We present a comprehensive study of ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$ using bulk sensitive hard and soft x-ray spectroscopy combined with local-density $\text{approximation}+\text{dynamical}$ mean-field theory (DMFT) calculations. Correlation effects on both the Cu and Ru ions can be observed. From the Cu $2p$ core-level spectra, we deduce the presence of magnetic ${\mathrm{Cu}}^{2+}$ ions hybridized with a reservoir of itinerant electrons. The strong photon energy dependence of the valence band allows us to disentangle the Ru, Cu, and O contributions and, thus, to optimize the DMFT calculations. The calculated spin and charge susceptibilities show that the transition metal oxide ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$ must be classified as a Kondo system and that the Kondo temperature is in the range of 500–1000 K.

The pairing of interacting fermions leading to superfluidity has two limiting regimes: the Bardeen-Cooper-Schrieffer (BCS) scheme for weakly interacting degenerate fermions and the Bose-Einstein condensation (BEC) of bosonic pairs of strongly interacting fermions. While the superconductivity that emerges in most metallic systems is the BCS-like electron pairing, strongly correlated electrons with poor Fermi liquidity can condense into the unconventional BEC-like pairs. Quantum spin liquids harbor extraordinary spin correlation free from order, and the superconductivity that possibly emerges by carrier doping of the spin liquids is expected to have a peculiar pairing nature. The present study experimentally explores the nature of the pairing condensate in a doped spin liquid candidate material and under varying pressure, which changes the electron-electron Coulombic interactions across the Mott critical value in the system. The transport measurements reveal that the superconductivity at low pressures is a BEC-like condensate from a non-Fermi liquid and crosses over to a BCS-like condensate from a Fermi liquid at high pressures. The Nernst-effect measurements distinctively illustrate the two regimes of the pairing in terms of its robustness to the magnetic field. The present Mott tuning of the BEC-BCS crossover can be compared to the Feshbach tuning of the BEC-BCS crossover of fermionic cold atoms.

Measuring the specific heat of herbertsmithite single crystals in high magnetic fields (up to 34 T) allows us to isolate the low-temperature kagome contribution while shifting away extrinsic Schottky-like contributions. The kagome contribution follows an original power law $C_p(T\to 0)\propto T^{\alpha }$ with $\alpha \sim 1.5$ and is found to be field independent between 28 and 34 T for temperatures $1\le T\le 4\mathrm{K}$. These are serious constraints when it comes to replication using low-temperature extrapolations of high-temperature series expansions. We manage to reproduce the experimental observations if about 10% of the kagome sites do not contribute. Between 0 and 34 T, the computed specific heat then has a minute field dependence supporting an algebraic temperature dependence in zero field, typical of a critical spin-liquid ground state. The need for an effective dilution of the kagome planes is discussed and is likely linked to the presence of copper ions on the interplane zinc sites. At very low temperatures and moderate fields, we also report some small field-induced anomalies in the total specific heat and start to elaborate on a phase diagram.

Ultrafast lasers are an increasingly important tool to control and stabilize emergent phases in quantum materials. Among a variety of possible excitation protocols, a particularly intriguing route is the direct light engineering of microscopic electronic parameters, such as the electron hopping and the local Coulomb repulsion (Hubbard $U$). In this work, we use time-resolved x-ray absorption spectroscopy to demonstrate the light-induced renormalization of the Hubbard $U$ in a cuprate superconductor, ${\mathrm{La}}_{1.905}{\mathrm{Ba}}_{0.095}{\mathrm{CuO}}_4$. We show that intense femtosecond laser pulses induce a substantial redshift of the upper Hubbard band while leaving the Zhang-Rice singlet energy unaffected. By comparing the experimental data to time-dependent spectra of single- and three-band Hubbard models, we assign this effect to an approximately 140-meV reduction of the on-site Coulomb repulsion on the copper sites. Our demonstration of a dynamical Hubbard $U$ renormalization in a copper oxide paves the way to a novel strategy for the manipulation of superconductivity and magnetism as well as to the realization of other long-range-ordered phases in light-driven quantum materials.

The interactions of the excited states of a single chromophore with static and dynamic electric fields spatially varying at the atomic scale are investigated in a joint experimental and theoretical effort. In this configuration, the spatial extension of the fields confined at the apex of a scanning tunneling microscope tip is smaller than that of the molecular exciton, a property used to generate fluorescence maps of the chromophore with intramolecular resolution. Theoretical simulations of the electrostatic and electrodynamic interactions occurring at the picocavity junction formed by the chromophore, the tip, and the substrate reveal the key role played by subtle variations of Purcell, Lamb, and Stark effects. They also demonstrate that hyper-resolved fluorescence maps of the line shift and linewidth of the excitonic emission can be understood as images of the static charge redistribution upon electronic excitation of the molecule and as the distribution of the dynamical charge oscillation associated with the molecular exciton, respectively.

Deterministic photon-photon gates enable the controlled generation of entanglement between mobile carriers of quantum information. Such gates have thus far been exclusively realized in the optical domain and by relying on postselection. Here, we present a nonpostselected, deterministic, photon-photon gate in the microwave frequency range realized using superconducting circuits. We emit photonic qubits from a source chip and route those qubits to a gate chip with which we realize a universal gate set by combining controlled absorption and reemission with single-qubit gates and qubit-photon controlled-phase gates. We measure quantum process fidelities of 75% for single- and of 57% for two-qubit gates, limited mainly by radiation loss and decoherence. This universal gate set has a wide range of potential applications in superconducting quantum networks.

Kagome metals $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, Rb, and Cs) exhibit a unique superconducting ground state coexisting with charge-density wave (CDW), whereas how these characteristics are affected by carrier doping remains unexplored because of the lack of an efficient carrier-doping method. Here we report successful electron doping to ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ by Cs dosing, as visualized by angle-resolved photoemission spectroscopy. We found that the electron doping with Cs dosing proceeds in an orbital-selective way, as characterized by a marked increase in electron filling of the Sb $5p_z$ and V $3d_{xz/yz}$ bands as opposed to the relatively insensitive nature of the V $3d_{xy/x^2-y^2}$ bands. By monitoring the temperature evolution of the CDW gap around the $\overline{M}$ point, we found that the CDW can be completely killed by Cs dosing while keeping the saddle point with the V $3d_{xy/x^2-y^2}$ character almost pinned at the Fermi level. The present result suggests a crucial role of multiorbital effect to the occurrence of CDW and provides an important step toward manipulating the CDW and superconductivity in $A{\mathrm{V}}_3{\mathrm{Sb}}_5$.

Recent developments in higherorder topological phases have revealed the relationship between nontrivial multipole moments in the bulk and the emergence of fractionally quantized charges at the boundary. Here, we put forth a proposal of the three-dimensional octupole insulator with fractionally quantized corner charges $\pm e/8$: sodium chloride, commonly known as table salt. The fractional quantization of the corner charge is unaffected by the quantum fluctuation of the electric charge per ion, as we demonstrate explicitly with ab initio calculations. We further show that the electrostatic signature of the fractional charge is well preserved even when the ideal crystal is sprinkled with defects, and provide a systematic analysis on how the corner charge contribution could be isolated from the electric-field corrections originating from realistic surface relaxation. Our results suggest that the observation of corner charges from quantized multipole moments in solids might be imminent.

We study magic angle graphene in the presence of both strain and particle-hole symmetry breaking due to nonlocal interlayer tunneling. We perform a self-consistent Hartree-Fock study that incorporates these effects alongside realistic interaction and substrate potentials and explore a comprehensive set of competing orders including those that break translational symmetry at arbitrary wave vectors. We find that at all nonzero integer fillings very small strains, comparable to those measured in scanning tunneling experiments, stabilize a fundamentally new type of time-reversal-symmetric and spatially nonuniform order. This order, which we dub the “incommensurate Kekulé spiral” (IKS) order, spontaneously breaks both the emergent valley-charge conservation and moiré translation symmetries but preserves a modified translation symmetry ${\widehat{T}}^{\prime }$—which simultaneously shifts the spatial coordinates and rotates the $U(1)$ angle which characterizes the spontaneous intervalley coherence. We discuss the phenomenological and microscopic properties of this order. We argue that our findings are consistent with all experimental observations reported so far, suggesting a unified explanation of the global phase diagram in terms of the IKS order.

Detection of the energy conversion pathways between photons, charge carriers, and the lattice is of fundamental importance to understand fundamental physics and to advance materials and devices. Yet, such insight remains incomplete due to experimental challenges in disentangling the various signatures on overlapping timescales. Here, we show that attosecond core-level x-ray absorption fine-structure spectroscopy (XANES) meets this challenge by providing an unambiguous and simultaneous view on the temporal evolution of the photon-carrier-phonon system. We provide surprising new results by applying the method to graphite, a seemingly well-studied system whose investigation is complicated by a variety of mechanisms occurring across a wide range of temporal scales. The simultaneous real-time measurement of electrons and holes reveals disparate scattering mechanisms for infrared excitation close to the Fermi energy. We find that ultrafast dephasing of the coherent carrier dynamics is governed by impact excitation (IE) for electrons, while holes exhibit a switchover from impact excitation to Auger heating (AH) already during the 11-fs duration of the infrared light field. We attribute this switchover to the limited scattering phase space in the $n$-doped material. We further elucidate the excitation mechanisms of strongly coupled optical phonons (SCOPs). The coherent excitation of both SCOPs is nondisplacive and is explained by the strong electron-phonon scattering, i.e., via a seemingly incoherent process. We identify the $A_1^{\prime }$ phonon as the dominating channel for dissipation of electronic coherence. Moreover, unobserved in graphite, we find high-frequency oscillations up to 90 THz, which arise from the modulation of the electronic density of states by the atomic displacements along the $E_{2g}$ and $A_1^{\prime }$ modes. These measurements establish the utility of core-level XANES with attosecond temporal resolution to achieve an unambiguous and simultaneous view on the temporal evolution of the photon-carrier-phonon system with surprising new results even for a seemingly well-studied system like graphite. While the graphite measurement was conducted around the $K$ edge of carbon, adapting the methodology to other materials only requires spectra coverage of the respective elemental edge of the material’s constituent. This flexibility makes our methodology widely applicable to detect and distinguish the various dynamic contributions to the flow of energy inside materials on their native timescales.

We introduce topological invariants for gapless systems and study the associated boundary phenomena. More generally, the symmetry properties of the low-energy conformal field theory (CFT) provide discrete invariants establishing the notion of symmetry-enriched quantum criticality. The charges of nonlocal scaling operators, or more generally, of symmetry defects, are topological and imply the presence of localized edge modes. We primarily focus on the $1+1d$ case where the edge has a topological degeneracy, whose finite-size splitting can be exponential or algebraic in system size depending on the involvement of additional gapped sectors. An example of the exponential case is given by tuning the spin-1 Heisenberg chain to a symmetry-breaking Ising phase. An example of the algebraic case arises between the gapped Ising and cluster phases: This symmetry-enriched Ising CFT has an edge mode with finite-size splitting scaling as $1/L^{14}$. In addition to such new cases, our formalism unifies various examples previously studied in the literature. Similar to gapped symmetry-protected topological phases, a given CFT can split into several distinct symmetry-enriched CFTs. This raises the question of classification, to which we give a partial answer—including a complete characterization of symmetry-enriched $1+1d$ Ising CFTs. Nontrivial topological invariants can also be constructed in higher dimensions, which we illustrate for a symmetry-enriched $2+1d$ CFT without gapped sectors.

In Heisenberg models with exchange anisotropy, transverse spin components are not conserved and can decay not only by transport, but also by dephasing. Here, we utilize ultracold atoms to simulate the dynamics of 1D Heisenberg spin chains and observe fast, local spin decay controlled by the anisotropy. However, even for isotropic interactions, we observe dephasing due to a new effect: an effective magnetic field created by superexchange. If spatially uniform, it leads only to uniform spin precession and is, therefore, typically ignored. However, we show through experimental studies and extensive numerical simulations how this superexchange-generated field is relevant and leads to additional dephasing mechanisms over the exchange anisotropy: There is dephasing due to (i) inhomogeneity of the effective field from variations of lattice depth between chains; (ii) a twofold reduction of the field at the edges of finite chains; and (iii) fluctuations of the effective field due to the presence of mobile holes in the system. The latter is a new coupling mechanism between holes and magnons. All these dephasing mechanisms have not been observed before with ultracold atoms and illustrate basic properties of the underlying Hubbard model.

Thanks to the nearsightedness principle, the low-energy electronic structure of solids can be represented by localized states such as the Wannier functions. Wannier functions are actively being applied to a wide range of phenomena in condensed matter systems. However, the Wannier-function-based representation is limited to a small number of bands and thus cannot describe the change of wave functions due to various kinds of perturbations, which require sums over an infinite number of bands. Here, we introduce the concept of the Wannier function perturbation, which provides a localized representation of wave function perturbations. Wannier function perturbation theory allows efficient calculation of numerous quantities involving wave function perturbation, among which we provide three applications. First, we calculate the temperature-dependent indirect optical absorption spectra of silicon near the absorption edge nonadiabatically, i.e., differentiating phonon-absorption and phonon-emission processes, and without arbitrary temperature-dependent shifts in energy. Second, we establish a theory to calculate the shift spin conductivity without any band-truncation error. Unlike the shift charge conductivity, an exact calculation of the shift spin conductivity is not possible within the conventional Wannier function methods because it cannot be obtained from geometric quantities for low-energy bands. We apply the theory to monolayer ${\mathrm{WTe}}_2$. Third, we calculate the spin Hall conductivity of the same material again without any band-truncation error. Wannier function perturbation theory is a versatile method that can be readily applied to calculate a wide range of quantities related to various kinds of perturbations.

Interactions between electrons and lattice vibrations are responsible for a wide range of material properties and applications. Recently, there has been considerable interest in the development of resonant inelastic x-ray scattering (RIXS) as a tool for measuring electron-phonon ($e$-ph) interactions. Here, we demonstrate the ability of RIXS to probe the interaction between phonons and specific electronic states both near to, and away from, the Fermi level. We perform carbon $K$-edge RIXS measurements on graphite, tuning the incident x-ray energy to separately probe the interactions of the ${\pi }^{*}$ and ${\sigma }^{*}$ electronic states. Our high-resolution data reveal detailed structure in the multiphonon RIXS features that directly encodes the momentum dependence of the $e$-ph interaction strength. We develop a Green’s-function method to model this structure, which naturally accounts for the phonon and interaction-strength dispersions, as well as the mixing of phonon momenta in the intermediate state. This model shows that the differences between the spectra can be fully explained by contrasting trends of the $e$-ph interaction through the Brillouin zone, being concentrated at the $\mathrm{\Gamma }$ and $K$ points for the ${\pi }^{*}$ states while being significant at all momenta for the ${\sigma }^{*}$ states. Our results advance the interpretation of phonon excitations in RIXS and extend its applicability as a probe of $e$-ph interactions to a new range of out-of-equilibrium situations.

In this paper, we characterize quasicrystalline interacting topological phases of matter, i.e., phases protected by some quasicrystalline structure. We show that the elasticity theory of quasicrystals, which accounts for both “phonon” and “phason” modes, admits nontrivial quantized topological terms with far richer structure than their crystalline counterparts. We show that these terms correspond to distinct phases of matter and also uncover intrinsically quasicrystalline phases, which have no crystalline analogs. For quasicrystals with internal U(1) symmetry, we discuss a number of interpretations and physical implications of the topological terms, including constraints on the mobility of dislocations in $d=2$ quasicrystals and a quasicrystalline generalization of the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem. We then extend these ideas much further and address the complete classification of quasicrystalline topological phases, including systems with point-group symmetry as well as noninvertible phases. We hence obtain the “quasicrystalline equivalence principle,” which generalizes the classification of crystalline topological phases to the quasicrystalline setting.

In superconductors, electrons with spin $s=1/2$ form Cooper pairs whose spin structure is usually singlet ($S=0$) or triplet ($S=1$). When the electronic structure near the Fermi level is characterized by fermions with angular momentum $j=3/2$ due to strong spin-orbit interactions, novel pairing states such as even-parity quintet ($J=2$) and odd-parity septet ($J=3$) states are allowed. Prime candidates for such exotic states are half-Heusler superconductors, which exhibit unconventional superconducting properties, but their pairing nature remains unsettled. Here, we show that the superconductivity in the noncentrosymmetric half-Heusler LuPdBi can be consistently described by the admixture of isotropic even-parity singlet and anisotropic odd-parity septet pairing, whose ratio can be tuned by electron irradiation. From magnetotransport and penetration depth measurements, we find that carrier concentrations and impurity scattering both increase with irradiation, resulting in a nonmonotonic change of the superconducting gap structure. Our findings shed new light on our fundamental understanding of unconventional superconducting states in topological materials.

Exposing a many-body system to external drives and losses can transform the nature of its phases and opens perspectives for engineering new properties of matter. How such characteristics are related to the underlying microscopic processes of the driven and dissipative system is a fundamental question. Here, we address this point in a quantum gas that is strongly coupled to a lossy optical cavity mode using two independent Raman drives, which act on the spin and motional degrees of freedom of the atoms. This setting allows us to control the competition between coherent dynamics and dissipation by adjusting the imbalance between the drives. For strong enough coupling, the transition to a superradiant phase occurs, as is the case for a closed system. Yet, by imbalancing the drives, we can enter a dissipation-stabilized normal phase and a region of multistability. Measuring the properties of excitations on top of the out-of-equilibrium phases reveals the microscopic elementary processes in the open system. Our findings provide prospects for studying squeezing in non-Hermitian systems, quantum jumps in superradiance, and dynamical spin-orbit coupling in a dissipative setting.

Quantum phase transitions play an important role in shaping the phase diagram of high-temperature cuprate superconductors. These cuprates possess intertwined orders which interact strongly with superconductivity. However, the evidence for the quantum critical point associated with the charge order in the superconducting phase remains elusive. Here, we reveal the short-range charge orders and the spectral signature of the quantum fluctuations in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (LSCO) near the optimal doping using high-resolution resonant inelastic x-ray scattering. On performing calculations through a diagrammatic framework, we discover that the charge correlations significantly soften several branches of phonons. These results elucidate the role of charge order in the LSCO compound, providing evidence for quantum critical scaling and discommensurations associated with charge order.

Evidence for the quantum spin Hall effect (QSHE) has been reported in several experimental systems, in the form of edge conductance approaching a quantized value at zero magnetic field. However, another fundamental feature of the QSHE, that of spin-momentum locking in the edge channel, has not been demonstrated. Here, we report that in an applied magnetic field the edge conductance in monolayer ${\mathrm{WTe}}_2$, a candidate QSHE material, is suppressed by the component of the field perpendicular to a particular axis, implying that the spin in the edge states lies along this axis. Surprisingly, the axis is independent of edge orientation, chemical potential, and sample, being fixed relative to the monolayer crystal structure, lying at $(40\pm 2)°$ to the layer normal within the mirror plane. This finding is consistent with a theoretical model in which the bulk bands nearest the Fermi energy have the same parity, leading to simple spin texture with a single, momentum-independent spin axis that is inherited by the edge modes. In addition, the results strengthen the case for spin-momentum locking and, therefore, that monolayer ${\mathrm{WTe}}_2$ is a natural two-dimensional topological insulator exhibiting the QSHE.

The recently discovered family of $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A$: K, Rb Cs) kagome metals possess a unique combination of nontrivial band topology, superconducting ground states, and signatures of electron correlations manifest via competing charge density wave order. Little is understood regarding the nature of the charge density wave (CDW) instability inherent to these compounds and the potential correlation with the onset of a large anomalous Hall response. To understand the impact of the CDW order on the electronic structure in these systems, we present quantum oscillation measurements on single crystals of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$. Our data provide direct evidence that the CDW invokes a substantial reconstruction of the Fermi surface pockets associated with the vanadium orbitals and the kagome lattice framework. In conjunction with density functional theory modeling, we are able to identify split oscillation frequencies originating from reconstructed pockets built from vanadium orbitals and Dirac-like bands. Complementary diffraction measurements are further able to demonstrate that the CDW instability has a correlated phasing of distortions between neighboring ${\mathrm{V}}_3{\mathrm{Sb}}_5$ planes, and the average structure in the CDW state is proposed. These results provide critical insights into the underlying CDW instability in $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ kagome metals and support minimal models of CDW order arising from within the vanadium-based kagome lattice.