The functional renormalization group has become a widely used tool for the analysis of the leading low-temperature correlations in weakly to moderately coupled many-fermion lattice systems. A bottleneck for quantitatively more precise results is that the treatment of the frequency dependence of the flowing interactions is numerically quite demanding. Yet the frequency dependence is needed to compute relevant self-energies and hence for controlled results on the energy scales for ordering or for the quasiparticle properties. Here we explore an approximate parametrization of the frequency dependence of the interaction vertex that is inspired by established simplifications in the theory of superconductivity and that keeps the numerical effort bounded. We demonstrate the validity of the approximation for Cooper pairing problems and apply it to the two-dimensional Hubbard model.

We present thermal expansion and magnetostriction measurements on a ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ single crystal of A/S type up to 17.9 T magnetic field applied along the crystallographic $a$ direction $\left(\mathrm{\Delta }L\parallel a\parallel H\right)$ and down to 0.015 K temperature. We identify clear thermodynamic anomalies at the superconducting transition $T_c$ and at two second-order transitions $T_{A,B}$ into ordered phases A and B. Our measurements establish the boundary of phase B at high field and low temperature. No evidence for additional high-field phases above B is found up to the maximum field. We speculate based on our experimental results that (i) phase B is similar to phase A of spin-density wave type and (ii) the first-order phase transition between A and B is caused by Fermi-surface reconstruction. We furthermore identify a quantum critical point at $H_c\simeq 17$ T, where $T_B$ is suppresssed to zero, and a bicritical point at (0.35 K, 7.0 T), where phase lines $T_{\text{A}}\left(H\right)$ and $T_{\text{B}}\left(H\right)$ meet.

The concept of a vestigial nematic order emerging from a “mother” spin or charge-density-wave state has been applied to describe the phase diagrams of several systems, including unconventional superconductors. In a perfectly clean system, the two orders appear simultaneously via a first-order quantum phase transition, implying the absence of quantum criticality. Here, we investigate how this behavior is affected by impurity-free droplets that are naturally present in inhomogeneous systems. Due to their quantum dynamics, finite-size droplets sustain long-range nematic order but not long-range density-wave order. Interestingly, rare droplets with moderately large sizes undergo a second-order nematic transition even before the first-order quantum transition of the clean system. This gives rise to an extended regime of inhomogeneous nematic order, which is followed by a density-wave quantum Griffiths phase. As a result, a smeared quantum nematic transition, separated from the density-wave quantum transition, emerges in moderately disordered systems.

The nuclear spin bath (NSB) dynamics and its quantum control are of importance for the storage and processing of quantum information within a semiconductor environment. In the presence of a carrier spin, primarily it is the hyperfine interaction that rules the high frequency NSB characteristics. Here, we first study the overall coherence decay and rephasings in a hyperfine-driven NSB through the temporal and spectral behaviors of the so-called Loschmidt echo (LE). Its dependence on the NSB size, initial polarization, and coupling inhomogeneity are separately investigated, which leads to a simple phenomenological expression that can accommodate all of these attributes. Unlike the prevailing emphasis on spin 1/2, the NSBs with larger spin quantum numbers are equally considered. For this case, additionally the effect of nuclear electric quadrupole interaction is taken into account where its biaxiality term is influential on the decoherence. The insights gained from model systems are then put to use for two generic realistic semiconductor systems, namely, a donor center and a quantum dot that represent small and large nanoscale NSB examples, respectively. The spectrum of LE for large quantum dots can reach the 100 MHz range, whereas, for donor centers, it reduces to a few MHz, making them readily amenable for dynamical decoupling techniques. The effect of quadrupole interaction on LE is seen to be negligible for large quantum dots, while it becomes significant for donor centers, most notably in the form of depolarizing a polarized NSB.

We present a spectroscopic technique for second harmonic generation (SHG) using femtosecond laser pulses at a 30-kHz repetition rate, which nevertheless provides high spectral resolution limited only by the spectrometer. The potential of this method is demonstrated by applying it to the yellow exciton series of ${\mathrm{Cu}}_2\mathrm{O}$. Besides even parity states with $S$ and $D$ envelopes, we also observe odd parity $P$ excitons with linewidths down to 100 $\mu \mathrm{eV}$, despite the broad excitation laser spectrum with a full width at half maximum of 14 meV. The underlying light-matter interaction mechanisms of SHG are elaborated by a group theoretical analysis which allows us to determine the linear and circular polarization dependencies, in good agreement with experiment.

There has been increasing interest in electronic ferroelectricity, which stems from deformation of the electronic wave function coupled with lattice symmetry breaking, invoking a Berry-phase description of electronic polarization beyond the conventional notion of ionic displacement. How does a ferroelectric transition of an electronic nature cross over to a conventional one of an ionic nature? This is a fundamental issue of ferroelectricity that has yet to be answered. Here, investigating a quasi-one-dimensional organic ferroelectric material, TTF-${\mathrm{QCl}}_4$, under pressures of up to 35 kbar, we reveal a pressure-temperature phase diagram that spans the electronic and ionic regimes of ferroelectric transitions in a single material. The global phase diagram revealed by nuclear quadrupole resonance experiments demonstrates that electronic ferroelectricity crosses over to conventional ionic ferroelectricity through the separation of charge-transfer instability and lattice symmetry breaking (dimerization), and that the previously reported dimer liquid phase is largely extended to high pressures.

We report first-principles calculations of electronic and mechanical properties of few-layer borophene with the inclusion of interlayer van der Waals (vdW) interaction. The anisotropic metallic behaviors are preserved from monolayer to few-layer structures. The energy splitting of bilayer borophene at $\mathrm{\Gamma }$ point near the Fermi level is about 1.7 eV, much larger than the values (0.5–1 eV) of other layered semiconductors, indicating much stronger vdW interactions in metallic layered borophene. In particular, the critical strains are enhanced by increasing the number of layers, leading to much more flexibility than that of monolayer structure. On the one hand, because of the buckled atomic structures, the out-of-plane negative Poisson's ratios are preserved as the layer number increases. On the other hand, we find that the in-plane negative Poisson's ratios disappear in layered borophene, which is very different from puckered black phosphorus. The negative Poisson's ratio will recover if we enlarge the interlayer distance to 6.3 Å. The physical origin behind the change of Poisson's ratios is the strong interlayer vdW interaction in layered borophene.

The excitation of four coherent phonon modes of different symmetries is realized in copper metaborate ${\mathrm{CuB}}_2{\mathrm{O}}_4$ via impulsive stimulated Raman scattering (ISRS). The phonons are detected by monitoring changes in the linear optical birefringence using the polarimetric detection (PD) technique. We compare the results of the ISRS-PD experiment to the polarized spontaneous Raman scattering spectra. We show that agreement between the two sets of data obtained by these allied techniques in a wide phonon frequency range of 4–14 THz can be achieved by taking into account the symmetry of the phonon modes and corresponding excitation and detection selection rules. It is also important to account for the difference between incoherent and coherent phonons in terms of their contributions to the Raman scattering process. This comparative analysis highlights the importance of the ratio between the frequency of a particular mode, and the pump and probe spectral widths. We analytically demonstrate that the pump and probe pulse durations of 90 and 50 fs, respectively, used in our experiments limit the highest frequency of the excited and detected coherent phonon modes to 12 THz, and define their relative amplitudes.

We present a quantitative investigation of magnetic domain-wall pinning in thin magnets with perpendicular anisotropy. A self-consistent description exploiting the universal features of the depinning and thermally activated subthreshold creep regimes observed in the field-driven domain-wall velocity is used to determine the effective pinning parameters controlling the domain-wall dynamics: The effective height of pinning barriers, the depinning threshold, and the velocity at depinning. Within this framework, the analysis of results published in the literature allows for a quantitative comparison of pinning properties for a set of magnetic materials in a wide temperature range. On the basis of scaling arguments, the microscopic parameters controlling the pinning: The correlation length of pinning, the collectively pinned domain-wall length (Larkin length), and the strength of pinning disorder are estimated from the effective pinning and the micromagnetic parameters. The analysis of thermal effects reveals a crossover between different pinning length scales and strengths at low reduced temperatures.

Local observables in generic periodically driven closed quantum systems are known to relax to values described by periodic infinite temperature ensembles. At the same time, ergodic static systems exhibit anomalous thermalization of local observables and satisfy a modified version of the eigenstate thermalization hypothesis (ETH), when disorder is present. This raises the question, how does the introduction of disorder affect relaxation in periodically driven systems? In this Rapid Communication, we analyze this problem by numerically studying transport and thermalization in an archetypal example. We find that thermalization is anomalous and is accompanied by subdiffusive transport with a disorder-dependent dynamical exponent. Distributions of matrix elements of local operators in the eigenbases of a family of effective time-independent Hamiltonians, which describe the stroboscopic dynamics of such systems, show anomalous departures from predictions of ETH, signaling that only a modified version of ETH is satisfied. The dynamical exponent is shown to be related to the scaling of the variance of these distributions with system size.

Recent theoretical studies predict potential multiferroicity in $AB{\mathrm{F}}_3$ fluoroperovskites, challenging their experimental confirmations. Here, we show that magnetic manganese fluoroperovskites ${\mathrm{NaMnF}}_3$, ${\mathrm{RbMnF}}_3$, and ${\mathrm{CsMnF}}_3$ reveal clear evidence of intrinsic lattice instability via the temperature behavior of the dielectric permittivity ${\varepsilon }_0\left(T\right)$. Mechanisms of the instability closely correlate with the geometric tolerance factor $t$ and differ from those in oxide perovskites. In particular, a dramatic 170% growth of the permittivity ${\varepsilon }_0\left(T\right)$ takes place at low temperatures in ${\mathrm{NaMnF}}_3$ with the smallest tolerance factor $t=0.78$. Below $T_N$, this growth is accompanied by a huge magnetodielectric effect of about 25%. These findings allow us to call ${\mathrm{NaMnF}}_3$ an incipient multiferroic and open up opportunities for designing multiferroics on the basis of fluorides using chemical and strain engineering.

A large broadening ($\sim 0.4\mathrm{meV}$) of quasielastic neutron scattering (QENS) signal in ${\mathrm{H}}_2\mathrm{O}$ ice $I_h$ at $T=5\mathrm{K}$ was observed by Bove et al. [Phys. Rev. Lett. 103, 165901 (2009)] and explained by a model of concerted proton tunneling. This result was rather unexpected, as prior studies never showed significant mobility in water at low temperatures and ambient pressure. There were a few attempts of theoretical understanding of the effect. Recent path-integral simulations as well as quantum lattice-gauge theory supported the possibility of the collective tunneling of protons in ice $I_h$, however other studies stated that concerted tunneling in ice $I_h$ should have very low frequency. Here, we report on QENS measurements of ${\mathrm{H}}_2\mathrm{O}$ ice $I_h$ at 1.8 and 5 K by using neutron scattering spectrometers with the energy resolution similar to and four times better than the energy resolution in the original experiment of Bove and co-workers. We did not observe any QENS broadening, and the measured spectra for the ice $I_h$ and the reference vanadium sample were almost identical. Therefore, we conclude that there is no proton tunneling in ice $I_h$ at temperatures down to 1.8 K measurable on an energy scale of 3.5 $\mu \mathrm{eV}$ and above. The literature data on low-temperature heat capacity of ice $I_h$ support this conclusion.

The superconductor-insulator transition (SIT), one of the most fascinating quantum phase transitions, is closely related to the competition between superconductivity and carrier localization in disordered thin films. Here, superconducting $\mathrm{Ti}{\mathrm{O}}_x$ films with different oxygen contents were grown on $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ substrates by a pulsed laser deposition technique. The increasing oxygen content leads to an increase of disorder, a reduction of carrier density, an enhancement of carrier localization, and therefore a decrease of superconducting transition temperature. A fascinating SIT emerges in cubic $\mathrm{Ti}{\mathrm{O}}_x$ films with increasing oxygen content and its critical sheet resistance is close to the quantum resistance $h/{\left(2e\right)}^2\sim 6.45\mathrm{k}\mathrm{\Omega }$. The scaling analyses of magnetic field–tuned SITs show that the critical exponent products zν increase from 1.02 to 1.31 with increasing disorder. Based on the results, the SIT can be described by the “dirty boson” model, and a schematic phase diagram for $\mathrm{Ti}{\mathrm{O}}_x$ films was constructed.

We propose an effective optical approach to monitor superconductors in a two-layer superconductor-normal metal structure. Effectively, such a hybrid system represents a resonator, where electrons are strongly coupled with light. We show that the interaction of light with the superconductor is strongly boosted in the presence of the neighboring metal and, as a result, the electromagnetic power absorption of the system is dramatically enhanced. It manifests itself in a giant Fano-type resonance which can uniquely characterize the elementary excitations of the system. Our approach is especially promising for topological superconductors, where Majorana fermions could be revealed and controlled by light.

We theoretically study the localized magnetic states and the Kondo screening of a magnetic impurity in the bulk of Weyl semimetals (SMs). The linear dispersion near the Weyl nodes and the anomalous broadening of the impurity level lead to a nonvanishing magnetic moment in a wide region of parameters. The magnetic susceptibility is significantly enhanced by increasing the chirality imbalance for the chemical potential fixed at the Weyl nodes. The Kondo effect takes place whenever the chemical potential is tuned away from the nodes. The low-temperature susceptibility is determined by both the Kondo screening and the broadening of the magnetic impurity level. In the presence of chiral anomaly, the Kondo screening displays opposite behaviors for the chemical potential situated below and above the Weyl nodes. The magnetic susceptibility can be tuned by the charge imbalance of the nodes, which provides a scheme to study the chiral anomaly in Weyl SMs.

Electron excitation spectra in Ti and Zr transition metals are calculated in the framework of time-dependent density functional theory. Several peaks found in the obtained loss functions are interpreted as collective excitations. The energy positions of the dominating bulk plasmons are in close agreement with the energy loss experiments. We investigated how the absorption of hydrogen modifies the dielectric properties of these materials. It is shown that the main plasmon energy blueshifts in a such process, again in agreement with experimental observations. On base of the calculated bulk dielectric functions of all these systems, we performed analysis of the excitation spectra at surfaces and nanoparticles. Several plasmon peaks in these systems with rather short lifetimes are found at reduced energies. It is shown how the nanoparticle excitation spectra are modified in the ultraviolet-frequency range upon hydrogen absorption.

We provide strong evidence for a quantum critical point (QCP) associated with the destruction of Kondo screening in the Anderson-Hubbard model for interacting electrons with quenched disorder. The evidence comprises three elements: (a) the identification of an energy scale, ${\omega }^{*}$, that delineates infrared Landau damping from higher frequency non-Fermi liquid(nFL) dynamics; (b) the finding that this crossover scale ${\omega }^{*}$ appears to vanish with increasing disorder; and (c) the concomitant appearance of a finite intercept in a broad distribution of Kondo scales. Our findings indicate a Kondo destruction scenario, albeit distinct from the local QCP picture. The nFL behavior is shown to stem from an interplay of strong electron-electron interactions and the systematic inclusion of short-range dynamical fluctuations induced by the underlying random potential. The results have been obtained through a computational framework based on the typical medium dynamical cluster approximation.