The Amontons-Coulomb friction law assumes that the frictional force between materials is independent of sliding velocity. However, as Coulomb noted, this is a rough approximation, and a second-order dependence of friction on the logarithm of sliding velocity is incorporated in a commonly used “rate- and state-dependent” friction representation. Here, we conduct shear experiments on mica, a layer-structured mineral, at temperatures ranging from 22 to $200°\mathrm{C}$ and under normal stress of 100 MPa. The friction coefficient clearly depends on the logarithmic sliding velocity at $22°\mathrm{C}$, but rate sensitivity decreases with increasing temperature until at $200°\mathrm{C}$, the friction coefficient is independent of sliding velocity. Our findings could initiate the development of velocity-independent frictional materials, realizing the ideal Amontons-Coulomb friction.

The interplay between localized magnetic moments and itinerant electrons gives rise to exotic quantum states in condensed matter systems. Here, we demonstrate an electrically tunable heavy fermion phase diagram in magic-angle twisted trilayer graphene, achieved by controlling the Kondo hybridization between localized flat-band electrons and itinerant Dirac electrons via a displacement field. Our results reveal a continuous quantum phase transition from an antiferromagnetic semimetal to a paramagnetic heavy fermion metal. At the quantum critical point, we observe effective mass divergence and Fermi surface reconstruction. This highly tunable platform offers unprecedented control over heavy fermion physics, establishing moiré heterostructures as a versatile arena for exploring correlated quantum phases—including potential unconventional superconductivity—in the two-dimensional limit.

Integrating essential physical priors into deep-learning first-principles methods is a critical fundamental problem. Here we demonstrate that the deep learning density functional theory Hamiltonian (DeepH) method can be substantially improved by changing the learning objective to a rotation-invariant and basis-free quantity—the real-space Kohn-Sham potential (named DeepH-R). Benefiting from the enhanced physical priors, DeepH-R achieves substantially improved prediction accuracy and generalization ability compared to previous DeepH approaches. Moreover, DeepH-R provides a more accurate and straightforward route to deep-learning density functional perturbation theory, and enables the training of foundation models of electronic structure with sub-meV accuracy, opening new opportunities for AI-driven materials discovery.

Infinite projected entangled-pair states (iPEPSs) provide a powerful variational framework for two-dimensional quantum matter and have been widely used to capture bosonic topological order, including chiral spin liquids. Here, we extend this approach to fermionic topological order by variationally optimizing U(1)-symmetric fermionic iPEPSs for a fractional Chern insulator (FCI), with bond dimensions up to $D=9$. We find evidence for a critical bond dimension, above which the ansatz faithfully represents the FCI phase. The FCI state is characterized using bulk observables, including the equal-time single-particle Green’s function and the pair-correlation function, as well as the momentum-resolved edge entanglement spectrum. To enable entanglement-spectrum calculations for large iPEPS unit cells, we introduce a compression scheme and show that the low-lying part of the spectrum is already well converged at relatively small cutoff dimensions.

The predictive accuracy of popular extensions to density-functional theory (DFT) such as $\mathrm{DFT}+U$ and DFT plus dynamical mean-field theory ($\mathrm{DFT}+\mathrm{DMFT}$) hinges on using realistic values for the screened Coulomb interaction $U$. Here, we present a systematic comparison of the two most widely used approaches to compute this parameter, i.e., linear response theory (LRT) and the constrained random-phase approximation (cRPA), using a unified framework based on the use of maximally localized Wannier functions. We show that, even in cases of partially filled well-separated interacting subspaces, for which there is no ambiguity in the application of both techniques, the $U$ in LRT and cRPA can differ as much as 30%. We demonstrate that this discrepancy arises from two main differences: neglecting the response of the exchange-correlation potential in cRPA and additional excitation channels in LRT. By taking these differences into account, we can achieve near perfect agreement between the two techniques. Moreover, we show that in cases with strong hybridization between interacting and screening subspaces, the application of cRPA becomes ambiguous and can lead to unrealistically small $U$ values, while LRT remains well-behaved. Our Letter formally connects both methods, sheds light on their strengths and limitations, and emphasizes the importance of using a consistent set of Wannier orbitals to ensure transferability of $U$ values between different implementations.

We propose a microscopic, weak-coupling mechanism by which generic Chern bands asymptotically relax toward ideal bands. We consider coupling interacting electrons to a Caldeira-Leggett-like Ohmic bosonic bath. Using the Born-Markov approximation, we analytically show that, upon taking the leading order contribution in momentum of the form factor, Slater determinant states of a Chern band under Hartree-Fock approximation evolve toward Slater determinant states corresponding to an ideal Chern band. We also numerically validate our proposal by performing simulation of a massive Dirac model with the extended Hubbard interaction, showing that the Berry curvature and quantum metric co-evolve toward saturation of the trace condition. Our proposal provides a concrete dissipative mechanism for driving Chern bands toward ideal quantum geometry, a fundamental building block for the stabilization of fractional Chern insulators.

Inspired by the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, we present exact solutions for a spin-1 chain with Kitaev-like couplings. We consider an expanded Kitaev model with bilinear and biquadratic terms. At an exactly solvable point, the Hamiltonian can be reexpressed as a sum of projection operators. Unlike the AKLT model where projectors act on total spin, we project the component of spin along the bond direction. This leads to exponential ground-state degeneracy, expressed in terms of fractionalized spin-$\frac{1}{2}$ objects. Each ground state can be expressed concisely as a matrix product state. We construct a phase diagram by varying the relative strength of bilinear and biquadratic terms. The fractionalized states provide a qualitative picture for the spin-1 Kitaev model, yielding approximate forms for the ground state and low-lying excitations.

Magnons in ferromagnets possess spin angular momentum defined by right-handed precession of the moment around the magnetization direction. In antiferromagnets with no net magnetization, left- and right-handed magnons are degenerate in the absence of an applied field. Ferrimagnets possess uncompensated magnetic sublattices, which should natively possess right- and left-handed magnons where their energy is split by the internal molecular field. Here, we show that $R{\mathrm{Mn}}_6{\mathrm{Sn}}_6$ ($R=\mathrm{Tb}$, Er) ferrimagnets possess right- and left-handed magnon bands that cross at finite momentum ($\mathbf{k}$) within the basal plane, defining modes with opposite dynamical chirality. Depending on the symmetry of the ferrimagnetic order, which may be manipulated by varying the rare-earth magnetic anisotropy or with an applied field, the band crossing may remain a nodal line or may be gapped. The gapped modes contain hybridized chiral excitations whose chirality becomes $\mathbf{k}$-dependent.

We experimentally investigate the terahertz spectrum of plasma excitations in a plasmonic crystal based on AlGaN/GaN two-dimensional electron system (2DES). While screened plasmon modes with linear dispersion are readily observed in such structures, unscreened modes localized in the slots between the gates have remained experimentally elusive. We discover this slot plasma excitation exhibiting square-root dispersion. It turns out that these slot plasmons follow an unconventional wave-vector quantization rule, $q_u=(N+1/4)\times \pi /l_u$ for even integers $N$, and require the excitation condition $q_{u}h\ll 1$, where $h$ is the gate-to-2DES distance and $l_u$ is the slot width. We develop an analytical model that accurately captures the observed dispersion and relaxation, revealing a nontrivial $-\pi /4$ phase shift upon plasmon reflection at the gate edge. Remarkably, the slot plasmons persist up to room temperature, thereby enabling a broad range of opportunities for the advancement of plasmonic devices.

For a class of translation-invariant free-fermion systems including those with uniform nearest-neighbor hopping) on a $d$-dimensional $L\times \cdots \times L$ hypercubic lattice, we prove that, starting from an arbitrary pure initial state, the system equilibrates with respect to the coarse-grained density within a timescale of order $L$. This scaling is optimal, since there exist initial states whose equilibration requires time of order $L$. Our result establishes $O(L)$ as the equilibration timescale, as is expected in normal macroscopic systems with a conserved quantity, such as total number of particles.

We show that oscillating (real-scalar) boson stars generically host an oscillating radial caustic. Sources near this caustic cross it every half period, thereby producing periodic caustic-crossing lensing. The resulting observables are phase locked to the lens oscillation: image-pair creation or annihilation, changing image morphology, achromatic photometric spikes, and astrometric motion. This signal provides a distinctive target for time-domain astronomy, and its detection would reveal an intrinsically time-dependent compact dark-sector object. Event-number estimates indicate a measurable discovery space with current astrometric and high-cadence photometric surveys, while null searches would constrain the abundance of such objects as dark matter. The predictions rely only on the dynamics of real-scalar condensates and extend naturally to self-interacting real scalars, including axionlike particles, and to ultralight vector bosons.

Using a combination of Hubble Space Telescope and James Webb Space Telescope imaging, a runaway supermassive black hole was recently identified with an inferred velocity of ${954}_{-126}^{+110}\mathrm{km}{\mathrm{s}}^{-1}$, likely ejected from a compact star-forming galaxy at $z\approx 0.96$. Assuming the runaway black hole originated from a gravitational-wave-driven merger of two supermassive black holes (SMBHs), we combine its measured recoil velocity with gravitational-wave recoil predictions from numerical relativity and black-hole perturbation theory to constrain the mass ratio and spin configuration of the progenitor binary that overcame the final-parsec problem and merged $\sim 70\mathrm{Myr}$ ago. We find that the progenitor binary must have been precessing, with a mass ratio $m_1/m_2\lesssim 6$, and that the more massive SMBH likely possessed a high dimensionless spin magnitude ($\sim 0.75$) in order to generate a recoil of this magnitude. Such SMBH mergers could represent an interesting source population for the upcoming Laser Interferometer Space Antenna mission, with characteristic signal-to-noise ratios of order $\gtrsim {10}^3$. Furthermore, the inferred progenitor SMBH properties suggest that the compact galaxy likely originated from a major, gas-rich (“wet”) merger between two galaxies of comparable mass, with a mass ratio $\lesssim 4$.

The interference patterns of ultracold atoms, observed after ballistic expansion from optical lattices, encode essential information about strongly correlated lattice systems, including phase coherence and nonlocal correlations. While the interference of lattice bosons has been extensively investigated, quantitative studies of the lattice fermion interference remain challenging. Here, we report the observation and quantitative characterization of interference patterns in low-temperature, homogeneous fermionic Hubbard gases. We develop a general method to extract the quasimomentum distribution and the first-order correlation function from these patterns. In the noninteracting limit, the coherence length remains very close to the average spacing between identical fermions over a wide range of fillings, revealing the fundamental upper bound imposed by Pauli exclusion on first-order coherence. By tuning the interaction strength and filling, we identify their interplay in the suppression of first-order coherence across the metal-to-Mott-insulator crossover. Moreover, at half filling, the measured correlations agree well with quantum Monte Carlo calculations and remain finite in the strong repulsion regime, revealing virtual tunneling and the underlying superexchange physics.

${\mathrm{AgNbO}}_3$ is a lead-free perovskite with considerable potential for energy storage and optoelectronic applications, yet its low-temperature crystal structure has remained controversial. In this Letter, we revisit its low-energy structural landscape using a systematic first-principles structural search based on symmetry-adapted phonon-mode theory. We uncover a previously unreported chiral ferroelectric phase with space group $R3$, which exhibits a large spontaneous polarization and a low polarization switching barrier, enabling polarization reversal under electric fields. Crucially, the structural chirality of this phase is intrinsically locked to the ferroelectric polarization, allowing electrical control of the chiral handedness. Consequently, chiral optical responses—including circular dichroism, circular photogalvanic effect, optical activity, and second-order nonlinear optics—can be reversibly switched by an external electric field. These results not only clarify the complex low-temperature structural behavior of ${\mathrm{AgNbO}}_3$ but also establish a rare purely inorganic platform for electric-field-tunable chirality, opening a pathway toward ultrafast, electrically controlled chiral optoelectronics.

With growing interest in structural chirality in periodic solids, it has been suggested that chirality might constitute a new ferroic order parameter. In the work described, we demonstrate, by means of a formal group-theoretical proof and a systematic group-subgroup analysis, that achiral-to-chiral transitions that produce either member of an enantiomorphic pair cannot be driven by a Brillouin-zone-center ($\mathrm{\Gamma }$-point) instability from a common achiral parent. We further substantiate this result by explicitly showing that none of the achiral parent space groups that admit symmetry-chiral phonon eigenvectors host them at the zone center. Given that a primary ferroic order parameter must, among other requirements, transform according to a zone-center irreducible representation, we conclude that phase transitions leading to enantiomorphic space groups cannot be classified as primary ferroic transitions. This predicts that any critical enhancement of fluctuations must occur at finite-$q$ rather than as a divergence of a uniform macroscopic susceptibility.

We carry out large-scale, sign-problem-free determinant quantum Monte Carlo simulations of the square lattice $\mathrm{SU}(N)$-symmetric two-channel Kondo lattice model at half-filling. We map out the zero-temperature phase diagram for $N=2$, 4, 6, and 8, as a function of the Kondo coupling strength. In the weak-coupling regime, we observe antiferromagnetic order of the localized moments. Remarkably, for $N\ge 6$, sufficiently strong Kondo coupling induces spontaneous channel symmetry breaking, forming a stripe dimerization pattern with a wave vector $\mathit{k}=(\pi ,0)$ alternating between channels. These findings are supported by a complementary large-$N$ saddle point analysis, which identifies the striped hybridization pattern as the energetically preferred configuration. The spatial symmetry breaking results in an anisotropic Fermi surface reconstruction.

We have used variational states to analyze the effects of band geometry on the two-dimensional Wigner crystal with one and two electrons per unit cell. At sufficiently low electron densities, we find that increasing Berry curvature drives a transition into a crystalline state composed of spin-triplet pairs carrying relative orbital angular momentum $m=-1$. The essential features of this transition are captured by an effective two-electron quantum dot problem in the presence of Berry curvature. Our results point to a purely electronic, strong-coupling mechanism for local spin-triplet pairing in correlated two-dimensional electron systems with quantum geometry.

The development of low-noise, high-sensitivity magnetic sensors is essential for applications such as automotive systems, biomedical imaging, and magnetic microscopy. However, sensor performance has long been impeded by a fundamental constraint that noise and sensitivity increase concomitantly, which imposes a performance limit. Here, we show that this limit can be overcome by engineering spin-texture dynamics. While maintaining high sensitivity, the sensor noise is demonstrated to decrease inversely with enhanced spin-texture dynamics. Leveraging this mechanism, using synthetic ferrimagnets with accelerated spin-texture dynamics, low-noise and high-sensitivity anomalous-Hall sensors are constructed. With an active sensing area of $20\times 20{\mathrm{\mu m}}^2$, the device demonstrates a field detectability of $15.7\mathrm{nT}/\surd \mathrm{Hz}$ at 1 Hz, nearly an order of magnitude improvement over existing sensors based on ferromagnetic materials. Our results establish active control of spin textures as a general pathway to ultrasensitive, low-noise magnetic sensing platforms.

We investigate how many-electron excited states emerge in twisted ${\mathrm{MoSe}}_2$ homobilayers when the lattice reconstructions evolve. Notably, we identify a new trion resonance that arises in the transition regime of lattice reconstruction, where gradual changes in atomic alignment between the layers occur. Magnetic field-dependent measurements, supported by first-principles calculations, indicate that the exciton forms at the K valley while the doped hole resides in the $\mathrm{\Gamma }$ valley. First-principles calculations further indicate that two nearly degenerate exciton resonances can arise, localized at different sites within the moiré supercell. We propose that the new trion resonance is a “charge-transfer” trion, in which the electron-hole pair is spatially separated from the doped hole. The emergence of these complex excited states stems from the distinct moiré potentials acting on holes and excitons, resulting in their different spatial distribution within the superlattice.