions $V(r)\sim 1/r^6$ for a choice of lattice parameters. Moreover, we can directly access topological loop operators, including the Fredenhagen-Marcu order parameter. We show how these can be measured experimentally using a dynamic protocol, providing a “smoking gun” experimental signature of the TQL phase. Finally, we show how to trap an emergent anyon and realize different topological boundary conditions, and we discuss the implications for exploring fault-tolerant quantum memories.

According to the classical theory of Brownian motion, the mean-squared displacement of diffusing particles evolves linearly with time, whereas the distribution of their displacements is Gaussian. However, recent experiments on mesoscopic particle systems have discovered Brownian yet non-Gaussian regimes where diffusion coexists with an exponential tail in the distribution of displacements. Here we show that, contrary to the present theoretical understanding, the length scale $\lambda$ associated with this exponential distribution does not necessarily scale in a diffusive way. Simulations of Lennard-Jones systems reveal a behavior $\lambda \sim t^{1/3}$ in three dimensions and $\lambda \sim t^{1/2}$ in two dimensions. We propose a scaling theory based on the idea of hopping motion to explain this result. In contrast, simulations of a tetrahedral gelling system, where particles interact by a nonisotropic potential, yield a temperature-dependent scaling of $\lambda$. We interpret this behavior in terms of an intermittent hopping motion. Our findings link the Brownian yet non-Gaussian phenomenon with generic features of glassy dynamics and open new experimental perspectives on the class of molecular and supramolecular systems whose dynamics is ruled by rare events.

The Raman effect, inelastic scattering of light by lattice vibrations (phonons), produces an optical response closely tied to a material’s crystal structure. Here we show that resonant optical excitation of IR and Raman phonons gives rise to a Raman-scattering effect that can induce giant shifts to the refractive index and induce new optical constants that are forbidden in the equilibrium crystal structure. We complete the description of light-matter interactions mediated by coupled IR and Raman phonons in crystalline insulators—currently the focus of numerous experiments aiming to dynamically control material properties—by including a forgotten pathway through the nonlinear lattice polarizability. Our work expands the toolset for control and development of new optical technologies by revealing that the absorption of light within the terahertz gap can enable control of optical properties of materials over a broad frequency range.

We report the discovery of a new three-dimensional (3D) topological Dirac semimetal (TDS) material KZnBi, coexisting with a naturally formed superconducting state on the surface under ambient pressure. Using photoemission spectroscopy together with first-principles calculations, a 3D Dirac state with linear band dispersion is identified. The characteristic features of massless Dirac fermions are also confirmed by magnetotransport measurements, exhibiting an extremely small cyclotron mass of $m^{*}=0.012$ $m_0$ and a high Fermi velocity of $v_F=1.04\times {10}^6\mathrm{m}/\mathrm{s}$. Interestingly, superconductivity occurs below 0.85 K on the (001) surface, while the bulk remains nonsuperconducting. The captured linear temperature dependence of the upper critical field suggests the possible non-$s$-wave character of this surface superconductivity. Our discovery serves a distinctive platform to study the interplay between 3D TDS and the superconductivity.

We introduce the time-dependent density matrix renormalization group (tDMRG) as a solution to a long-standing problem in spintronics—how to describe spin-transfer torque (STT) between flowing spins of conduction electrons and localized spins within a magnetic material by treating the dynamics of both spin species fully quantum mechanically. In contrast to conventional Slonczewski-Berger STT, where the localized spins are viewed as classical vectors obeying the Landau-Lifshitz-Gilbert equation and where their STT-driven dynamics is initiated only when the spin polarization of flowing electrons and localized spins are noncollinear, quantum STT can occur when these vectors are collinear but antiparallel. Using tDMRG, we simulate the time evolution of a many-body quantum state of electrons and localized spins, where the former are injected as a spin-polarized current pulse while the latter comprise a quantum Heisenberg ferromagnetic metallic (FM) spin-$\frac{1}{2}$ $XXZ$ chain initially in the ground state with spin polarization antiparallel to that of injected electrons. The quantum STT reverses the direction of localized spins, but without rotation from the initial orientation, when the number of injected electrons exceeds the number of localized spins. Such nonclassical reversal, which is absent from Landau-Lifshitz-Gilbert dynamics, is strikingly inhomogeneous across the FM chain, and it can be accompanied by reduction of the magnetization associated with localized spins, even to zero at specific locations. This feature arises because quantum STT generates a highly entangled nonequilibrium many-body state of all flowing and localized spins, despite starting from the initially unentangled ground state of a mundane FM. Furthermore, the mutual information between localized spins at the FM edges remains nonzero even at infinite separation as the signature of dynamical buildup of long-range entanglement. The growth in time of entanglement entropy differentiates between the quantum and conventional (i.e., noncollinear) setups for STT, reaching a much larger asymptotic value in the former case.

Condensed matter systems admit topological collective excitations above a trivial ground state, an example being Chern insulators formed by Dirac bosons with a gap at finite energies. However, in contrast to electrons, there is no particle-number conservation law for collective excitations, which gives rise to particle-number-nonconserving many-body interactions whose influence on single-particle topology is an open issue of fundamental interest in the field of topological quantum materials. Taking magnons in ferromagnets as an example, we uncover topological magnon insulators that are stabilized by interactions through opening Chern-insulating gaps in the magnon spectrum. This finding can be traced back to the fact that the particle-number nonconserving interactions break the effective time-reversal symmetry of the harmonic theory. Hence, magnon-magnon interactions are a source of topology that can introduce chiral edge states, whose chirality depends on the magnetization direction. Importantly, interactions do not necessarily cause detrimental damping but can give rise to topological magnons with exceptionally long lifetimes. We identify two mechanisms of interaction-induced topological phase transitions—one driven by an external field, the other by temperature—and show that they cause unconventional sign reversals of transverse transport signals, in particular, of the thermal Hall conductivity. We identify candidate materials where this many-body mechanism is expected to occur, such as the metal-organic kagome-lattice magnet Cu(1,3-benzenedicarboxylate), the van der Waals honeycomb-lattice magnet ${\mathrm{CrI}}_3$, and the multiferroic kamiokite (${\mathrm{Fe}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$). Our results demonstrate that particle-number-nonconserving many-body interactions play an important role in generating nontrivial single-particle topology.

The rotational Brownian motion of colloidal spheres in dense suspensions reflects local hydrodynamics and contact forces, which are both key to nonlinear rheological phenomena such as shear-thickening and jamming, and transport in crowded environments, including intracellular migration and blood flow. To fully elucidate the role of rotational dynamics experimentally, it is crucial to measure the translational and rotational motion of all spheres simultaneously. Here, we directly access hydrodynamic and frictional coupling in colloidal suspensions up to arbitrarily high volume fractions using compositionally uniform colloidal spheres with an off-center, fully embedded core. We reveal interparticle hydrodynamic rotation-rotation coupling in charged colloidal crystals. We also find that higher local crystallinity in denser hard-sphere crystalline sediments enhances rotational diffusivity and that nearly arrested particles exhibit a stick-slip rotational motion due to frictional coupling. Our findings shed new light on the largely unexplored, local rotational dynamics of spherical particles in dense particulate materials.

In many unconventional superconductors, the presence of a pseudogap—a suppression in the electronic density of states extending above the critical temperature—has been a long-standing mystery. Here, we employ combined in situ electrical transport and angle-resolved photoemission spectroscopy measurements to reveal an unprecedentedly large pseudogap regime in single-layer $\mathrm{FeSe}/\mathrm{SrTi}{\mathrm{O}}_3$, an interfacial superconductor where incoherent Cooper pairs are initially formed above $T_{\mathrm{\Delta }}\approx 60\mathrm{K}$ but where a zero-resistance state is achieved only below $T_0<30\mathrm{K}$. We show that this behavior is accompanied by distinct transport signatures of two-dimensional phase fluctuating superconductivity, suggesting a mixed vortex state hosting incoherent Cooper pairs which persist well above the maximum clean limit $T_c$ of approximately 40 K. Our work establishes the critical role of reduced dimensionality in driving the complex interplay between Cooper pairing and phase coherence in two-dimensional high-$T_c$ superconductors, providing a paradigm for understanding and engineering higher-$T_c$ interfacial superconductors.

We study many-body quantum dynamics using Floquet quantum circuits in one space dimension as simple examples of systems with local interactions that support ergodic phases. Physical properties can be expressed in terms of multiple sums over Feynman histories, which for these models are paths or many-body orbits in Fock space. A natural simplification of such sums is the diagonal approximation, where the only terms that are retained are ones in which each path is paired with a partner that carries the complex conjugate weight. We identify the regime in which the diagonal approximation holds and the nature of the leading corrections to it. We focus on the behavior of the spectral form factor (SFF) and of matrix elements of local operators, averaged over an ensemble of random circuits, making comparisons with the predictions of random matrix theory (RMT) and the eigenstate thermalization hypothesis (ETH). We show that properties are dominated at long times by contributions to orbit sums in which each orbit is paired locally with a conjugate, as in the diagonal approximation, but that in large systems these contributions consist of many spatial domains, with distinct local pairings in neighboring domains. The existence of these domains is reflected in deviations of the SFF from RMT predictions, and of matrix element correlations from ETH predictions; deviations of both kinds diverge with system size. We demonstrate that our physical picture of orbit-pairing domains has a precise correspondence in the spectral properties of a transfer matrix that acts in the space direction to generate the ensemble-averaged SFF. In addition, we find that domains of a second type control non-Gaussian fluctuations of the SFF. These domains are separated by walls that are related to the entanglement membrane, known to characterize the scrambling of quantum information.

Triangular lattice of rare-earth ions with interacting effective spin-$1/2$ local moments is an ideal platform to explore the physics of quantum spin liquids (QSLs) in the presence of strong spin-orbit coupling, crystal electric fields, and geometrical frustration. The Yb delafossites, $\mathrm{NaYb}C{h}_2$ ($Ch=\mathrm{O}$, S, Se) with Yb ions forming a perfect triangular lattice, have been suggested to be candidates for QSLs. Previous thermodynamics, nuclear magnetic resonance, and powder-sample neutron scattering measurements on ${\mathrm{NaYbCh}}_2$ have supported the suggestion of the QSL ground states. The key signature of a QSL, the spin excitation continuum, arising from the spin quantum number fractionalization, has not been observed. Here we perform both elastic and inelastic neutron scattering measurements as well as detailed thermodynamic measurements on high-quality single-crystal ${\mathrm{NaYbSe}}_2$ samples to confirm the absence of long-range magnetic order down to 40 mK, and further reveal a clear signature of magnetic excitation continuum extending from 0.1 to 2.5 meV. The comparison between the structure of the magnetic excitation spectra and the theoretical expectation from the spinon continuum suggests that the ground state of ${\mathrm{NaYbSe}}_2$ is a QSL with a spinon Fermi surface.

In twisted homobilayer transition metal dichalcogenides, intra- and interlayer valley excitons hybridize with the layer configurations spatially varying in the moiré. The ground state valley excitons are trapped at two high-symmetry points with opposite electric dipoles in a moiré supercell, forming a honeycomb superlattice of nearest-neighbor dipolar attraction. We find that the spatial texture of layer configuration results in a luminescence anomaly of the moiré trapped excitons, where a tiny displacement by interactions dramatically increases the brightness and changes polarization from circular to linear. At full filling, radiative recombination predominantly occurs at edges and vacancies of the exciton superlattice. The anomaly also manifests in the cascaded emission of small clusters, producing chains of polarization entangled photons. An interlayer bias can switch the superlattice into a single-orbital triangular lattice with repulsive interactions only, where the luminescence anomaly can be exploited to distinguish ordered states and domain boundaries at fractional filling.

Recent experimental and theoretical works have made much progress toward understanding nonequilibrium phenomena in thermalizing systems, which act as thermal baths for their small subsystems, and many-body localized systems, which fail to do so. The description of time evolution in many-body systems is generally challenging due to the dynamical generation of quantum entanglement. In this work, we introduce an approach to study quantum many-body dynamics, inspired by the Feynman-Vernon influence functional. Focusing on a family of interacting, Floquet spin chains, we consider a Keldysh path-integral description of the dynamics. The central object in our approach is the influence matrix, which describes the effect of the system on the dynamics of a local subsystem. For translationally invariant models, we formulate a self-consistency equation for the influence matrix. For certain special values of the model parameters, we obtain an exact solution which represents a perfect dephaser (PD). Physically, a PD corresponds to a many-body system that acts as a perfectly Markovian bath on itself: at each period, it measures every spin. For the models considered here, we establish that PD points include dual-unitary circuits investigated in recent works. In the vicinity of PD points, the system is not perfectly Markovian, but rather acts as a bath with a short memory time. In this case, we demonstrate that the self-consistency equation can be solved using matrix-product states (MPS) methods, as the influence matrix temporal entanglement is low. A combination of analytical insights and MPS computations allows us to characterize the structure of the influence matrix in terms of an effective “statistical-mechanics” description. We finally illustrate the predictive power of this description by analytically computing how quickly an embedded impurity spin thermalizes. The influence matrix approach formulated here provides an intuitive view of the quantum many-body dynamics problem, opening a path to constructing models of thermalizing dynamics that are solvable or can be efficiently treated by MPS-based methods and to further characterizing quantum ergodicity or lack thereof.

Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a correction term that is independent of its size. We conjecture that these states have an efficient dual description in terms of a set of marginal density matrices on bounded regions, obeying the same entropy scaling law locally. We prove a restricted version of this conjecture for translationally invariant systems in two spatial dimensions. Specifically, we prove that a translationally invariant marginal obeying three nonlinear constraints—all of which follow from the entropy scaling law straightforwardly—must be consistent with some global state on an infinite lattice. Moreover, we derive a closed-form expression for the maximum-entropy density compatible with those marginals, deriving a variational upper bound on the thermodynamic free energy. The main assumptions of our construction are satisfied exactly by solvable models of topological order and approximately by finite-temperature Gibbs states of certain quantum spin Hamiltonians.

The mechanism behind the nematicity of FeSe is not known. Through elastoresitivity measurements it has been shown to be an electronic instability. However, thus far measurements have extended only to small strains, where the response is linear. Here, we apply large elastic strains to FeSe and perform two types of measurement. (1) Using applied strain to control twinning, the nematic resistive anisotropy at temperatures below the nematic transition temperature $T_s$ is determined. (2) Resistive anisotropy is measured as nematicity is induced through applied strain at fixed temperature above $T_s$. In both cases, as nematicity strengthens, the resistive anisotropy peaks at about 7%, then decreases. Below $\approx 40\mathrm{K}$, the nematic resistive anisotropy changes sign. We discuss possible implications of this behavior for theories of nematicity. In addition, we report the following. (1) Under experimentally accessible conditions with bulk crystals, stress, rather than strain, is the conjugate field to the nematicity of FeSe. (2) At low temperatures the twin boundary resistance is $\sim 10\%$ of the sample resistance, and must be properly subtracted to extract intrinsic resistivities. (3) Biaxial in-plane compression increases both in-plane resistivity and the superconducting critical temperature $T_c$, consistent with a strong role of the $yz$ orbital in the electronic correlations.

We present a full symmetry classification of fermion matter in and out of thermal equilibrium. Our approach starts from first principles, the ten different classes of linear and antilinear state transformations in fermionic Fock spaces, and symmetries defined via invariance properties of the dynamical equation for the density matrix. The object of classification is then the generators of reversible dynamics, dissipation and fluctuations, featuring’ in the generally irreversible and interacting dynamical equations. A sharp distinction between the symmetries of equilibrium and out-of-equilibrium dynamics, respectively, arises from the different role played by “time” in these two cases: In unitary quantum mechanics as well as in “microreversible” thermal equilibrium, antilinear transformations combined with an inversion of time define time-reversal symmetry. However, out of equilibrium an inversion of time becomes meaningless, while antilinear transformations in Fock space remain physically significant, and hence must be considered in autonomy. The practical consequence of this dichotomy is a novel realization of antilinear symmetries (six out of the ten fundamental classes) in nonequilibrium quantum dynamics that is fundamentally different from the established rules of thermal equilibrium. At large times, the dynamical generators thus symmetry classified determine the steady-state nonequilibrium distributions for arbitrary interacting systems. To illustrate this principle, we consider the fixation of a symmetry protected topological phase in a system of interacting lattice fermions. More generally, we consider the practically important class of mean field interacting systems, represented by Gaussian states. This class is naturally described in the language of non-Hermitian matrices, which allows us to compare to previous classification schemes in the literature.

We induce strong nonlocal interactions in a 2D Fermi gas in an optical lattice using Rydberg dressing. The system is approximately described by a $t-V$ model on a square lattice where the fermions experience isotropic nearest-neighbor interactions and are free to hop only along one direction. We measure the interactions using many-body Ramsey interferometry and study the lifetime of the gas in the presence of tunneling, finding that tunneling does not reduce the lifetime. To probe the interplay of nonlocal interactions with tunneling, we investigate the short-time-relaxation dynamics of charge-density waves in the gas. We find that strong nearest-neighbor interactions slow down the relaxation. Our work opens the door for quantum simulations of systems with strong nonlocal interactions such as extended Fermi-Hubbard models.

Being able to accurately describe the dynamics steady states of driven and/or dissipative but quantum correlated lattice models is of fundamental importance in many areas of science: from quantum information to biology. An efficient numerical simulation of large open systems in two spatial dimensions is a challenge. In this work, we develop a tensor network method, based on an infinite projected entangled pair operator ansatz, applicable directly in the thermodynamic limit. We incorporate techniques of finding optimal truncations of enlarged network bonds by optimizing an objective function appropriate for open systems. Comparisons with numerically exact calculations, both for the dynamics and the steady state, demonstrate the power of the method. In particular, we consider dissipative transverse quantum Ising, driven-dissipative hard-core boson, and dissipative anisotropic $XY$ models in non-mean-field limits, proving able to capture substantial entanglement in the presence of dissipation. Our method enables us to study regimes that are accessible to current experiments but lie well beyond the applicability of existing techniques.

The van der Waals compound, ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$, is the first intrinsic magnetic topological insulator, providing a materials platform for exploring exotic quantum phenomena such as the axion insulator state and the quantum anomalous Hall effect. However, intrinsic structural imperfections lead to bulk conductivity, and the roles of magnetic defects are still unknown. With higher concentrations of the same types of magnetic defects, the isostructural compound ${\mathrm{MnSb}}_2{\mathrm{Te}}_4$ is a better model system for a systematic investigation of the connections among magnetism, topology, and lattice defects. In this work, the impact of antisite defects on the magnetism and electronic structure is studied in ${\mathrm{MnSb}}_2{\mathrm{Te}}_4$. Mn-Sb site mixing leads to complex magnetic structures and tunes the interlayer magnetic coupling between antiferromagnetic and ferromagnetic. The detailed nonstoichiometry and site mixing of ${\mathrm{MnSb}}_2{\mathrm{Te}}_4$ crystals depend on the growth parameters, which can lead to $\approx 40\%$ of Mn sites occupied by Sb and $\approx 15\%$ of Sb sites by Mn in as-grown crystals. Single-crystal neutron diffraction and electron microscopy studies show nearly random distribution of the antisite defects. Band structure calculations suggest that the Mn-Sb site mixing favors a ferromagnetic interlayer coupling, consistent with experimental observation, but is detrimental to the band inversion required for a nontrivial topology. Our results suggest a long-range magnetic order of Mn ions sitting on Bi sites in ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. The effects of site mixing should be considered in all layered heterostructures that consist of alternating magnetic and topological layers, including the entire family of $\mathrm{MnTe}({\mathrm{Bi}}_2{\mathrm{Te}}_3{)}_n$, its Sb analogs, and their solid solution.

Anisotropic magnetoresistance (AMR) is a ubiquitous and versatile probe of magnetic order in contemporary spintronics research. Its origins are usually ascribed to extrinsic effects (i.e., spin-dependent electron scattering), whereas intrinsic (i.e., scattering-independent) contributions are neglected. Here, we measure AMR of polycrystalline thin films of the standard ferromagnets Co, Ni, ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$, and ${\mathrm{Ni}}_{50}{\mathrm{Fe}}_{50}$ over the frequency range from dc to 28 THz. The large bandwidth covers the regimes of both diffusive and ballistic intraband electron transport and, thus, allows us to separate extrinsic and intrinsic AMR components. Analysis of the THz response based on Boltzmann transport theory reveals that the AMR of the Ni, ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$, and ${\mathrm{Ni}}_{50}{\mathrm{Fe}}_{50}$ samples is of predominantly extrinsic nature. However, the Co thin film exhibits a sizable intrinsic AMR contribution, which is constant up to 28 THz and amounts to more than $2/3$ of the dc AMR contrast of 1%. These features are attributed to the hexagonal structure of the Co crystallites. They are interesting for applications in terahertz spintronics and terahertz photonics. Our results show that broadband terahertz electromagnetic pulses provide new and contact-free insights into magnetotransport phenomena of standard magnetic thin films on ultrafast timescales.