The thermodynamic limit is foundational to statistical mechanics, underlying our understanding of many-body phases. It assumes that, as the system size grows infinitely at fixed density of particles, unambiguous macroscopic phases emerge that are independent of the system’s boundary shape. We present explicit quantum spin and dimer Hamiltonians whose ground states violate this principle. Our construction relies on the previous mathematical work on classical dimers on the Aztec diamond and the square-octagon fortress, where geometry-dependent phase behaviors are observed in the infinite-size limit. We reverse engineer quantum spin Hamiltonians on the square and the square-octagon lattices whose ground states at the Rokhsar-Kivelson points are described by classical dimer coverings. On diamond-shaped domains, we find macroscopic boundary regions exhibiting distinct quantum phases from those on square-shaped domains. We study the nature of these phases by calculating the dimer-dimer and vison correlators and adapt Kasteleyn matrix based analytical and numerical methods for computing the vison correlator, which are significantly more efficient than standard Monte Carlo techniques. Our results show that the square-octagon lattice supports a single gapped short-range entangled phase, with exponentially decaying dimer correlators and a constant vison correlator. When the same model is considered on a diamond-shaped domain, two additional macroscopic regions emerge, with one near the corners and exhibiting staggered dimer order, and another exhibiting critical correlations.

“Hidden” phases, generated using ultrafast laser pulses (few hundred femtoseconds), with distinct properties than at the thermodynamic equilibrium, are appealing for technologies, as they can be long-lived, with a lifetime of hours or weeks, and reversible with temperature sweeping or extra pulses. In this regard, ${\mathrm{La}}_{2/3}{\mathrm{Ca}}_{1/3}{\mathrm{MnO}}_3$ (LCMO) stands out due to its tunability through epitaxial strain, which can drive the bulk ferromagnetic metal into an antiferromagnetic insulator (AFI), and its susceptibility to photoinduced transitions. Indeed, AFI LCMO displays a long-lived photoinduced transition into a putative hidden phase whose exact nature and excitations are still largely unknown. Here, we combine ultrafast photoexcitation in the near infrared with in situ transport, x-ray absorption, and resonant inelastic x-ray scattering (RIXS) to investigate the excitations (polarons, phonons, and orbital) of the photoexcited phase of LCMO and contrast them with the thermodynamic phases achieved through strain and temperature. In the thermodynamic regime, we establish the correlation between polarons and transport placing them in the “strong coupling” regime of the Holstein model. Upon photoexcitation of LCMO-AFI, we uncover a long-lived phase characterized by the softening of the polaron excitations, the partial suppression of the Jahn-Teller distortion, and nearly unchanged phonons, showing the emergence of a photoexcited state absent in the equilibrium phase diagram. Finally, by varying temperature, epitaxial strain, and photoexcitation fluence, we construct a polaron phase diagram and identify the key spectroscopic signatures of each phase. Our laser-RIXS approach establishes a versatile platform for exploring photoinduced hidden phases in quantum materials in nonstroboscopic conditions.

We use high-resolution chemical potential measurements to extract the entropy of monolayer and bilayer graphene in the quantum Hall regime via the Maxwell relation $[(d\mu )/(dT)]{|}_N=-[(dS)/(dN)]{|}_T$. Measuring the entropy from $T=300\mathrm{K}$ down to $T=200\mathrm{mK}$, we identify the sequential emergence of quantum Hall ferromagnetism, fractional quantum Hall states, and various charge orders by comparing the measured entropy in different temperature regimes with theoretical models. At the lowest temperature of $T\approx 200\mathrm{mK}$ we perform a detailed study of the entropy near even-denominator fractional quantum Hall states in bilayer graphene, and comment on the possible topological origin of the observed excess entropy.

Quantum thermodynamics addresses the dynamics of heat flow in quantum devices driven out of equilibrium. Although mesoscopic circuits at low temperatures provide a flexible platform to explore this dynamics, experimental studies are wanting, because thermal timescales in nanodevices are often too fast. Here, we engineer and investigate with noise thermometry a mesoscopic thermal circuit where heat flows between electron, phonon, and nuclear systems can occur on slower timescales. The central constituent of this device is a micrometer-scale metallic island electrically connected to large cold electron reservoirs through two to four ballistic quantum Hall channels, a component frequently used for exploring stationary thermal currents. We uncover a two-step thermalization process specific to the mesoscopic scale, involving a fast initial temperature step followed by a much slower rise extending over minutes. This observation is quantitatively accounted for by the balance between heat flows through electronic quantum channels, to cold phonons, and to the nuclear spins in the metallic island. The disclosed mesoscopic thermalization takes a step into the field of quantum thermodynamical phenomena, highlighting their distinctive nature on a central constituent of quantum circuits. The implications for the thermal engineering of nanodevices include the thermal characterization of exotic states at high magnetic field.

In thermoelectric (TE) and other functional electronic materials, chemical doping is commonly employed to tune the carrier density toward an optimal Fermi level and, in turn, maximize the electrical transport. However, in some systems, such as the emerging high-performance $p$-type TE material $\alpha$-MgAgSb, chemical doping is challenging due to its weak chemical bonds and extremely low solubility of heteroatomic dopants, which makes it difficult to increase the hole carrier density and realize the otherwise predictable improvements in the TE power factor. Here, we report a doping-free strategy to enhance the TE performance of $\alpha$-MgAgSb by utilizing a phase-transition-induced self-doping process. Annealing at the phase-transition temperature of 593 K lowers the formation energy of Ag vacancies in the high-temperature $\beta$ phase, and these vacancies are subsequently retained upon cooling back to the $\alpha$ phase. As a result, the hole concentration increases markedly from $4.5\times {10}^{19}$ to $1.3\times {10}^{20}{\mathrm{cm}}^{-3}$, activating multiple valence bands and boosting the room-temperature power factor by $\sim 35\%$ to $30\mathrm{\mu }\mathrm{W}{\mathrm{cm}}^{-1}{\mathrm{K}}^{-2}$. A single-leg device fabricated from the optimized material achieves a high conversion efficiency of 10.7% and a maximum output power of 71.1 mW at $\mathrm{\Delta }T=285\mathrm{K}$. This work demonstrates a viable pathway for enhancing TE performance via phase-transition engineering.

Diamond, an archetype of hardness and brittleness, can nonetheless display striking elastic compliance at the nanoscale, in sharp contrast to its ultrastiff, fracture prone bulk behavior. Despite recent experimental progress, the atomic scale origin of this anomalous elasticity remains unresolved. Here, we uncover a pronounced size- dependent softening in nanodiamond, with the effective axial Young’s modulus decreasing from about 1000 to about 700 GPa as the particle diameter shrinks from 13 to 4 nm. By integrating in situ transmission electron microscopy nanomechanical testing with first principles calculations and molecular dynamics simulations, we show that this stiffness reduction does not arise from the surface atomic layers, which remain comparatively stiff, but instead from weakened bonding in a distinct interfacial region between the surface and the crystalline core. These under-coordinated regions localize strain and accommodate large elastic deformation. The results uncover a previously overlooked interfacial mechanism that governs elasticity in brittle nanomaterials and offer design principles for nanomechanical resonators, quantum devices, and thermal transport applications with tunable stiffness.

Electromagnetic fields induce electronic transitions, generate currents, and fundamentally alter quantum states of matter through strong light-matter interactions. As one established route, Floquet engineering provides a powerful framework to dress electronic states with time-periodic fields, giving rise to quasistationary Floquet states. With increasing field strength, nonperturbative responses of the dressed states emerge, yet their nonlinear dynamics remain challenging to interpret. In this work, we explore the emergence of nonadiabatic Landau-Zener transitions among Floquet states in Cu(111) under intense optical fields. With increasing field strength, we reveal a transition from perturbative dressing to a regime where nonadiabatic tunneling among Floquet states dominate the electronic dynamics. These insights are obtained through interferometrically time-resolved multiphoton photoemission spectroscopy, which serves as a sensitive probe of transient Floquet state dynamics. Numerical simulations and the theory of instantaneous Floquet states allow us to directly examine real-time excitation pathways in this nonperturbative photoemission regime. Our results clarify different light-dressing regimes in materials and provide microscopic insight relevant to ultrafast light wave electronics.

Driving a quantum system out of equilibrium while preserving its subtle quantum mechanical correlations on large scales presents a major challenge, both fundamentally and for technological applications. At its core, this challenge is pinpointed by the question of how quantum effects can persist at asymptotic scales, analogous to quantum critical points in equilibrium. In this work, we construct such a scenario using fermions as building blocks. These fermions undergo an absorbing-to-absorbing state transition between two topologically distinct and quantum-correlated dark states. Starting from a microscopic, interacting Lindbladian, we derive an effective Lindblad-Keldysh field theory in which critical fermions couple to a bosonic bath with hydrodynamic fluctuations associated with particle number conservation. A key feature of this field theory is an emergent symmetry that protects the purity of the fermions’ state even in the presence of the thermal bath. We quantitatively characterize the critical point using a leading-order expansion around the upper critical dimension, thereby establishing the nonequilibrium universality class of fermions. The symmetry protection mechanism, which exhibits parallels to the problem of directed percolation, suggests a pathway toward a broader class of robust, universal quantum phenomena in fermionic systems.

Moiré semiconductors offer flat bands where Coulomb interactions and band topology intertwine, while the interlayer coupling plays a core role in the formation of moiré potential. However, the limited interlayer coupling strength and the lack of efficient tuning methods hinder further exploration of correlated phenomena in moiré semiconductors. We introduce a cryogenic dual-gated diamond-anvil platform using helium as a pressure medium, enabling reversible hydrostatic tuning together with magneto-optical spectroscopy in twisted bilayer ${\mathrm{WSe}}_2$. Pressure enhances the moiré potential, redshifts excitons, and stabilizes Stoner ferromagnetism otherwise absent at a 3.1° twist. Simultaneously, the half-filled $C=1$ Chern insulating state strengthens, exhibiting a reduced saturation field. Moreover, we observed a topological phase transition from Chern insulator to Mott insulator at around 2 GPa. First-principles calculations reveal that a $\mathrm{\Gamma }-K$ valence band maximum switching drives this transition by converting an Ising-like topological $K$-valley miniband into a spin-degenerate trivial $\mathrm{\Gamma }$ miniband. Our findings demonstrate hydrostatic pressure as a powerful, continuous control axis for correlated magnetism and topological band engineering in moiré materials.

Many-body systems that saturate the quantum bound on chaos are attracting interest across a wide range of fields. Notable examples include the Sachdev-Ye-Kitaev model and its variations, all characterized by some form or randomness and all-to-all couplings. Here, we study many-body quantum chaos in a quantum impurity model showing non-Fermi-liquid physics, the overscreened multichannel $SU(N)$ Kondo model. We exactly compute the low-temperature behavior of the out-of-time order correlator in the limit of large $N$ and large number of channels, $K$, at a fixed ratio $\gamma =K/N$. Because of strong correlations at the impurity site, the spin fractionalizes in auxiliary fermions and bosons. We show that all the degrees of freedom of our theory acquire a Lyapunov exponent that is linear in temperature as $T\to 0$, with a prefactor that depends on $\gamma$. Remarkably, for $N=K$, the impurity spin displays maximal chaos, while bosons and fermions only reach half of the maximal Lyapunov exponent. Our results highlight two key features: a nondisordered model that is maximally chaotic due to strong correlations at its boundary, with the maximal chaos appearing in a composite gauge-invariant operator, the impurity spin, and not in the auxiliary single-particle degrees of freedom.

Inhomogeneous domain nucleation and stochastic motion of the domain wall (DW) during the polarization switching process in conventional ferroelectrics introduce a spectrum of intricate kinetic challenges for the reliable and precise manipulation of polarization states, a prerequisite for many ferroelectric implementations. Combining deep-learning-assisted molecular dynamics simulations, microscopic-scale in situ observations, and device-scale electrical measurements, it reveals that sliding ferroelectrics inherently circumvent these issues, with an intrinsic domain-nucleation-free polarization reversal. Using $3R\text{−}{\mathrm{MoS}}_2$ as a model system, we demonstrate that DW motion occurs along a well-defined 1D pathway in a collective manner, without domain nucleation. Leveraging this predictable domain dynamics, we demonstrate deterministic multistate polarization switching, achieving remarkable precision and repeatability with a variation coefficient of less than 0.2%, 10 times improved over conventional ferroelectrics. This work provides valuable insights into the unique kinetics of DW motion in sliding ferroelectrics and offers opportunities for ferroelectric multistate devices with ultraprecision control.

Anyons are two-dimensional particles with fractional exchange statistics that emerge as elementary excitations of fractional quantum Hall phases. Experimentally, their exchange statistics can be measured in the edge-state Fabry-Pérot interferometer, wherein the presence of $N_{qp}$ localized anyons contributes a phase $N_{qp}{\theta }_a$ to the interference pattern where ${\theta }_a$ is twice the exchange phase. Here we report the observation of large, hysteretic phase jumps in a monolayer graphene Fabry-Pérot interferometer at $\nu =1/3$. When the filling factor is increased from $\nu <1/3$ toward the center of the plateau, we observe phase slips with magnitude $\mathrm{\Delta }\theta \approx 2\pi /3$, consistent with the addition of individual quasiparticles to the interferometer bulk. These phase slips occur as instantaneous jumps in the interference signal, with intervals between the jumps indicating quasiparticle equilibration times exceeding 20 min. We use this long timescale to investigate the effect of changes in interferometer area $A_I$ and $N_{qp}$ independently at fixed magnetic field, revealing a striking memory effect in the phase slip magnitude. In particular, as the $\nu =1/3$ plateau is approached from higher filling, we observed phase slips with $\mathrm{\Delta }\theta$ significantly larger than $2\pi /3$ over the same range of gate voltage where quantized jumps are seen for increasing $\nu$. We discuss this asymmetry in terms of bulk-edge coupling of quasiparticles localized near the edge or in the bulk, and argue that this effect can be qualitatively reconciled with theoretical expectations for strongly interacting quasiparticles in the presence of weak disorder and strongly nonequilibrium charge dynamics. Besides providing a replication of interferometric measurements sensitive to ${\theta }_a$, our results highlight the key role played by charge dynamics on signatures of the anyon phase, and demonstrate that fractional quasiparticles can be indefinitely localized in nonequilibrium configurations.

Nuclear spins near group-IV defects in diamond are promising candidates for quantum memories in quantum network applications. Here, we demonstrate high-fidelity control of a single ${}^{13}\mathrm{C}$ nuclear spin coupled to a tin-vacancy center in diamond. We perform a combination of optical and microwave pumping to achieve initialization into a combined electronuclear spin state with a fidelity of 99.74(3)%. Harnessing a superconducting waveguide for radio-frequency driving, we demonstrate precise nuclear-spin control: Ramsey measurements reveal a coherence time of $T_2^{*}=1.5(1)\mathrm{ms}$, and we use dynamical decoupling to extend it to 1.35(3) s. We perform randomized benchmarking, yielding a single-qubit gate fidelity of 99.92(1)%. This demonstrates a coherent spin-photon system with promising properties for quantum network nodes.

We study superconductivity in paramagnetic and ferromagnetically ordered phases in a two-dimensional electron system with parabolic fermionic dispersion and short-range repulsive interaction. In the paramagnetic phase, we find that a weak momentum dependence of a paramagnon propagator parametrically reduces the onset temperature for the pairing compared to that in phenomenological theories, which assume a strong dispersion of a paramagnon, and also changes the topology of the gap function. In the ferromagnetic phase, we show that the order instantly polarizes low-energy fermionic excitations. We derive the fully renormalized pairing interaction between low-energy fermions, mediated by two transverse Goldstone modes, and show that it is attractive in a spatially odd channel. The pairing temperature in the ferromagnetic phase is found to be a fraction of the Fermi energy, significantly larger than in the paramagnetic phase near the transition. Our results are relevant for understanding superconductivity in proximity to itinerant ferromagnetism in multivalley graphene systems, particularly the ones with full valley and spin polarization.

Superconductors are famously capable of supporting persistent electrical currents, that is, currents that flow without any measurable decay as long as the material is kept in the superconducting state. We introduce here a class of materials—superconducting altermagnets—that can both generate and carry persistent spin currents. This includes spin-polarized electrical supercurrent as well as pure spin supercurrent that facilitates spin transport in the absence of any charge transport. A key to this remarkable property is the realization that the leading superconducting instability of altermagnetic metals consists of two independent condensates formed of spin-up and spin-down electrons. In the nonrelativistic limit, the two condensates are decoupled and can, thus, naturally support persistent currents with any spin polarization, including pure spin supercurrents realized in the charge counterflow regime. We describe a novel “spin-current dynamo effect” that can be used to generate pure spin supercurrent in such systems by driving a charge current along certain crystallographic directions. Away from the nonrelativistic limit, when spin-orbit interactions and magnetic disorder are present, we find that the spin current generically develops spatial oscillations but, importantly, no dissipation or decay. This is in stark contrast to spin currents in normal diffusive metals which tend to decay on relatively short length scales. We illustrate the above properties by performing model calculations relevant to two distinct classes of altermagnets and various device geometries.

Rhombohedral graphene multilayers host various broken-symmetry metallic phases as well as superconductors whose pairing mechanism and order parameter symmetry remain unsettled. Strikingly, experiments have revealed prominent superconducting regions in rhombohedral bilayer and trilayer graphene devices with proximity-induced Ising spin-orbit coupling. We propose that these superconductors descend from a common spin-canted normal state that spontaneously breaks a U(1) spin symmetry and thus supports soft magnon modes. In particular, we show that these soft modes can mediate pairing through interband scattering events that are symmetry forbidden in the absence of spin-orbit coupling, thus providing a promising explanation for spin-orbit-enabled pairing. Numerous other experimental observations—including nontrivial dependence of superconductivity on the spin-orbit coupling strength, in-plane magnetic fields, and Fermi surface structure—also naturally follow from our scenario.

We construct a family of two-dimensional topological stabilizer codes on continuous variable (CV) degrees of freedom, which generalize homological rotor codes and the toric-GKP code. Our topological codes are built using the concept of boson condensation—we start from a parent stabilizer code based on an $\mathbb{R}$ gauge theory and condense various bosonic excitations. This produces a large class of topological CV stabilizer codes, including ones that are characterized by the anyon theories of $\mathrm{U}(1{)}_{2n}\times \mathrm{U}(1{)}_{-2m}$ Chern-Simons theories, for arbitrary pairs of positive integers $(n,m)$. Most notably, this includes anyon theories that are nonchiral and nevertheless do not admit a gapped boundary. It is widely believed that such anyon theories cannot be realized by any stabilizer model on finite-dimensional systems. We conjecture that these CV codes go beyond codes obtained from concatenating a topological qudit code with a local encoding into CVs, and thus constitute the first example of topological codes that are intrinsic to CV systems. Moreover, we study the Hamiltonians associated with the topological CV stabilizer codes and show that, although they have a gapless spectrum, they can become gapped with the addition of a quadratic perturbation. We show that similar methods can be used to construct a gapped Hamiltonian whose anyon theory agrees with a $\mathrm{U}(1{)}_2$ Chern-Simons theory. Our work initiates the study of scalable stabilizer codes that are intrinsic to CV systems and highlights how error-correcting codes can be used to design and analyze many-body systems of CVs that model lattice gauge theories.

Dimensionality tuning is an important method to modify the electronic states of quantum materials. However, the mechanism of such tuning in heavy fermion systems and its connection with transport properties remain largely unexplored. Here by combining molecular beam epitaxy, in situ angle-resolved photoemission spectroscopy and transport measurements, we study the electronic states of the heavy-fermion compound ${\mathrm{CeSi}}_2$ as a function of film thickness. In three-dimensional thick films, our measurements reveal a dispersive Kondo peak at the Fermi level ($E_F$) and satellite peaks originating from crystal electric field (CEF) excitations, characteristic of heavy-fermion systems. For two-dimensional ultrathin films, the CEF satellites are largely suppressed while the ground-state Kondo peak at $E_F$ remains strong, although it develops at lower temperatures. Simultaneously, the maximum temperature $T_{\max }$ of the magnetic resistivity, ${\rho }_m(T)$, changes from $\approx 100\mathrm{K}$ in thick films to $\approx 35\mathrm{K}$ in ultrathin films. This can be attributed to the dimensionality-driven reduction of CEF excitations during the Kondo process, in good agreement with spectroscopic results. Our work provides direct insight to understand the quantum confinement effects on strongly correlated $4f$-electron systems and opens up new opportunities to explore emergent phenomena in two-dimensional heavy-fermion materials.

Friction causes mechanical energy dissipation and material degradation in machinery and devices. While phononic friction is well understood via anharmonic lattice dynamics, the physics of electronic friction remains unclear due to challenges in separating electronic degrees of freedom from phononic ones in experiments and analyzing the nonequilibrium interactions between ionic movement and electronic dynamics in theory. To tackle this problem, we construct a sliding device featuring 2D crystalline interfaces that possess ultrasmooth and minimally interacting surfaces, achieving the state of structural superlubricity with no wear and minimal friction. Using electrical and mechanical controls, we tuned the nature of interfacial electronic coupling and charge densities in materials in an on-device manner, which allows us to disentangle the electron and phonon contributions to friction. Our experimental data and theoretical analysis supported by first-principles calculations demonstrate that electronic friction can well surpass phononic contributions and dominate energy dissipation at structural superlubricity contacts. These findings offer fresh insights into the mechanism of electronic friction and promising opportunities for friction control in device applications.

Noncollinear magnets are notoriously difficult to describe within first-principles approaches based on density-functional theory because of the presence of low-lying spin excitations. At the level of ground-state calculations, several methods exist to constrain the magnetic moments to a predetermined configuration and thereby accelerate convergence toward self-consistency. Their use in a perturbative context, however, remains very limited. Here, we present a general methodological framework to achieve parametric control over the local spin moments at the linear-response level. Our strategy builds on the concept of Legendre transform to switch between various flavors of magnetic functionals and to relate their second derivatives via simple linear-algebra operations. Thereby, we can address an arbitrary response function at the time-dependent density-functional level of theory with optimal accuracy and minimal computational effort. In the low-frequency limit, we identify the leading correction to the existing adiabatic formulation of the problem [S. Ren et al., Phys. Rev. X 14, 011041 (2024)], consisting in a renormalization of the phonon and magnon masses due to electron inertia. As a demonstration, we apply our methodology to the terahertz optical response of bulk ${\mathrm{CrI}}_3$ and ${\mathrm{Cr}}_2{\mathrm{O}}_3$, where we identify contributions from hybrid (electro)magnons with mixed spin-lattice character.