We present a unifying framework that allows us to study the mixed crystalline-electromagnetic responses of topological semimetals in spatial dimensions up to $D=3$ through dimensional augmentation and reduction procedures. We show how this framework illuminates relations between the previously known topological semimetals and use it to identify a new class of quadrupolar nodal line semimetals for which we construct a lattice tight-binding Hamiltonian. We further utilize this framework to quantify a variety of mixed crystalline-electromagnetic responses, including several that have not previously been explored in existing literature, and show that the corresponding coefficients are universally proportional to weighted momentum-energy multipole moments of the nodal points (or lines) of the semimetal. We introduce lattice gauge fields that couple to the crystal momentum and describe how tools including the gradient expansion procedure, dimensional reduction, compactification, and the Kubo formula can be used to systematically derive these responses and their coefficients. We further substantiate these findings through analytical physical arguments, microscopic calculations, and explicit numerical simulations employing tight-binding models.

Topological semimetals with massless Dirac and Weyl fermions represent the forefront of quantum materials research. In two dimensions, a peculiar class of fermions that are massless in one direction and massive in the perpendicular direction was predicted 16 years ago. These highly exotic quasiparticles—the semi-Dirac fermions—ignited intense theoretical and experimental interest but remain undetected. Using magneto-optical spectroscopy, we demonstrate the defining feature of semi-Dirac fermions—$B^{2/3}$ scaling of Landau levels—in a prototypical nodal-line metal ZrSiS. In topological metals, including ZrSiS, nodal lines extend the band degeneracies from isolated points to lines, loops, or even chains in the momentum space. With ab initio calculations and theoretical modeling, we pinpoint the observed semi-Dirac spectrum to the crossing points of nodal lines in ZrSiS. Crossing nodal lines exhibit a continuum absorption spectrum but with singularities that scale as $B^{2/3}$ at the crossing. Our work sheds light on the hidden quasiparticles emerging from the intricate topology of crossing nodal lines and highlights the potential to explore quantum geometry with linear optical responses.

Materials-realistic microscopic theoretical descriptions of copper-based superconductors are challenging due to their complex crystal structures combined with strong electron interactions. Here, we demonstrate how density functional theory can accurately describe key structural, electronic, and magnetic properties of the normal state of the prototypical cuprate ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+x}$ (Bi-2212). We emphasize the importance of accounting for energy-lowering structural distortions, which then allows us to (a) accurately describe the insulating antiferromagnetic (AFM) ground state of the undoped parent compound (in contrast to the metallic state predicted by previous ab initio studies); (b) identify numerous low-energy competing spin and charge stripe orders in the hole-overdoped material nearly degenerate in energy with the AFM ordered state, indicating strong spin fluctuations; (c) predict the lowest-energy hole-doped crystal structure including its long-range structural distortions and oxygen dopant positions that match high-resolution scanning transmission electron microscopy measurements; and (d) describe electronic bands near the Fermi energy with flat antinodal dispersions and Fermi surfaces that are in agreement with angle-resolved photoemission spectroscopy (ARPES) measurements and provide a clear explanation for the structural origins of the so-called “shadow bands.” We also show how one must go beyond band theory and include fully dynamic spin fluctuations via a many-body approach when aiming to make quantitative predictions to measure the ARPES spectra in the overdoped material. Finally, regarding spatial inhomogeneity, we show that the local structure at the ${\mathrm{CuO}}_2$ layer, rather than dopant electrostatic effects, modulates the local charge-transfer gaps, local correlation strengths, and by extension the local superconducting gaps.

The observation of unexpected polarization textures such as vortices, skyrmions, and merons in various oxide heterostructures has challenged the widely accepted picture of ferroelectric domain walls as being Ising-like. Bloch components in the 180° domain walls of ${\mathrm{PbTiO}}_3$ have recently been reported in ${\mathrm{PbTiO}}_3/{\mathrm{SrTiO}}_3$ superlattices and linked to domain wall chirality. While this opens exciting perspectives, the ubiquity of this Bloch component remains to be further explored. In this work, we present a comprehensive investigation of domain walls in ${\mathrm{PbTiO}}_3/{\mathrm{SrTiO}}_3$ superlattices, involving a combination of first- and second-principles calculations, phase-field simulations, diffuse scattering calculations, and synchrotron-based diffuse x-ray scattering. Our theoretical calculations highlight that the previously predicted Bloch polarization in the 180° domain walls in ${\mathrm{PbTiO}}_3/{\mathrm{SrTiO}}_3$ superlattices might be more sensitive to the boundary conditions than initially thought and is not always expected to appear. Employing diffuse scattering calculations for larger systems, we develop a method to probe the complex structure of domain walls in these superlattices via diffuse x-ray scattering measurements. Through this approach, we investigate depolarization-driven ferroelectric polarization rotation at the domain walls. Our experimental findings, consistent with our theoretical predictions for realistic domain periods, do not reveal any signatures of a Bloch component in the centers of the 180° domain walls of ${\mathrm{PbTiO}}_3/{\mathrm{SrTiO}}_3$ superlattices, suggesting that the precise nature of domain walls in the ultrathin ${\mathrm{PbTiO}}_3$ layers is more intricate than previously thought and deserves further attention.

Topologically protected edge channels show prospects for quantum devices. They have been found experimentally in two-dimensional quantum spin Hall insulators (QSHIs), weak topological insulators, and higher-order topological insulators, but the number of materials realizing these topologies is still quite limited. Here, we provide evidence for topological edge states within a novel topology named three-dimensional QSHIs. Its topology originates solely from a nonzero ${\mathbf{S}}_{\mathit{z}}$ spin Chern number for each ${\mathbf{k}}_{\mathit{z}}$ plane of the crystal and is realized in bulk $\alpha \text{−}{\mathrm{Bi}}_4{\mathrm{I}}_4$ with trivial symmetry indicators, as we show by density-functional-theory calculations. We experimentally observe the related edge states at each type of monolayer and bilayer step of this material by scanning tunneling microscopy. Consistently, the edge states are neither interrupted nor backscattered by defects at the step edges corroborating their helical character as expected from the nontrivial topology. Furthermore, two individual edge channels are directly observed at bilayer steps without visible interaction gap opening, demonstrating the robustness of these edge modes against vertical stacking. Our results establish $\alpha \text{−}{\mathrm{Bi}}_4{\mathrm{I}}_4$ as the first material realization of a 3D QSHI whose definition goes beyond the scope of topological symmetry indicators, and provide a pathway for realizing nearly quantized spin Hall conductivity per unit cell in a bulk crystal.

The ground state of an homogeneous electron gas is a paradigmatic state that has been used to model and predict the electronic structure of matter at equilibrium for nearly a century. For half a century, it has been successfully used to predict ground states of quantum systems via the local density approximation (LDA) of density functional theory (DFT), and systematic improvements in the form of generalized gradient approximations and evolution thereon. Here, we introduce the LDA for excited states by considering a particular class of nonthermal ensemble states of the homogeneous electron gas. These states find sound foundation and application in ensemble DFT—a generalization of DFT that can deal with ground and excited states on equal footing. The ensemble LDA is shown to successfully predict difficult low-lying excitations in atoms and molecules for which approximations based on local spin density approximation and time-dependent LDA fail.

Topology, like symmetry, is a fundamental concept in understanding general properties of physical systems. In condensed matter, nontrivial topology may manifest itself as singular features in the energy spectrum or the quantization of electrical properties such as conductance and magnetic flux. Using microwave spectroscopy, we determine that a superconducting circuit with three Josephson tunnel junctions in parallel can possess degeneracies indicative of intrinsic nontrivial topology. We identify three topological invariants, one of which is related to a hidden quantum mechanical supersymmetry. Measurements show that devices fabricated in different topological regimes fall on a simple phase diagram, which should be robust to junction imperfections and geometric inductance. Josephson tunnel junction circuits, which are readily fabricated with conventional microlithography techniques, allow access to a wide range of topological systems that may have no condensed matter analog. Notable spectral features of these circuits, such as degeneracies and flat bands, may find use in quantum information, sensing, and metrology.

We study a model of electrons moving in a parent band of uniform Berry curvature. At sufficiently high parent Berry curvature, we show that strong repulsive interactions generically lead to the formation of an anomalous Hall crystal: a topological state with spontaneously broken continuous translation symmetry. Our results are established via a mapping to a problem of Wigner crystallization in a regular 2D electron gas. Interestingly, we find that a periodic electrostatic potential induces a competing state with opposite Chern number. Our theory offers a unified perspective for understanding several aspects of the recently observed integer and fractional quantum anomalous Hall effects in rhombohedral multilayer graphene and provides a recipe for engineering new topological states.

Vortex pinning is a crucial factor that determines the critical current of practical superconductors and enables their diverse applications. However, the underlying mechanism of vortex pinning has long been elusive, lacking a clear microscopic explanation. Here, using high-resolution scanning tunneling microscopy, we studied single vortex pinning induced by point defect in layered FeSe-based superconductors. We found the defect-vortex interaction drives low-energy vortex bound states away from $E_{\mathrm{F}}$, creating a “mini” gap that effectively lowers the system energy and enhances pinning. By measuring the local density of states, we directly obtained the elementary pinning energy and estimated the pinning force via the spatial gradient of pinning energy. The results are consistent with bulk critical current measurement. Furthermore, we showed that a general microscopic quantum model incorporating defect-vortex interaction can naturally capture our observation. It suggests that the local pairing near pinned vortex core is actually enhanced compared to unpinned vortex, which is beyond the traditional understanding that nonsuperconducting regions pin vortices. Our study thus unveils a general microscopic mechanism of vortex pinning in superconductors and provides insights for enhancing the critical current of practical superconductors.

The quantum Wigner crystal is a many-body state where Coulombic repulsion quenches the kinetic energy of electrons, causing them to crystallize into a lattice. Experimental realization of a quantum Wigner crystal at zero magnetic field has been a long-sought goal. Here, we report on the experimental evidence of a Wigner solid in ultra-thin films of cadmium arsenide (${\mathrm{Cd}}_3{\mathrm{As}}_2$) at zero magnetic field. We show that a finite bias depins the domains and produces an unusually sharp-threshold current-voltage behavior. Hysteresis and voltage fluctuations point to domain motion across the pinning potential and disappear at finite temperature as thermal fluctuations overcome the potential. The application of a small magnetic field destroys the Wigner solid, pointing to an unconventional origin. We use Landau-level spectroscopy to show that the formation of the Wigner solid is closely connected to a topological transition as the film thickness is reduced.

We study paramagnetic quantum criticality in the periodic Anderson model (PAM) using cellular dynamical mean-field theory (CDMFT), with the numerical renormalization group (NRG) as a cluster impurity solver. The PAM describes itinerant $c$ electrons hybridizing with a lattice of localized $f$ electrons. At zero temperature, it exhibits a much-studied quantum phase transition from a Kondo phase to a Ruderman-Kittel-Kasuya-Yosida (RKKY) phase when the hybridization is decreased through a so-called Kondo breakdown quantum critical point (KB QCP). There, Kondo screening of $f$ spins by $c$ electrons breaks down, so that $f$ excitations change their character from somewhat itinerant to mainly localized, while $c$ excitations remain itinerant. Building on Phys. Rev. Lett. 101, 256404 (2008), which interpreted the KB transition as an orbital-selective Mott transition, we here elucidate its nature in great detail by performing a high-resolution, real-frequency study of various dynamical quantities (susceptibilities, self-energies, and spectral functions). NRG allows us to study the quantum critical regime governed by the QCP and located between two temperature scales, $T_{\mathrm{FL}}<T_{\mathrm{NFL}}$. In this regime, we find fingerprints of non-Fermi-liquid (NFL) behavior in several dynamical susceptibilities. Surprisingly, CDMFT self-consistency is essential to stabilize the QCP and the NFL regime. The Fermi-liquid (FL) scale $T_{\mathrm{FL}}$ decreases toward and vanishes at the KB QCP; at temperatures below $T_{\mathrm{FL}}$, FL behavior emerges. At $T=0$, we find the following properties. The KB transition is continuous. The $f$ quasiparticle weight decreases continuously as the transition is approached from either side, vanishing only at the KB QCP. Therefore, the quasiparticle weight of the $f$ band is nonzero not only in the Kondo phase, but also in the RKKY phase; hence, the FL quasiparticles comprise $c$ and $f$ electrons in both phases. The Fermi surface (FS) volumes in the two phases differ, implying a FS reconstruction at the KB QCP. Whereas the large-FS Kondo phase has a two-band structure as expected, the small-FS RKKY phase unexpectedly has a three-band structure. We provide a detailed analysis of quasiparticle properties of both the Kondo and, for the first time, also the RKKY phase and uncover their differences. The FS reconstruction is accompanied by the appearance of a Luttinger surface on which the $f$ self-energy diverges. The volumes of the Luttinger and Fermi surfaces are related to the charge density by a generalized Luttinger sum rule. We interpret the small FS volume and the emergent Luttinger surface as evidence for $f$-electron fractionalization in the RKKY phase. Finally, we compute the temperature dependence of the Hall coefficient and the specific heat, finding good qualitative agreement with experiments.

We show that the path integral of conformal field theories in $D$ dimensions (${\mathrm{CFT}}_D$) can be constructed by solving for eigenstates of a renormalization group (RG) operator following from the Turaev-Viro formulation of a topological field theory (topological quantum field theory) (TQFT) in $D+1$ dimensions (${\mathrm{TQFT}}_{D+1}$), explicitly realizing the holographic sandwich relation between a symmetric theory and a TQFT. Generically, exact eigenstates corresponding to symmetric ${\mathrm{TQFT}}_D$ follow from Frobenius algebra in ${\mathrm{TQFT}}_{D+1}$. For $D=2$, we construct eigenstates that produce 2D rational CFT path integrals exactly, which curiously connect a continuous-field theoretic path integral with the Turaev-Viro state sum. We also devise and illustrate numerical methods for $D=2$, 3 to search for ${\mathrm{CFT}}_D$ as phase transition points between symmetric ${\mathrm{TQFT}}_D$. Finally, since the RG operator is in fact an exact analytic holographic tensor network, we compute “bulk-boundary” correlators and compare them with the AdS/CFT dictionary at $D=2$. Promisingly, they are numerically compatible given our accuracy, although further works will be needed to explore the precise connection to the AdS/CFT correspondence.

Single atomic defects are prominent windows to look into host quantum states because collective responses from the host states emerge as localized states around the defects. Friedel oscillations and Kondo clouds in Fermi liquids are quintessential examples. However, the situation is quite different for quantum spin liquid (QSL), an exotic state of matter with fractionalized quasiparticles and topological order arising from a profound impact of quantum entanglement. Elucidating the underlying local electronic property has been challenging due to the charge neutrality of fractionalized quasiparticles and the insulating nature of QSLs. Here, using spectroscopic-imaging scanning tunneling microscopy, we report atomically resolved images of monolayer $\alpha \text{−}{\mathrm{RuCl}}_3$, the most promising Kitaev QSL candidate, on metallic substrates. We find quantum interference in the insulator manifesting as incommensurate and decaying spatial oscillations of the local density of states around defects with a characteristic bias dependence. The oscillation differs from any known spatial structures in its nature and does not exist in other Mott insulators, implying it is an exotic oscillation involved with excitations unique to $\alpha \text{−}{\mathrm{RuCl}}_3$. Numerical simulations suggest that the observed oscillation can be reproduced by assuming that itinerant Majorana fermions of Kitaev QSL are scattered across the Majorana Fermi surface. The oscillation provides a new approach to exploring Kitaev QSLs through the local response against defects like Friedel oscillations in metals.

In a lattice model subject to a perpendicular magnetic field, when the lattice constant is comparable to the magnetic length, one enters the “Hofstadter regime,” where continuum Landau levels become fractal magnetic Bloch bands. Strong mixing between bands alters the nature of the resulting quantum phases compared to the continuum limit; lattice potential, magnetic field, and Coulomb interaction must be treated on equal footing. Using determinant quantum Monte Carlo and density matrix renormalization group techniques, we study this regime numerically in the context of the Hubbard-Hofstadter model on a triangular lattice. In the field-filling phase diagram, we find a broad wedge-shaped region of ferromagnetic ground states for filling factor $\nu \le 1$, bounded below by filling factor $\nu =1$ and bounded above by half filling the lowest Hofstadter subband. We observe signatures of SU(2) quantum Hall ferromagnetism at filling factors $\nu =1$ and $\nu =3$. The phases near $\nu =1$ are particle-hole asymmetric, and we observe a rapid decrease in ground-state spin polarization consistent with the formation of skyrmions only on the electron doped side. At large fields, above the ferromagnetic wedge, we observe a low-spin metallic region with spin correlations peaked at small momenta. We argue that the phenomenology of this region likely results from exchange interaction mixing fractal Hofstadter subbands. The phase diagram derived beyond the continuum limit points to a rich landscape to explore interaction effects in magnetic Bloch bands.

The study of the mechanism of exchange-bias phenomena and the achievement of its efficient control are of great importance, as it promotes the revelation of unique exchange interactions and the development of exotic applications. However, it is challenging due to the elusive interface between magnetic phases. In this study, we report an unprecedented exchange-bias phenomenon observed in ultrathin, uncompensated, antiferromagnetic ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. The magnitude and direction of the exchange field can be intentionally controlled by designing a magnetic-field sweep protocol without a field cooling process. The combined experimental and theoretical simulation results indicate that the spin-flip process assisted by the ubiquitous defect-induced pinning domain sites with varying inner exchange interactions might give rise to the emergence and robustness of this peculiar exchange bias. The temperature and thickness dependence of the exchange-bias phenomena are systematically investigated for further study and exploitation of its unique properties. This mechanism allows for highly tunable exchange bias in prevalent magnetic systems by engineering the properties of domain structures and also offers promising avenues for the design of spintronic devices combing its topology based on ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$.

Superconducting nickelates are a new family of strongly correlated electron materials with a phase diagram closely resembling that of superconducting cuprates. While analogy with the cuprates is natural, very little is known about the metallic state of the nickelates, making these comparisons difficult. We probe the electronic dispersion of thin-film superconducting five-layer ($n=5$) and metallic three-layer ($n=3$) nickelates by measuring the Seebeck coefficient $S$. We find a temperature-independent and negative $S/T$ for both $n=5$ and $n=3$ nickelates. These results are in stark contrast to the strongly temperature-dependent $S/T$ measured at similar electron filling in the cuprate ${\mathrm{La}}_{1.36}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_{0.24}{\mathrm{CuO}}_4$. The electronic structure calculated from density-functional theory can reproduce the temperature dependence, sign, and amplitude of $S/T$ in the nickelates using Boltzmann transport theory. This demonstrates that the electronic structure obtained from first-principles calculations provides a reliable description of the fermiology of superconducting nickelates and suggests that, despite indications of strong electronic correlations, there are well-defined quasiparticles in the metallic state. Finally, we explain the differences in the Seebeck coefficient between nickelates and cuprates as originating in strong dissimilarities in impurity concentrations. Our study demonstrates that the high elastic scattering limit of the Seebeck coefficient reflects only the underlying band structure of a metal, analogous to the high magnetic field limit of the Hall coefficient. This opens a new avenue for Seebeck measurements to probe the electronic band structures of relatively disordered quantum materials.

Efficient coupling of optically active qubits to optical cavities is a key challenge for solid-state-based quantum optics experiments and future quantum technologies. Here we present a quantum photonic interface based on a single tin-vacancy center in a micrometer-thin diamond membrane coupled to a tunable open microcavity. We use the full tunability of the microcavity to selectively address individual tin-vacancy centers within the cavity mode volume. Purcell enhancement of the tin-vacancy center optical transition is evidenced both by optical excited state lifetime reduction and by optical linewidth broadening. As the emitter selectively reflects the single-photon component of the incident light, the coupled emitter-cavity system exhibits strong quantum nonlinear behavior. On resonance, we observe a transmission dip of 50% for low incident photon number per Purcell-reduced excited state lifetime, while the dip disappears as the emitter is saturated with higher photon number. Moreover, we demonstrate that the emitter strongly modifies the photon statistics of the transmitted light by observing photon bunching. This work establishes a versatile and tunable platform for advanced quantum optics experiments and proof-of-principle demonstrations on quantum networking with solid-state qubits.

During a quantum measurement, superpositions of states with different observable properties probabilistically collapse into one with a sharp value of the measured observable. In macroscopic quantum systems, this collapse arises via a continuous measurement-induced phase transition (MIPT) at a critical value of the strength of interaction with the measurement apparatus. MIPTs lie outside established paradigms for equilibrium or nonequilibrium critical phenomena and delineate distinct, stable dynamical and computational phases of matter. Quantum computers enable programmable simulation of the interaction of a measurement apparatus with a dynamical quantum system, to explore MIPT phenomena over a range of system sizes while retaining quantum coherence. Yet, existing experimental protocols rely on fundamentally nonscalable postselection techniques or direct classical simulation of quantum circuits. Here, we report the scalable observation of finite-size scaling evidence for an observable-sharpening MIPT in monitored quantum circuits in a chain of ${}^{171}{\mathrm{Yb}}^{+}$ ions in Quantinuum’s H1-1 trapped-ion quantum processor. By leveraging an equivalent description as a statistical physics problem, we implement scalable classical algorithms to infer the value of the measured observable from a single experimental shot. This technique enables a truly scalable protocol to observe observable-sharpening MIPTs in generic classes of circuits that cannot be directly classically simulated and also provides enhanced means to detect and suppress errors in the quantum simulation.

A surprising “planar” thermal Hall effect, whereby the field is parallel to the current, has recently been observed in a few magnetic insulators; this effect has been attributed to exotic excitations such as Majorana fermions or chiral magnons. Here, we investigate the possibility of a planar thermal Hall effect in three different cuprate materials, in which the conventional thermal Hall conductivity ${\kappa }_{\mathrm{xy}}$ (with an out-of-plane field perpendicular to the current) is dominated by either electrons or phonons. Our measurements show that the planar ${\kappa }_{\mathrm{xy}}$ from electrons in cuprates is zero, as expected from the absence of a Lorentz force in the planar configuration. By contrast, we observe a sizable planar ${\kappa }_{\mathrm{xy}}$ in those samples where the thermal Hall response is due to phonons, even though it should, in principle, be forbidden by the high crystal symmetry. Our findings call for a careful reexamination of the mechanisms responsible for the phonon thermal Hall effect in insulators.

We demonstrate that the absorption of femtosecond hard x-ray pulses excites quasispherical, high-amplitude, and high-wave-vector coherent acoustic phonon wave packets using an all hard-x-ray pump-probe scattering experiment. The time- and momentum-resolved diffuse scattering signal is consistent with an ensemble of 3D strain wave packets induced by the rapid electron cascade dynamics following photoionization at uncorrelated excitation centers. We quantify key parameters of this process, including the localization size of the stress field and the photon energy conversion efficiency into elastic energy. The parameters are determined by the photoelectron and Auger electron cascade dynamics, as well as the electron-phonon interaction. In particular, we obtain the localization size of the observed strain wave packet to be 1.5 and 2.5 nm for bulk ${\mathrm{SrTiO}}_3$ and ${\mathrm{KTaO}}_3$ single crystals, respectively. The results provide crucial information on the mechanism of x-ray energy deposition into matter and shed light on the shortest collective length scales accessible to coherent acoustic phonon generation using x-ray excitation.