Motivated by recent progress in the superconductivity nonreciprocal phenomena, we study the general theory of Josephson diodes. The central ingredient for Josephson diodes is the asymmetric proximity process inside the tunneling barrier. From the symmetry breaking point of view, there are two types of Josephson diodes: inversion breaking and time-reversal breaking. For the inversion breaking case, applying voltage bias could effectively tune the proximity process like the voltage-dependent Rashba coupling or electric polarization giving rise to $I_c(V)\ne I_c(-V)$ and $I_{r+}\ne I_{r-}$. For the time-reversal breaking case, the current flow could adjust the internal time-reversal breaking field like magnetism or time-reversal breaking electron-electron pairing, which leads to $I_{c+}\ne I_{c-}$. All these results provide a complete understanding and the general principles of realizing Josephson diodes, especially the recently found ${\mathrm{NbSe}}_2/{\mathrm{Nb}}_3{\mathrm{Br}}_8/{\mathrm{NbSe}}_2$ Josephson diodes.

Two different heat-transport mechanisms are discussed in solids. In crystals, heat carriers propagate and scatter particlelike as described by Peierls’s formulation of the Boltzmann transport equation for phonon wave packets. In glasses, instead, carriers behave wavelike, diffusing via a Zener-like tunneling between quasidegenerate vibrational eigenstates, as described by the Allen-Feldman equation. Recently, it has been shown that these two conduction mechanisms emerge from a Wigner transport equation, which unifies and extends the Peierls-Boltzmann and Allen-Feldman formulations, allowing one to describe also complex crystals where particlelike and wavelike conduction mechanisms coexist. Here, we discuss the theoretical foundations of such transport equation as is derived from the Wigner phase-space formulation of quantum mechanics, elucidating how the interplay between disorder, anharmonicity, and the quantum Bose-Einstein statistics of atomic vibrations determines thermal conductivity. This Wigner formulation argues for a preferential phase convention for the dynamical matrix in the reciprocal Bloch representation and related off-diagonal velocity operator’s elements; such convention is the only one yielding a conductivity which is invariant with respect to the nonunique choice of the crystal’s unit cell and is size consistent. We rationalize the conditions determining the crossover from particlelike to wavelike heat conduction, showing that phonons below the Ioffe-Regel limit (i.e., with a mean free path shorter than the interatomic spacing) contribute to heat transport due to their wavelike capability to interfere and tunnel. Finally, we show that the present approach overcomes the failures of the Peierls-Boltzmann formulation for crystals with ultralow or glasslike thermal conductivity, with case studies of materials for thermal barrier coatings and thermoelectric energy conversion.

The interlayer coupling is emerging as a new parameter for tuning the physical properties of two-dimensional (2D) van der Waals materials. When two identical semiconductor monolayers are stacked with a twist angle, the periodic interlayer coupling modulation due to the moiré superlattice may endow exotic physical phenomena, such as moiré excitons and correlated electronic phases. To gain insight into these new phenomena, it is crucial to unveil the underlying coupling between atomic layers. Recently, the rhombohedral-stacked transition metal dichalcogenide (TMD) bilayer has attracted significant interest because of the emergence of an out-of-plane polarization from nonferroelectric monolayer constituents. However, as a key parameter responsible for the physical properties, the interlayer coupling and its relationship with ferroelectricity remain elusive. Here, we probe the asymmetric interlayer coupling between the conduction band of one layer and the valence band from the other layer in a $3R\text{−}{\mathrm{MoS}}_2$ bilayer, which can be understood as a result of a layer-dependent Berry phase winding. By performing optical spectroscopy in a dual-gated device, we show an effective type-II band alignment exists at $K$ points in the $3R\text{−}{\mathrm{MoS}}_2$ bilayer. Furthermore, by unraveling various contributions to the band offset, we quantitatively determine the asymmetric interlayer coupling and spontaneous polarization in $3R\text{−}{\mathrm{MoS}}_2$. Our results unveil the physical nature of stacking-induced ferroelectricity in TMD homostructures and have important implications for moiré physics in 2D semiconductors.

A vison is an excitation of the Kitaev spin liquid which carries a ${\mathbb{Z}}_2$ gauge flux. While immobile in the pure Kitaev model, it becomes a dynamical degree of freedom in the presence of perturbations. We study an isolated vison in the isotropic Kitaev model perturbed by a small external magnetic field $h$, an off-diagonal exchange interaction $\mathrm{\Gamma }$, and a Heisenberg coupling $J$. In the ferromagnetic Kitaev model, the dressed vison obtains a dispersion linear in $\mathrm{\Gamma }$ and $h$ and a fully universal low-$T$ mobility, $\mu =6\hslash v_m^2/(k_{B}T{)}^2$, where $v_m$ is the velocity of Majorana fermions. In contrast, in the antiferromagnetic (AFM) Kitaev model interference effects suppress coherent propagation and an incoherent Majorana-assisted hopping leads to a $T$-independent mobility. The motion of a single vison due to Heisenberg interactions is strongly suppressed for both signs of the Kitaev coupling. Vison bands in AFM Kitaev models can be topological and may lead to characteristic features in the thermal Hall effects in Kitaev materials. Furthermore, we argue that vison diffusion leads to universal signatures in quench experiments.

Monitored quantum circuits can exhibit an entanglement transition as a function of the rate of measurements, stemming from the competition between scrambling unitary dynamics and disentangling projective measurements. We study how entanglement dynamics in nonunitary quantum circuits can be enriched in the presence of charge conservation, using a combination of exact numerics and a mapping onto a statistical mechanics model of constrained hard-core random walkers. We uncover a charge-sharpening transition that separates different scrambling phases with volume-law scaling of entanglement, distinguished by whether measurements can efficiently reveal the total charge of the system. We find that while Rényi entropies grow sub-ballistically as $\sqrt{t}$ in the absence of measurement, for even an infinitesimal rate of measurements, all average Rényi entropies grow ballistically with time $\sim t$. We study numerically the critical behavior of the charge-sharpening and entanglement transitions in U(1) circuits, and show that they exhibit emergent Lorentz invariance and can also be diagnosed using scalable local ancilla probes. Our statistical mechanical mapping technique readily generalizes to arbitrary Abelian groups, and offers a general framework for studying dissipatively stabilized symmetry-breaking and topological orders.

Identifying phase transitions and classifying phases of matter is central to understanding the properties and behavior of a broad range of material systems. In recent years, machine-learning (ML) techniques have been successfully applied to perform such tasks in a data-driven manner. However, the success of this approach notwithstanding, we still lack a clear understanding of ML methods for detecting phase transitions, particularly of those that utilize neural networks (NNs). In this work, we derive analytical expressions for the optimal output of three widely used NN-based methods for detecting phase transitions. These optimal predictions correspond to the results obtained in the limit of high model capacity. Therefore, in practice, they can, for example, be recovered using sufficiently large, well-trained NNs. The inner workings of the considered methods are revealed through the explicit dependence of the optimal output on the input data. By evaluating the analytical expressions, we can identify phase transitions directly from experimentally accessible data without training NNs, which makes this procedure favorable in terms of computation time. Our theoretical results are supported by extensive numerical simulations covering, e.g., topological, quantum, and many-body localization phase transitions. We expect similar analyses to provide a deeper understanding of other classification tasks in condensed matter physics.

Recent series of theoretical and experimental reports have driven attention to time-reversal symmetry-breaking spintronic and spin-splitting phenomena in materials with collinear-compensated magnetic order incompatible with conventional ferromagnetism or antiferromagnetism. Here we employ an approach based on nonrelativistic spin-symmetry groups that resolves the conflicting notions of unconventional ferromagnetism or antiferromagnetism by delimiting a third basic collinear magnetic phase. We derive that all materials hosting this collinear-compensated magnetic phase are characterized by crystal-rotation symmetries connecting opposite-spin sublattices separated in the real space and opposite-spin electronic states separated in the momentum space. We describe prominent extraordinary characteristics of the phase, including the alternating spin-splitting sign and broken time-reversal symmetry in the nonrelativistic band structure, the planar or bulk $d$-, $g$-, or $i$-wave symmetry of the spin-dependent Fermi surfaces, spin-degenerate nodal lines and surfaces, band anisotropy of individual spin channels, and spin-split general, as well as time-reversal invariant momenta. Guided by the spin-symmetry principles, we discover in ab initio calculations outlier materials with an extraordinary nonrelativistic spin splitting, whose eV-scale and momentum dependence are determined by the crystal potential of the nonmagnetic phase. This spin-splitting mechanism is distinct from conventional relativistic spin-orbit coupling and ferromagnetic exchange, as well as from the previously considered anisotropic exchange mechanism in compensated magnets. Our results, combined with our identification of material candidates for the phase ranging from insulators and metals to a parent crystal of cuprate superconductors, underpin research of novel quantum phenomena and spintronic functionalities in high-temperature magnets with light elements, vanishing net magnetization, and strong spin coherence. In the discussion, we argue that the conflicting notions of unconventional ferromagnetism or antiferromagnetism, on the one hand, and our symmetry-based delimitation of the third phase, on the other hand, favor a distinct term referring to the phase. The alternating spin polarizations in both the real-space crystal structure and the momentum-space band structure characteristic of this unconventional magnetic phase suggest a term altermagnetism. We point out that $d$-wave altermagnetism represents a realization of the long-sought-after counterpart in magnetism of the unconventional $d$-wave superconductivity.

Quantum spin liquids (QSLs) as novel phases of matter with long-range entanglement and deconfined quantum critical points (DQCPs) as descriptions for unconventional phase transitions between two ordered states beyond the standard paradigm, such as the transition between antiferromagnetic (AFM) and valence-bond solid (VBS) phases, are two representative emerging phenomena. These implications for understanding correlated materials and developing theoretical frameworks for many-body physics are of crucial importance. Here, we show that a gapless QSL can naturally emerge from a DQCP. Via large-scale tensor network simulations of a square-lattice spin-$1/2$ frustrated Heisenberg model, both QSL-state and DQCP-type AFM-VBS transitions are observed. By tuning the coupling constants, the AFM-VBS transition vanishes, and instead, a gapless QSL phase gradually develops in between. Remarkably, along the phase boundaries of AFM-QSL and QSL-VBS transitions, we always observe the same correlation-length exponents, $\nu \approx 1.0$, which is intrinsically different from the one of the DQCP-type transition, indicating new types of universality classes. Our results explicitly demonstrate a new scenario for understanding the emergence of gapless QSL from an underlying DQCP. The discovered QSL phase survives in a large region of tuning parameters, and we expect its experimental realization in solid-state materials or quantum simulators.

Discrete time crystals represent a paradigmatic nonequilibrium phase of periodically driven matter. Protecting its emergent spatiotemporal order necessitates a mechanism that hinders the spreading of defects, such as localization of domain walls in disordered quantum spin chains. In this work, we establish the effectiveness of a different mechanism arising in clean spin chains: the confinement of domain walls into “mesonic” bound states. We consider translationally invariant quantum Ising chains periodically kicked at arbitrary frequency, and we discuss two possible routes to domain-wall confinement: longitudinal fields and interactions beyond nearest neighbors. We study the impact of confinement on the order-parameter evolution by constructing domain-wall-conserving effective Hamiltonians and analyzing the resulting dynamics of domain walls. On the one hand, we show that for arbitrary driving frequency, the symmetry-breaking-induced confining potential gets effectively averaged out by the drive, leading to deconfined dynamics. On the other hand, we rigorously prove that increasing the range $R$ of spin-spin interactions $J_{i,j}$ beyond nearest neighbors enhances the order-parameter lifetime exponentially in $R$. Our theory predictions are corroborated by a combination of exact and matrix-product-state simulations for finite and infinite chains, respectively. The long-lived stability of spatiotemporal order identified in this work does not rely on Floquet prethermalization nor on eigenstate order, but rather on the nonperturbative origin of vacuum-decay processes. We point out the experimental relevance of this new mechanism for stabilizing a long-lived time-crystalline response in Rydberg-dressed spin chains.

Engineering the electromagnetic environment of a quantum emitter gives rise to a plethora of exotic light-matter interactions. In particular, photonic lattices can seed long-lived atom-photon bound states inside photonic band gaps. Here, we report on the concept and implementation of a novel microwave architecture consisting of an array of compact superconducting resonators in which we have embedded two frequency-tunable artificial atoms. We study the atom-field interaction and access previously unexplored coupling regimes, in both the single- and double-excitation subspace. In addition, we demonstrate coherent interactions between two atom-photon bound states, in both resonant and dispersive regimes, that are suitable for the implementation of swap and cz two-qubit gates. The presented architecture holds promise for quantum simulation with tunable-range interactions and photon transport experiments in the nonlinear regime.

The synthesis of single-cycle pulses of compressed light and microwave signals sparked novel areas of fundamental research. In the field of acoustics, however, such a generation has not been introduced yet. For numerous applications, the large spatial extent of surface acoustic waves (SAW) causes unwanted perturbations and limits the accuracy of physical manipulations. Particularly, this restriction applies to SAW-driven quantum experiments with single flying electrons, where extra modulation renders the exact position of the transported electron ambiguous and leads to undesired spin mixing. Here, we address this challenge by demonstrating single-shot chirp synthesis of a strongly compressed acoustic pulse. Employing this solitary SAW pulse to transport a single electron between distant quantum dots with an efficiency exceeding 99%, we show that chirp synthesis is competitive with regular transduction approaches. Performing a time-resolved investigation of the SAW-driven sending process, we outline the potential of the chirped SAW pulse to synchronize single-electron transport from many quantum-dot sources. By superimposing multiple pulses, we further point out the capability of chirp synthesis to generate arbitrary acoustic waveforms tailorable to a variety of (opto)nanomechanical applications. Our results shift the paradigm of compressed pulses to the field of acoustic phonons and pave the way for a SAW-driven platform of single-electron transport that is precise, synchronized, and scalable.

The spin Hall effect and the inverse spin Hall effect are important spin-charge conversion mechanisms. The direct spin Hall effect induces a surface spin accumulation from a transverse charge current due to spin-orbit coupling even in nonmagnetic conductors. However, most detection schemes involve additional interfaces, leading to large scattering in reported data. Here we perform interface-free x-ray spectroscopy measurements at the Cu $L_{3,2}$ absorption edges of highly Bi-doped Cu (${\mathrm{Cu}}_{95}{\mathrm{Bi}}_5$). The detected x-ray magnetic circular dichroism signal corresponds to an induced magnetic moment of $(2.2\pm 0.5)\times {10}^{-12}{\mu }_B{\mathrm{A}}^{-1}{\mathrm{cm}}^2$ per Cu atom averaged over the probing depth, which is of the same order of magnitude as found for Pt measured by magneto-optics. The results highlight the importance of interface-free measurements to assess material parameters and the potential of CuBi for spin-charge conversion applications.

Constraints in the dynamics of quantum many-body systems can dramatically alter transport properties and relaxation timescales even in the absence of static disorder. Here, we report on the observation of such constrained dynamics arising from the distinct mobility of two species in the one-dimensional mass-imbalanced Fermi-Hubbard model, realized with ultracold ytterbium atoms in a state-dependent optical lattice. By displacing the trap potential and monitoring the subsequent dynamical response of the system, we identify suppressed transport and slow relaxation with a strong dependence on the mass imbalance and interspecies interaction strength, consistent with eventual thermalization for long times. Our observations demonstrate the potential for quantum simulators to provide insights into unconventional relaxation dynamics arising from constraints.

The flow of charge and entropy in solids usually depends on collisions decaying quasiparticle momentum. Hydrodynamic corrections can emerge, however, if most collisions among quasiparticles conserve momentum and the mean-free path approaches the sample dimensions. Here, through a study of electrical and thermal transport in antimony (Sb) crystals of various sizes, we document the emergence of a two-component fluid of electrons and phonons. Lattice thermal conductivity is dominated by electron scattering down to 0.1 K and displays prominent quantum oscillations. The Dingle mobility does not vary despite an order-of-magnitude change in transport mobility. The Bloch-Grüneisen behavior of electrical resistivity is suddenly aborted below 15 K and replaced by a quadratic temperature dependence. At the Kelvin temperature range, the phonon scattering time and the electron-electron scattering time display a similar amplitude and temperature dependence. Taken together, the results draw a consistent picture of a bifluid where frequent momentum-conserving collisions between electrons and phonons dominate the transport properties.

We show that the topology of the Fermi sea of a $D$-dimensional Fermi gas is reflected in the multipartite entanglement characterizing $D+1$ regions that meet at a point. For odd $D$ we introduce the multipartite mutual information and show that it exhibits a ${\log }^{D}L$ divergence as a function of system size $L$ with a universal coefficient that is proportional to the Euler characteristic ${\chi }_F$ of the Fermi sea. This provides a generalization, for a Fermi gas, of the well-known result for $D=1$ that expresses the $\log L$ divergence of the bipartite entanglement entropy in terms of the central charge $c$ characterizing a conformal field theory. For even $D$ we introduce a charge-weighted entanglement entropy that is manifestly odd under a particle-hole transformation. We show that the corresponding charge-weighted mutual information exhibits a similar ${\log }^{D}L$ divergence proportional to ${\chi }_F$. Our analysis relates the universal behavior of the multipartite mutual information in the absence of interactions to the $D+1$ order equal-time density correlation function, which we show exhibits a universal behavior in the long wavelength limit proportional to ${\chi }_F$. Our analytic results are based on the replica method. In addition, we perform a numerical study of the charge-weighted mutual information for $D=2$ that confirms several aspects of the analytic theory. Finally, we consider the effect of interactions perturbatively within the replica theory. We show that for $D=3$ the ${\log }^{3}L$ divergence of the topological mutual information is not perturbed by weak short-ranged interactions, though for $D=2$ the charge-weighted mutual information is perturbed. Thus, for $D=3$ the multipartite mutual information provides a robust classification that distinguishes distinct topological Fermi liquid phases.

We study the excitations that emerge upon doping the translationally invariant correlated insulating states in magic-angle twisted bilayer graphene at various integer filling factors $\nu$. We identify parameter regimes where these are excitations associated with skyrmion textures in the spin or pseudospin degrees of freedom, and explore both short-distance pairing effects and the formation of long-range ordered skyrmion crystals. We perform a comprehensive analysis of the pseudospin skyrmions that emerge upon doping insulators at even $\nu$, delineating the regime in parameter space where these are the lowest-energy charged excitations by means of self-consistent Hartree-Fock calculations on the interacting Bistritzer-MacDonald model. We explicitly demonstrate the purely electron-mediated pairing of skyrmions, a key ingredient behind a recent proposal of skyrmion superconductivity. Building upon this, we construct hopping models to extract the effective masses of paired skyrmions, and discuss our findings and their implications for skyrmion superconductivity in relation to experiments, focusing on the dome-shaped dependence of the transition temperature on the twist angle. We also investigate the properties of spin skyrmions about the quantized anomalous Hall insulator at $\nu =+3$. In both cases, we demonstrate the formation of robust spin or pseudospin skyrmion crystals upon doping to a finite density away from integer filling.

A two-dimensional electron system placed in a magnetic field develops Landau levels, where strong Coulomb interactions lead to the appearance of many-body correlated ground states. Quantum numbers similar to the electron spin enable the understanding and control of complex ground state order and collective excitations. Owing to its spin, valley, and orbital degrees of freedom, Bernal-stacked bilayer graphene offers a rich platform to pursue correlated phenomena in two dimensions. In this work, we fabricate dual-gated Bernal-stacked bilayer graphene devices and demonstrate unprecedented fine control over its valley isospin degrees of freedom using a perpendicular electric field. Higher sample quality enables us to probe regimes obscured by disorder in previous studies. We present evidence for a new even-denominator fractional quantum Hall state at filling factor $\nu =5/2$. The $5/2$ state is found to be spontaneously valley polarized in the limit of vanishing valley Zeeman splitting, consistent with a theoretical prediction made regarding the spin polarization of the Moore-Read state. In the vicinity of the even-denominator fractional quantum Hall states, we observe the appearance of the predicted Levin-Halperin daughter states of the Moore-Read Pfaffian wave function at $\nu =3/2$ and $7/2$ and of the anti-Pfaffian at $\nu =5/2$ and $-1/2$. These observations suggest the breaking of particle-hole symmetry in bilayer graphene. We construct a comprehensive valley polarization phase diagram for the Jain sequence fractional states surrounding filling factor $3/2$. These results are well explained by a two-component composite fermion model, further demonstrating the SU(2) nature of the valley isospin in bilayer graphene. Our experiment paves the path for future efforts of manipulating the valley isospin in bilayer graphene to engineer exotic topological orders and quantum information processes.

We investigate an experimental toy-model system of a pseudospin-half square-lattice Hubbard Hamiltonian in $[{({\mathrm{SrIrO}}_3)}_1/{({\mathrm{CaTiO}}_3)}_1]$ to include both nontrivial complex hopping and moderate electron correlation. While the former induces electronic Berry phases as anticipated from the weak-coupling limit, the latter stabilizes an antiferromagnetic Mott insulator ground state analogous to the strong-coupling limit. Their combined results in the real system are found to be an anomalous Hall effect with a nonmonotonic temperature dependence due to the competition of the antiferromagnetic order and charge excitations in the Mott state, and an exceptionally large Ising anisotropy that is captured as a giant magnon gap beyond the superexchange approach. The unusual phenomena highlight the rich interplay of electronic topology and electron correlation in the intermediate-coupling regime that is largely unexplored and challenging in theoretical modeling.

Purifying a high-temperature ensemble of quantum particles toward a known state is a key requirement to exploit quantum many-body effects. An alternative to passive cooling, which brings a system to its ground state, is active feedback, which stabilizes the system at a chosen target state. This alternative, if realized, offers additional control capabilities for the design of quantum states. Here we present a feedback algorithm applied to a quantum system, which is capable of stabilizing the collective state of an ensemble from its maximum entropy state to the limit of single quantum fluctuations. Our algorithmic approach maximizes the rate of state purification given the system’s physical constants; thus it remains the optimal feedback approach even in the presence of dissipation and disorder. We test experimentally the robustness of this feedback on the highly inhomogeneous nuclear-spin ensemble of a semiconductor quantum dot, reducing nuclear-spin fluctuations 83-fold, down to 5.7(2) spin macrostates. Simulations demonstrate that without system-specific inhomogeneities, our algorithm can purify the system down to single-spin fluctuations. Further, we exploit our algorithmic approach to tailor nontrivial nuclear-spin distributions that go beyond simple polarization, including weighted bimodality and latticed multistability. This control is a precursor toward quantum-correlated macrostates, which an extended version of our algorithm could generate in homogeneous systems.

Monopole operators are studied in a large family of quantum critical points between Dirac spin liquids and topological quantum spin liquids (QSLs): chiral and $Z_2$ QSLs. These quantum phase transitions are described by conformal field theories (CFTs): quantum electrodynamics in $2+1$ dimensions with $2N$ flavors of two-component massless Dirac fermions and a four-fermion interaction term. For the transition to a chiral spin liquid, it is the Gross-Neveu interaction (${\mathrm{QED}}_3\text{−}\mathrm{GN}$), while for the transitions to $Z_2$ QSLs, it is a superconducting pairing term with general spin and valley structure (generalized ${\mathrm{QED}}_3\text{−}{Z}_2\mathrm{GN}$). Using the state-operator correspondence, we obtain monopole scaling dimensions to subleading order in $1/N$. For monopoles with a minimal topological charge $q=1/2$, the scaling dimension is $2N\times 0.26510$ at leading order, with the quantum correction being 0.118911(7) for the chiral spin liquid, and 0.102846(9) for the simplest $Z_2$ case (the expression is also given for a general pairing term). Although these two anomalous dimensions are nearly equal, the underlying quantum fluctuations possess distinct origins. The analogous result in ${\mathrm{QED}}_3$ is also obtained, and we find a subleading contribution of $-0.038138(5)$, which is slightly different from the value $-0.0383$ first obtained in the literature. The scaling dimension of a ${\mathrm{QED}}_3\text{−}\mathrm{GN}$ monopole with minimal charge is very close to the scaling dimensions of other operators predicted to be equal by a conjectured duality between ${\mathrm{QED}}_3\text{−}\mathrm{GN}$ with $2N=2$ flavors and the ${\mathrm{C}\mathrm{P}}^1$ model. Additionally, nonminimally charged monopoles with equal charges on both sides of the duality have similar scaling dimensions. By studying the large-$q$ asymptotics of the scaling dimensions in ${\mathrm{QED}}_3$, ${\mathrm{QED}}_3\text{−}\mathrm{GN}$, and ${\mathrm{QED}}_3\text{−}{Z}_2\mathrm{GN}$, we verify that the constant $O(q^0)$ coefficient precisely matches the universal nonperturbative prediction for CFTs with a global U(1) symmetry. Finally, we identify numerous open questions regarding the fate of monopoles and their hierarchies at transitions to spin liquids and ordered phases.