We present a formalism for strongly correlated systems with fermions coupled to bosonic modes. We construct the three-particle irreducible functional $\mathcal{K}$ by successive Legendre transformations of the free energy of the system. We derive a closed set of equations for the fermionic and bosonic self-energies for a given $\mathcal{K}$. We then introduce a local approximation for $\mathcal{K}$, which extends the idea of dynamical mean-field theory (DMFT) approaches from two- to three-particle irreducibility. This approximation entails the locality of the three-leg electron-boson vertex $\mathrm{\Lambda }(i\omega ,i\mathrm{\Omega })$, which is self-consistently computed using a quantum impurity model with dynamical charge and spin interactions. This local vertex is used to construct frequency- and momentum-dependent electronic self-energies and polarizations. By construction, the method interpolates between the spin-fluctuation or $GW$ approximations at weak coupling and the atomic limit at strong coupling. We apply it to the Hubbard model on two-dimensional square and triangular lattices. We complement the results of [T. Ayral and O. Parcollet, Phys. Rev. B 92, 115109 (2015)] by (i) showing that, at half-filling, as DMFT, the method describes the Fermi-liquid metallic state and the Mott insulator, separated by a first-order interaction-driven Mott transition at low temperatures, (ii) investigating the influence of frustration, and (iii) discussing the influence of the bosonic decoupling channel.

We use time-of-flight (TOF) inelastic-neutron-scattering (INS) spectroscopy to investigate the doping dependence of magnetic excitations across the phase diagram of ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ with $x=0$, 0.0175, 0.0215, 0.05, and $0.11$. The effect of electron doping by partially substituting Fe by Co is to form resonances that couple with superconductivity, broaden, and suppress low-energy ($E\le 80$ meV) spin excitations compared with spin waves in undoped NaFeAs. However, high-energy ($E>80$ meV) spin excitations are weakly Co-doping-dependent. Integration of the local spin dynamic susceptibility ${\chi }^{\prime \prime }\left(\omega \right)$ of ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ reveals a total fluctuating moment of 3.6 ${\mu }_B^2$/Fe and a small but systematic reduction with electron doping. The presence of a large spin gap in Co-overdoped nonsuperconducting ${\mathrm{NaFe}}_{0.89}{\mathrm{Co}}_{0.11}\mathrm{As}$ suggests that Fermi surface nesting is responsible for low-energy spin excitations. These results parallel the Ni-doping evolution of spin excitations in ${\mathrm{BaFe}}_{2-x}{\mathrm{Ni}}_x{\mathrm{As}}_2$ in spite of the differences in crystal structures and Fermi surface evolution in these two families of iron pnictides, thus confirming the notion that low-energy spin excitations coupling with itinerant electrons are important for superconductivity, while weakly doping-dependent high-energy spin excitations result from localized moments.

The study of magnetic correlations in dipolar-coupled nanomagnet systems with synchrotron x-ray scattering provides a means to uncover emergent phenomena and exotic phases, in particular in systems with thermally active magnetic moments. From the diffuse signal of soft x-ray resonant magnetic scattering, we have measured magnetic correlations in a highly dynamic artificial kagome spin ice with sub-70-nm Permalloy nanomagnets. On comparing experimental scattering patterns with Monte Carlo simulations based on a needle-dipole model, we conclude that kagome ice I phase correlations exist in our experimental system even in the presence of moment fluctuations, which is analogous to bulk spin ice and spin liquid behavior. In addition, we describe the emergence of quasi-pinch-points in the magnetic diffuse scattering in the kagome ice I phase. These quasi-pinch-points bear similarities to the fully developed pinch points with singularities of a magnetic Coulomb phase, and continually evolve into the latter on lowering the temperature. The possibility to measure magnetic diffuse scattering with soft x rays opens the way to study magnetic correlations in a variety of nanomagnetic systems.

Ramsey interferometry provides a natural way to determine the coherence time of most qubit systems. Recent experiments on quantum dots, however, demonstrated that dynamical nuclear spin polarization can strongly influence the measurement process, making it difficult to extract the $T_2^{*}$ coherence time using standard optical Ramsey pulses. Here, we demonstrate an alternative method for spin coherence measurement that is based on first-order coherence of photons generated in spin-flip Raman scattering. We show that if a quantum emitter is driven by a weak monochromatic laser, Raman coherence is determined exclusively by spin coherence, allowing for a direct determination of spin $T_2^{*}$ time. When combined with coherence measurements on Rayleigh scattered photons, our technique enables us to identify coherent and incoherent contributions to resonance fluorescence, and to minimize the latter. We verify the validity of our technique by comparing our results to those determined from Ramsey interferometry for electron and heavy-hole spins.

The scattering cancellation technique is a powerful tool to reduce the scattered field from electrically small objects in a specific frequency window. The technique relies on covering the object of interest with a shell that scatters light into a far field of equal strength as the object but with a phase shift of $\pi$. The resulting destructive interference prohibits its detection in measurements that probe the scattered light. Whereas at radio or microwave frequencies feasible designs have been proposed that allow us to tune the operational frequency upon request, similar capabilities have not yet been explored in the visible. However, such an ability is necessary to capitalize on the technique in many envisioned applications. Here, we solve the problem and study the use of small metallic nanoparticles with an ellipsoidal shape as the material from which the shell is made to build an isotropic geometry. Changing the aspect ratio of the ellipsoids allows us to change the operational frequency. The basic functionality is explored with two complementary analytical approaches. Additionally, we present a powerful multiscattering algorithm that can be used to perform full-wave simulations of clusters of arbitrary particles. We utilize this method to analyze the scattering of the presented designs numerically. Herein we provide useful guidelines for the fabrication of this cloak with self-assembly methods by investigating the effects of disorder.

We explore the quantum phase transition between Peierls and charge-density-wave insulating states in the one-dimensional, half-filled, extended Hubbard model with explicit bond dimerization. We show that the critical line of the continuous Ising transition terminates at a tricritical point, belonging to the universality class of the tricritical Ising model with central charge $c=7/10$. Above this point, the quantum phase transition becomes first order. Employing a numerical matrix-product-state based (infinite) density-matrix renormalization group method we determine the ground-state phase diagram, the spin and two-particle charge excitations gaps, and the entanglement properties of the model with high precision. Performing a bosonization analysis we can derive a field description of the transition region in terms of a triple sine-Gordon model. This allows us to derive field theory predictions for the power-law (exponential) decay of the density-density (spin-spin) and bond-order-wave correlation functions, which are found to be in excellent agreement with our numerical results.

Metal-ferroelectric interfaces form the basis of novel electronic devices. A key effect determining the device functionality is the bias-dependent change of the electronic energy-level alignment at the interface. Here, hard x-ray photoelectron spectroscopy (HAXPES) is used to determine the energy-level alignment at two metal-ferroelectric interfaces—Au versus ${\mathrm{SrRuO}}_3$ on the relaxor ferroelectric $\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){}_{0.72}{\mathrm{Ti}}_{0.28}{\mathrm{O}}_3$ (PMN-PT)—directly in situ as a function of electrical bias. The bias-dependent average shifts of the PMN-PT core levels are found to have two dominant contributions on the $0.1$–1-eV energy scale: one depending on the metal electrode and the remanent electric polarization and the other correlated with electric-field-induced strain. Element-specific deviations from the average shifts are smaller than $0.1$ eV and appear to be related to predicted dynamical charge variations in PMN-PT. In addition, the efficiency of ferroelectric polarization switching is shown to be reduced near the coercive field under x-ray irradiation. The results establish HAXPES as a tool for the in operando investigation of metal-ferroelectric interfaces and suggest electric-field-induced modifications of the polarization distribution as a novel way to control the barrier height at such interfaces.

Angle-resolved photoemission spectroscopy (ARPES) is the most direct tool to measure the electronic structure of materials. In particular, fine features of the spectra can be analyzed for evaluating the electron self-energy. Owing to a setup allowing ARPES investigation with submicron resolution and state-of-the-art energy and momentum resolution, we show here first that ARPES spectra of pristine and virtually undoped monolayer graphene acquired on a small spot do not display manifestations of self-energy. We next demonstrate that, although the region of the sample investigated is a unique graphene domain, it displays faint spatial inhomogeneity, both in its crystallographic orientation and its thickness, which is undetectable with conventional ARPES but renders the spectra improper for self-energy extraction. These results indicate that care should be taken when analyzing ARPES spectra obtained with poor spatial resolution.

We discover a robust coexistence of superconductivity and ferromagnetism in an iron arsenide ${\mathrm{RbEuFe}}_4{\mathrm{As}}_4$. The new material crystallizes in an intergrowth structure of ${\mathrm{RbFe}}_2{\mathrm{As}}_2$ and ${\mathrm{EuFe}}_2{\mathrm{As}}_2$, such that the Eu sublattice turns out to be primitive instead of being body-centered in ${\mathrm{EuFe}}_2{\mathrm{As}}_2$. The FeAs layers, featured by asymmetric As coordinations, are hole doped due to charge homogenization. Our combined measurements of electrical transport, magnetization, and heat capacity unambiguously and consistently indicate bulk superconductivity at 36.5 K in the FeAs layers and ferromagnetism at 15 K in the Eu sublattice. Interestingly, the Eu-spin ferromagnetic ordering belongs to a rare third-order transition, according to the Ehrenfest classification of phase transitions. We also identify an additional anomaly at $\sim 5$ K, which is possibly associated with the interplay between superconductivity and ferromagnetism.

Magnetization measurements of ${\mathrm{LaCoO}}_3$ have been carried out up to 133 T, generated with a destructive pulse magnet at a wide temperature range from 2 to 120 K. A novel magnetic transition was found at $B>100$ T and $T>T^{*}=32\pm 5$ K, which is characterized by its transition field increasing with increasing temperature. At $T<T^{*}$, the previously reported transition at $B\sim 65$ T was observed. Based on the obtained $B\text{−}T$ phase diagram and the Clausius-Clapeyron relation, the entropy of the high-field phase at 80 K is found to be smaller for about $1.5$ J ${\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$ than that of the low-field phase. We suggest that the observed two high-field phases may originate in different spatial orders of the spin states and possibly other degrees of freedom such as orbitals. An inherent strong correlation of spin states among cobalt sites should have triggered the emergence of the ordered phases in ${\mathrm{LaCoO}}_3$ at high magnetic fields.

Probing the center-of-mass of an ultracold atomic cloud can be used to measure Chern numbers, the topological invariants underlying the quantum Hall effects. In this work, we show how such center-of-mass observables can have a much richer dependence on topological invariants than previously discussed. In fact, the response of the center of mass depends not only on the current density, typically measured in a solid-state system, but also on the particle density, which itself can be sensitive to the topology of the band structure. We apply a semiclassical approach, supported by numerical simulations, to highlight the key differences between center-of-mass responses and more standard conductivity measurements. We illustrate this by analyzing both the two- and four-dimensional quantum Hall effects. These results have important implications for experiments in engineered topological systems, such as ultracold gases and photonics.

The theory of flexoelectricity and that of nonlocal elasticity are closely related, and are often considered together when modeling strain-gradient effects in solids. Here I show, based on a first-principles lattice-dynamical analysis, that their relationship is much more intimate than previously thought, and their consistent simultaneous treatment is crucial for obtaining correct physical answers. In particular, I identify a gauge invariance in the theory, whereby the energies associated to strain-gradient elasticity and flexoelectrically induced electric fields are individually reference dependent, and only when summed up they yield a well-defined result. To illustrate this, I construct a minimal thermodynamic functional incorporating strain-gradient effects, and establish a formal link between the continuum description and ab initio phonon dispersion curves to calculate the relevant tensor quantities. As a practical demonstration, I apply such a formalism to bulk ${\mathrm{SrTiO}}_3$, where I find an unusually strong contribution of nonlocal elasticity, mediated by the interaction between the ferroelectric soft mode and the transverse acoustic branches. These results have important implications towards the construction of well-defined thermodynamic theories where flexoelectricity and ferroelectricity coexist. More generally, they open exciting new avenues for the implementation of hierarchical multiscale concepts in the first-principles simulation of crystalline insulators.

Detailed tunneling spectroscopy of vortex core states can provide important insight to the momentum structure of the superconducting order parameter. We present a theoretical study of vortex bound states in iron-based superconductors by use of a realistic five-band model relevant to these systems, and superconductivity stabilized by spin-fluctuation-generated pairing vertices yielding an $s\pm$ gap structure. The computed local density of states agrees remarkably well with both the bias dependence of the local conductance and the spatial structure of the low-bias conductance as obtained by scanning tunneling microscopy measurements on LiFeAs [T. Hanaguri et al., Phys. Rev. B 85, 214505 (2012)].

We have carried out an investigation on the magnetoelectric properties of the presumed multiferroic ${\mathrm{Y}}_2\mathrm{CoMn}{\mathrm{O}}_6$ with different degrees of Co/Mn atomic ordering. The magnetic ground state was studied by neutron diffraction, showing a collinear ferromagnetic (FM) ordering of Co and Mn moments with a small antiferromagnetic canting. No superstructure peaks from an E-type magnetic structure were detected in our measurements. Magnetic measurements reveal FM transitions with pinned magnetic domains. The degree of Co/Mn ordering affects the Curie temperature only a little, but has strong effects on the magnetic hysteresis loops, and the FM moment signal at high field increases with increasing such order. The loops display steps at critical fields whose number and extent depends on each specimen. The most ordered sample exhibits the greatest steps ascribed to the alignment of magnetic domains separated by antiphase boundaries. All samples are insulators exhibiting low dielectric loss and dielectric constants at low temperature. On warming, they show a step increase in the real dielectric permittivity accompanied by peaks in the dielectric loss typical of thermally activated hopping processes. At room temperature, the huge values of the dielectric constant reveal the presence of Maxwell-Wagner depletion layers. Pyroelectric measurements reveal a high polarization at low temperature for these compounds that increases with increasing the Co/Mn ordering. There is no correlation between the magnetic transition and the onset of pyroelectric current. No significant changes are observed in the pyroelectric effect measured under an external magnetic field, so magnetoelectric coupling is negligible. This paper identifies the pyroelectric current as thermally stimulated depolarization current ascribed to the reorientation of defect dipoles with activation energy of about 0.05 eV. Therefore, no ferroelectric transition occurs in these compounds, discarding the existence of intrinsic magnetoelectric multiferroicity.

In this paper we demonstrate a versatile concept for a planar cavity polariton beam amplifier using nonresonant excitation. In contrast to resonant excitation schemes, background carriers are injected which form excitons, providing both gain and a repulsive potential for a polariton condensate. Using an attractive potential environment induced by a locally elongated cavity layer, the repulsive potential of the injected background carriers is compensated, and a significant amplification of polariton beams is achieved without beam distortion.

The parquet decomposition of the self-energy into classes of diagrams, those associated with specific scattering processes, can be exploited for different scopes. In this work, the parquet decomposition is used to unravel the underlying physics of nonperturbative numerical calculations. We show the specific example of dynamical mean field theory and its cluster extensions [dynamical cluster approximation (DCA)] applied to the Hubbard model at half-filling and with hole doping: These techniques allow for a simultaneous determination of two-particle vertex functions and self-energies and, hence, for an essentially “exact” parquet decomposition at the single-site or at the cluster level. Our calculations show that the self-energies in the underdoped regime are dominated by spin-scattering processes, consistent with the conclusions obtained by means of the fluctuation diagnostics approach [O. Gunnarsson et al., Phys. Rev. Lett. 114, 236402 (2015)]. However, differently from the latter approach, the parquet procedure displays important changes with increasing interaction: Even for relatively moderate couplings, well before the Mott transition, singularities appear in different terms, with the notable exception of the predominant spin channel. We explain precisely how these singularities, which partly limit the utility of the parquet decomposition and, more generally, of parquet-based algorithms, are never found in the fluctuation diagnostics procedure. Finally, by a more refined analysis, we link the occurrence of the parquet singularities in our calculations to a progressive suppression of charge fluctuations and the formation of a resonance valence bond state, which are typical hallmarks of a pseudogap state in DCA.

We study the many-body localization aspects of single-particle mobility edges in fermionic systems. We investigate incommensurate lattices and random disorder Anderson models. Many-body localization and quantum nonergodic properties are studied by comparing entanglement and thermal entropy, and by calculating the scaling of subsystem particle-number fluctuations, respectively. We establish a nonergodic extended phase as a generic intermediate phase (between purely ergodic extended and nonergodic localized phases) for the many-body localization transition of noninteracting fermions where the entanglement entropy manifests a volume law (hence, “extended”), but there are large fluctuations in the subsystem particle numbers (hence, “nonergodic”). Based on the numerical results, we expect such an intermediate phase scenario may continue to hold even for the many-body localization in the presence of interactions as well. We find for many-body fermionic states in noninteracting one-dimensional Aubry-André and three-dimensional Anderson models that the entanglement entropy density and the normalized particle-number fluctuation have discontinuous jumps at the localization transition where the entanglement entropy is subthermal but obeys the “volume law.” In the vicinity of the localization transition, we find that both the entanglement entropy and the particle-number fluctuations obey a single parameter scaling based on the diverging localization length. We argue using numerical and theoretical results that such a critical scaling behavior should persist for the interacting many-body localization problem with important observable consequences. Our work provides persuasive evidence in favor of there being two transitions in many-body systems with single-particle mobility edges, the first one indicating a transition from the purely localized nonergodic many-body localized phase to a nonergodic extended many-body metallic phase, and the second one being a transition eventually to the usual ergodic many-body extended phase.

Topological band structures in electronic systems like topological insulators and semimetals give rise to highly unusual physical properties. Analogous topological effects have also been discussed in bosonic systems, but the novel phenomena typically occur only when the system is excited by finite-frequency probes. A mapping recently proposed by C. L. Kane and T. C. Lubensky [Nat. Phys. 10, 39 (2014)], however, establishes a closer correspondence. It relates the zero-frequency excitations of mechanical systems to topological zero modes of fermions that appear at the edges of an otherwise gapped system. Here we generalize the mapping to systems with an intrinsically gapless bulk. In particular, we construct mechanical counterparts of topological semimetals. The resulting gapless bulk modes are physically distinct from the usual acoustic Goldstone phonons and appear even in the absence of continuous translation invariance. Moreover, the zero-frequency phonon modes feature adjustable momenta and are topologically protected as long as the lattice coordination is unchanged. Such protected soft modes with tunable wave vector may be useful in designing mechanical structures with fault-tolerant properties.

The recent observation of a transmitted THz pulse oscillating at three times the frequency of the incident light paves the way to a powerful protocol to access resonant excitations in a superconductor. Here we show that this nonlinear optical process is dominated by light-induced excitation of Cooper pairs, while the collective amplitude (Higgs) fluctuations of the superconducting order parameter give in general a negligible contribution. We also predict a nontrivial dependence of the signal on the direction of the light polarization with respect to the lattice symmetry, which can be tested in systems such as, e.g., cuprate superconductors.

Defect-assisted recombination is an important limitation on efficiency of optoelectronic devices. However, since nonradiative capture rates decrease exponentially with the energy of the transition, the mechanisms by which such recombination can take place in wide-band-gap materials are unclear. Using electronic structure calculations we uncover the crucial role of electronic excited states in nonradiative recombination processes. The impact is elucidated with examples for the group-III nitrides, for which accumulating experimental evidence indicates that defect-assisted recombination limits efficiency. Our work provides insights into the physics of nonradiative recombination, and the mechanisms are suggested to be ubiquitous in wide-band-gap semiconductors.