Hybrid multiterminal Josephson junctions (JJs) are expected to harbor a novel class of Andreev bound states (ABSs), including topologically nontrivial states in four-terminal devices. In these systems, topological phases emerge when ABSs depend on at least three superconducting phase differences, resulting in a three-dimensional (3D) energy spectrum characterized by Weyl nodes at zero energy. Here, we realize a four-terminal JJ in a hybrid $\mathrm{Al}/\mathrm{InAs}$ heterostructure, where ABSs form a synthetic 3D band structure. We probe the energy spectrum using tunneling spectroscopy and identify spectral features associated with the formation of a tri-Andreev molecule, a bound state whose energy depends on three superconducting phases and, therefore, is able to host topological ABSs. The experimental observations are well described by a numerical model. The calculations predict the appearance of four Weyl nodes at zero energy within a gap smaller than the experimental resolution. These topological states are theoretically predicted to remain stable within an extended region of the parameter space, well accessible by our device. These findings establish an experimental foundation to study high-dimensional synthetic band structures in multiterminal JJs and to realize topological Andreev bands.

“Strange” metals that do not follow the predictions of Fermi liquid theory are prevalent in materials that feature superconductivity arising from electron interactions. In recent years, it has been hypothesized that spatial randomness in electron interactions must play a crucial role in strange metals for their hallmark linear-in-temperature ($T$) resistivity to survive down to low temperatures where phonon and umklapp processes are ineffective, as is observed in experiments. However, a clear picture of how this happens has not yet been provided in a realistic model free from artificial constructions, such as large-$N$ limits and replica tricks. We study a realistic model of two-dimensional metals with spatially random antiferromagnetic interactions in a nonperturbative regime, using numerically exact high-performance, large-scale hybrid Monte Carlo simulation and exact averages over the quenched spatial randomness. Our simulations reproduce strange metals’ key experimental signature of linear-in-$T$ resistivity with a universal “Planckian” transport scattering rate ${\mathrm{\Gamma }}_{\mathrm{tr}}\sim k_{B}T/\hslash$ that is independent of coupling constants. We further find that strange metallicity in these systems is not associated with a quantum critical point and, instead, arises from a phase of matter with gapless antiferromagnetic fluctuations that lacks long-range correlations and spans an extended region of parameter space: A feature that is also observed in several experiments. These gapless antiferromagnetic fluctuations take the form of spatially localized overdamped modes, whose presence could possibly be detected using recently developed nanoscale magnetometry methods. Our work paves the way for an eventual microscopic understanding of the role of spatial disorder in determining important properties of correlated-electron materials.

The classification of topological phases of matter is a fundamental challenge in quantum many-body physics, with applications to quantum technology. Recently, this classification has been extended to the setting of adaptive finite-depth local unitary (AFDLU) circuits, which allow global classical communication. In this setting, the trivial phase is the collection of all topological states that can be prepared via AFDLU. Here, we propose a complete classification of the trivial phase by showing how to prepare all solvable anyon theories that admit a gapped boundary via AFDLU, extending recent results on solvable groups. Our construction includes non-Abelian anyons with irrational quantum dimensions, such as Ising anyons, and more general acyclic anyons. Specifically, we introduce a sequential gauging procedure, with an AFDLU implementation, to produce a string-net ground state in any topological phase described by a solvable anyon theory with gapped boundary. In addition, we introduce a sequential ungauging and regauging procedure, with an AFDLU implementation, to apply string operators of arbitrary length for anyons and symmetry twist defects in solvable anyon theories. We apply our procedure to the quantum double of the group $S_3$ and to several examples that are beyond solvable groups, including the doubled Ising theory, the ${\mathbb{Z}}_3$ Tambara-Yamagami string net, and doubled $\mathrm{SU}(2{)}_4$ anyons.

Systems such as Wigner crystals and incommensurate charge density waves that spontaneously break a continuous translation symmetry have unusual transport properties arising from their ability to slide coherently in space. Recent experimental and theoretical studies suggest that spontaneous translation symmetry breaking in some two-dimensional materials with nontrivial quantum geometry (e.g., rhombohedral pentalayer graphene) leads to a topologically nontrivial electron crystal state called the anomalous Hall crystal and characterized by a vanishing linear-response dc longitudinal conductivity and a nonvanishing Hall conductivity. In this work we present a theoretical investigation of the sliding dynamics of this new type of electron crystal, taking into account the system’s nontrivial quantum geometry. We find that when accelerated by an external electric field, the crystal acquires a transverse anomalous velocity that stems from not only the Berry curvature of the parent band but also the Galilean noninvariance of the crystal state (i.e., crystal states with different momenta are not related by simple momentum boosts). We further show that acceleration of the crystal modifies its internal current from the static crystal value that is determined by the Chern number of the crystal state. The net Hall conductance including contributions from center-of-mass motion and internal current is in general not quantized. As an experimentally relevant example, we present numerical results in rhombohedral pentalayer graphene and discuss possible experimental implications.

Nonequilibrium states of quantum materials can exhibit exotic properties and enable unprecedented functionality and applications. These transient states are inherently inhomogeneous, characterized by the formation of topologically protected structures, requiring nanometer spatial resolution on femtosecond timescales to resolve their evolution. Using ultrafast total x-ray scattering at a free electron laser and a sophisticated scaling analysis, we gain unique access to the dynamics on the relevant mesoscopic length scales. Our results provide direct evidence that ultrafast excitation of ${\mathrm{LaTe}}_3$ leads to formation of topological vortex strings of the charge density wave. These dislocations of the charge density wave exhibit anomalous, subdiffusive dynamics, slowing the equilibration process, providing rare insight into the nonequilibrium mesoscopic response in a quantum material. Our findings establish a general framework to investigate properties of topological defects, which are expected to be ubiquitous in nonequilibrium phase transitions and may arrest equilibration and enhance competing orders.

The metallic oxide ${\mathrm{RuO}}_2$ has emerged as a promising altermagnet candidate, owing to reports of this material hosting antiferromagnetic ordering accompanied by a spin-split electronic band structure characteristic of time-reversal symmetry breaking. However, recent studies have robustly questioned this scenario. Here we map the Fermi surface of pristine single-crystalline ${\mathrm{RuO}}_2$. By measuring magnetic quantum oscillations of a bulk thermodynamic property, our study resolves the electronic structure present in the bulk of ${\mathrm{RuO}}_2$. Several Fermi sheets are discerned, with a range of effective quasiparticle masses up to 5 times that of the bare electron mass. We compare our measurements with the predictions for altermagnetic and nonmagnetic Fermi surfaces deduced from density functional theory calculations. The quantum oscillatory frequency spectra correspond very poorly to the profile expected for the case of altermagnetism; by contrast, they correspond well to the nonmagnetic scenario. Our findings place significant constraints on the bulk magnetic properties of ${\mathrm{RuO}}_2$ and strongly suggest that this material is an itinerant electron paramagnet.

In this study, we investigate the potential of electronic interferometers for probing the quantum state of electromagnetic radiation on a chip at subnanosecond timescales. We propose to use single-electron excitations propagating within an electronic Mach-Zehnder interferometer in the Aharonov-Bohm-dominated regime. We discuss how information about the quantum state of the electromagnetic radiation is encoded into the interference contribution to the average outgoing electrical current. By investigating squeezed radiation and single-edge magnetoplasmons probed by leviton pulses in a realistic setup, we show that single-electron interferometers have the potential to probe quantum radiation in the time domain with subnanosecond to picosecond time resolution. Our research could have significant implications for probing the fundamental properties of light in the microwave to terahertz domains at extremely short timescales.

Semiconductor spin qubits have emerged as a promising platform for quantum computing, following a significant improvement in their control fidelities over recent years. Increasing the qubit count remains challenging, beginning with the fabrication of small features and complex fan-outs. A particular challenge has been formed by the need for individual barrier gates to control the exchange interaction between adjacent spin qubits. Here, we propose a method to vary two-qubit interactions without applying pulses on individual barrier gates while also remaining insensitive to detuning noise in first order. Experimentally we find that changing plunger gate voltages over 300 mV can tune the exchange energy $J$ from 100 kHz to 60 MHz. This allows us to perform two-qubit operations without changing the barrier gate voltage. Based on these findings we conceptualize a spin qubit architecture without individual barrier gates, simplifying the fabrication while maintaining the control necessary for universal quantum computation.

The non-Hermitian skin effect characterized by a proliferation of exponentially localized edge modes in open-boundary systems has led to the discovery of numerous novel physical phenomena that challenge the limits of conventional band theory. In sharp contrast to this familiar exponential localization, we report a distinct phenomenon—the algebraic non-Hermitian skin effect—which arises generically in non-Hermitian systems with two or more spatial dimensions. In such cases, the amplitude of skin modes typically decays from the boundary following a power law, rather than an exponential form—a behavior not captured by existing theoretical frameworks. To bridge this gap and describe the transition in localization from one to higher dimensions, we develop a generalized Fermi surface framework applicable to open-boundary systems in arbitrary dimensions. This framework not only reproduces known results for the exponential skin effect in 1D, but also predicts a new class of skin effects with algebraic decay in 2D and above. We demonstrate this framework in both tight-binding and continuum models in two and three dimensions. This investigation not only unveils a novel category of the non-Hermitian skin effect but also offers a comprehensive theoretical structure that describes skin effects in any non-Hermitian system, irrespective of its spatial dimensionality.

Fluctuations of conserved quantities within a subsystem are nonlocal observables that provide unique insights into quantum many-body systems. In this paper, we study bipartite charge (and spin) fluctuations across interaction-driven “metal-insulator transitions” out of Landau Fermi liquids. The “charge insulators” include a class of non-Fermi-liquid states of fractionalized degrees of freedom, such as compressible composite Fermi liquids (for spinless electrons) and incompressible spin-liquid Mott insulators (for spin-$1/2$ electrons). We find that charge fluctuations $\mathcal{F}$ exhibit distinct leading-order scalings across the transition: $\mathcal{F}\sim L\log (L)$ in Landau Fermi liquids and $\mathcal{F}\sim L$ in charge insulators, where $L$ is the linear size of the subsystem. In composite Fermi liquids, under certain conditions, we also identify a universal constant term $-\mathrm{f}(\theta )|{\sigma }_{xy}|/(2\pi )$ when the subsystem geometry contains a sharp corner, where $\mathrm{f}(\theta )$ denotes a function of the corner angle and ${\sigma }_{xy}$ is the Hall conductivity. At the critical point, provided the transition is continuous, the leading scaling $\mathcal{F}\sim L$ is accompanied by a subleading universal corner contribution $-\log (L)\mathrm{f}(\theta )C_{\rho }/2$ with the same angle dependence $\mathrm{f}(\theta )$, and the universal coefficient $C_{\rho }$ is directly related to the predicted universal jumps in longitudinal and Hall resistivities. These results establish fluctuation-transport relations, paving the way for numerical and experimental studies of unconventional quantum criticalities in metals.

The bootstrap method aims to solve problems by imposing constraints on the space of physical observables, which often follow from physical assumptions such as positivity and symmetry. Here, we employ a bootstrap approach to study interacting electrons in the lowest Landau level by minimizing the energy as a function of the static structure factor subject to a set of constraints, bypassing the need to construct the full many-body wave function. This approach rigorously lower bounds the ground state energy, making it complementary to conventional variational upper bounds. We show that the lower bound we obtain is relatively tight, within at most a few percent from the ground state energy computed with exact diagonalization at small system sizes, and generally gets tighter as we include more constraints. We also show that, by combining the bootstrap lower bounds with variational Monte Carlo calculations for various quantum Hall states, we can obtain two-sided bounds on the ground state energy that rigorously bounds the error to below a few percentage for large system sizes where exact diagonalization is not accessible. Beyond the energetics, our results reproduce the correct power law dependence of the pair correlation function at short distances and the existence of a large entanglement gap in the two-particle entanglement spectra for the Laughlin states at $\nu =1/3$. We further identify signatures of the composite Fermi liquid state close to half filling. This shows that the bootstrap approach is capable, in principle, of describing nontrivial gapped topologically ordered, as well as gapless, phases. We further study the evolution of the ground state energy and correlation functions as we interpolate between the lowest and first Landau levels at half filling and find indications of a phase transition from a composite Fermi liquid to a non-Abelian state. We also discuss more generally how the geometry of the allowed set of structure factors can be used to diagnose phase transitions. At the end, we discuss possible extensions and current limitations of this approach and how they can be overcome in future studies. Our work establishes numerical bootstrap as a promising method to study many-body phases in topological bands, paving the way to its application in moiré platforms where the energetic competition between fractional quantum anomalous Hall, symmetry broken, and gapless states remains poorly understood.

Multi-$\mathbf{Q}$ magnetic structures on two-dimensional (2D) lattices provide a key route to realizing topological physics in 2D magnetism. A major experimental challenge is to unambiguously confirm their formation by excluding the possibility of topologically trivial multidomain single- or double-$\mathbf{Q}$ magnetic orders, which cannot be distinguished using conventional diffraction techniques. Here, we propose that long-wavelength spin dynamics offers a universal diagnostic for triangular lattices: Triple-$\mathbf{Q}$ orders that preserve rotational symmetry and single- or double-$\mathbf{Q}$ orders that break it exhibit qualitatively distinct anisotropies in their Goldstone-mode velocities, stemming from fundamental differences in their underlying spin configurations. We validate this concept using the metallic triangular-lattice antiferromagnet ${\mathrm{Co}}_{0.325}{\mathrm{TaS}}_2$, which hosts both a stripe-type single-$\mathbf{Q}$ state and a triple-$\mathbf{Q}$ tetrahedral ordering at different temperatures. Using inelastic neutron-scattering and spin dynamics simulations, we first refine the spin Hamiltonian by fitting the paramagnetic excitation spectra, allowing us to develop an unbiased model independent of magnetic ordering. We then show that the observed velocity profiles of the Goldstone modes agree with the high-temperature model’s predictions: markedly anisotropic for the single-$\mathbf{Q}$ phase and near isotropic for the triple-$\mathbf{Q}$ phase. Importantly, this contrast persists across various exchange parameters, highlighting its model-independent nature and suggesting potential applicability to other 2D lattice systems. Beyond the long-wavelength regime, we present a substantial discrepancy between the measured and simulated magnon spectra exclusively in the triple-$\mathbf{Q}$ phase. We attribute this discrepancy to magnon energy renormalization arising from order-of-magnitude-enhanced magnon-magnon interactions in the triple-$\mathbf{Q}$ phase, due to its noncollinear configuration. This work provides universal insight into the dynamical properties of topological multi-$\mathbf{Q}$ magnetic orderings in 2D lattice structures, offering a broadly applicable diagnostic to distinguishing them from topologically trivial single- or double-$\mathbf{Q}$ counterparts. The unequivocal confirmation of the triple-$\mathbf{Q}$ structure in ${\mathrm{Co}}_{0.325}{\mathrm{TaS}}_2$ further establishes it as a prominent material platform for exploring topological spin textures in the genuine 2D limit.

Polarons are quasiparticles that arise from the interaction of electrons or holes with lattice vibrations. Though polarons are well studied across multiple disciplines, experimental observations of polarons in two-dimensional crystals are sparse. We use scanning tunneling microscopy and spectroscopy to measure inelastic excitations of polaronic bound states emerging from coupling of nonpolar zone-boundary phonons to Bloch electrons in $n$-doped metallic single-layer ${\mathrm{MoS}}_2$. The latter is kept chemically pristine via contactless chemical doping. Tunneling into the vibrationally coupled polaronic states leads to a series of evenly spaced peaks in the differential conductance on either side of the Fermi level. Combining density functional (perturbation) theory with a recently developed ab initio electron-lattice downfolding technique, we show that the energy spacing stems from the longitudinal-acoustic phonon mode that flattens at the Brillouin zone edge and is responsible for the formation of stable multipolarons in metallic ${\mathrm{MoS}}_2$.

The natural existence of crystalline symmetry in real materials manifests the importance of understanding crystalline symmetry-protected topological phases, especially for interacting systems. In this paper, we systematically construct and classify all the point-group crystalline topological superconductors and insulators in three-dimensional (3D) interacting fermion systems using the novel concept of a topological crystal. The corresponding higher-order topological surface theory can also be systematically studied via higher-order bulk-boundary correspondence. In particular, we discover several intrinsically interacting topological phases that cannot be realized in any free-fermion systems. Moreover, the crystalline equivalence principle for 3D interacting fermionic systems is also verified, with an additional subtle “twist” on the spin of fermions.

Superconducting transition-edge sensors are renowned for their extraordinary photon sensitivity and energy resolution, finding applications spanning quantum information, astronomy, and nanophotonics. Here, we report the development of bolometric superconducting optical nanoscopy (BOSON), a novel platform that integrates bolometric detection at the superconducting transition edges with near-field optical techniques. BOSON enables the mapping of photoinduced changes in superconductivity with unprecedented spatial resolution and photon sensitivity. By incorporating BOSON with low-dimensional materials, we achieved polariton imaging at nanowatt excitation levels—at least 4 orders of magnitude lower than the power typically required in prior near-field nanoscopy experiments. Our findings highlight the potential for BOSON to advance scanning-probe-based optical platforms to enable the detection of photons, polaritons, and Cooper pair dynamics at the nanoscale. This paves the way for quantum sensing applications using single-polariton detection and can offer deeper insights into quasiparticle dynamics.

Rhombohedral stacked graphene (RSG) contains two key ingredients for the realization of correlated topological phases of matter: flat electronic bands and concentrated Berry curvature. The fractional quantum anomalous Hall effect was recently observed in an RSG-hexagonal boron nitride (hBN) moiré heterostructure when the conduction electrons were pushed away from the moiré interface by an applied electric displacement field. The question then arises about whether such topological states can also develop in RSG-hBN in a strong moiré potential. Here, we explore the physics in the moiré-proximal limit through capacitance measurements that allow us to determine the electronic compressibility and extract energy gaps of incompressible states. We report the observation of integer and fractional Chern insulator states at low magnetic field in this limit at filling factors $\nu =1$, $2/3$, and $1/3$ in addition to numerous trivial and topological charge density waves. We map out a correlated phase diagram that is highly sensitive to both displacement and magnetic fields, establishing the moiré-proximal regime as a tunable platform for studying the interplay between band topology and strong lattice effects.

A two-dimensional electron system exposed to a strong magnetic field produces a plethora of strongly interacting fractional quantum Hall (FQH) states, the complex topological orders of which are revealed through exotic emergent particles, such as composite fermions, and fractionally charged Abelian and non-Abelian anyons. Much insight has been gained by the study of multicomponent FQH states, where spin and pseudospin indices of the electron contribute additional correlation. Traditional multicomponent FQH states develop in situations where the components share the same orbital states and the resulting interactions are pseudospin independent; this homo-orbital nature is also crucial to their theoretical understanding. Here, we study “hetero-orbital” two-component FQH states, in which the orbital index is part of the pseudospin, rendering the multicomponent interactions strongly SU(2) anisotropic in the pseudospin space. Such states, obtained in bilayer graphene at the isospin transition between $\mathit{N}=0$ and $\mathit{N}=1$ electron Landau levels, are markedly different from previous homo-orbital two-component FQH states. In particular, we observe strikingly different behaviors for the parallel-vortex and reverse-vortex attachment composite fermion states, and an anomalously strong two-component $2/5$ state over a wide range of magnetic field before it abruptly disappears at a high field. Our findings, combined with detailed theoretical calculations, reveal the surprising robustness of the hetero-orbital FQH effects, significantly enriching our understanding of FQH physics in this novel regime.

Despite their importance for exotic quantum effects, the surface electronic structure of magnetic topological insulators ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ and ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ remains poorly understood. Using high-efficiency spin- and angle-resolved photoemission spectroscopy, we directly image the spin-polarization and orbital character of the surface states in both compounds and map our observations onto a model wave function to describe the complex spin-orbital texture, which solidifies our understanding of the surface band structure by establishing the single-band nature of the most prominent states. Most importantly, our analysis reveals a new mechanism for reducing the magnetic gap of the topological surface states based on the orbital composition of the wave function.

Quantum fluctuations can disrupt long-range order in one-dimensional systems and replace it with the universal paradigm of the Tomonaga-Luttinger liquid (TLL), a critical phase of matter characterized by power-law decaying correlations and linearly dispersing excitations. Using a Rydberg quantum simulator, we study how TLL physics manifests in the low-energy properties of a spin chain, interacting under either the ferromagnetic or the antiferromagnetic dipolar XY Hamiltonian. Following quasiadiabatic preparation, we directly observe the power-law decay of spin-spin correlations in real space, allowing us to extract the Luttinger parameter. In the presence of an impurity, the chain exhibits tunable Friedel oscillations of the local magnetization. Moreover, by utilizing a quantum quench, we directly probe the propagation of correlations, which exhibit a light-cone structure related to the linear sound mode of the underlying TLL. Our measurements demonstrate the influence of the long-range dipolar interactions, renormalizing the parameters of TLL with respect to the case of nearest-neighbor interactions. Finally, comparison to numerical simulations exposes the high sensitivity of TLLs to doping and finite-size effects.

Fractional excitations hold immense promise for both fundamental physics and quantum technologies. However, constructing lattice models for their dynamics under gauge fields remains a formidable challenge due to inherent obstructions. Here, we introduce a novel and systematic framework for deriving low-energy lattice models of fractional orbitals coupled to tight-binding gauge fields. Departing from conventional geometric approaches, our method systematically eliminates the high-energy states via virtual hopping, thereby deriving the gauge potential and quantum metric through a superexchange mechanism. We demonstrate the framework by constructing Wannier orbitals for Majorana states and a tight-binding $Z_2$ gauge field across various flux-crystalline phases in the Kitaev spin model on a honeycomb lattice. Our study reveals a striking phase transition between two nontrivial topological phases characterized by gapless flat band with extensive degeneracy. Furthermore, we develop a gauge-invariant mean-field theory for interacting Majorana orbitals, leading to a fractional Chern state. Our work establishes a general framework for gauge-mediated tight-binding models and a gauge-invariant mean-field theory for interacting fractional orbitals that can be readily extended to U(1), SU(N) lattice gauge theories.