Third-order elasticity (TOE) theory predicts strain-induced changes in second-order elastic coefficients (SOECs) and can model elastic wave propagation in stressed media. Although third-order elastic tensors have been determined based on first principles in previous studies, their current definition is based on an expansion of thermodynamic energy in terms of the Lagrangian strain near the natural, or zero pressure, reference state. This definition is inconvenient for predictions of SOECs under significant initial stresses. Therefore, when TOE theory is necessary to study the strain dependence of elasticity, the seismological community has resorted to an empirical version of the theory. This study reviews the thermodynamic definition of the third-order elastic tensor and proposes using an “effective” third-order elastic tensor. An explicit expression for the effective third-order elastic tensor is given and verified. We extend the ab initio approach to calculate third-order elastic tensors under finite pressure and apply it to two cubic systems, namely, NaCl and MgO. As applications and validations, we evaluate (a) strain-induced changes in SOECs and (b) pressure derivatives of SOECs based on ab initio calculations. Good agreement between third-order elasticity-based predictions and numerically calculated values confirms the validity of our theory.

We provide analytical and numerical insights into the phase diagram and other properties of the extended Kitaev-Heisenberg model on the honeycomb lattice in the easy-plane limit, in which interactions are only between spin components that belong to the plane of magnetic ions. This parameter subspace allows for a much-needed systematic quantitative investigation of spin excitations in the ordered phases and of their generic features. Specifically, we demonstrate that in this limit one can consistently take into account magnon interactions in both zero-field zigzag and field-polarized phases. For the nominally polarized phase, we propose a regularization of the unphysical divergences that occur at the critical field and are plaguing the $1/S$ approximation in this class of models. For the explored parameter subspace, all symmetry-allowed terms of the standard parametrization of the extended Kitaev-Heisenberg model, such as $K$, $J$, and $\mathrm{\Gamma }$, are significant, making the offered consideration relevant to a much wider parameter space. The dynamical structure factor near the paramagnetic critical point illustrates this relevance by showing features that are reminiscent of the ones observed in $\alpha \text{−}{\mathrm{RuCl}}_3$, underscoring that they are not unique and should be common to a wide range of parameters of the model and, by extension, to other materials.

We report on the low-energy magnetic excitations and the evolution of local magnetic fields in ${\mathrm{CrI}}_3$ in a broad frequency regime of 30–330 GHz and in magnetic fields up to 15 T. Modeling the magnon branches by means of a domain-based ferromagnetic resonance model provides the microscopic parameters describing the magnetic excitations in the two-dimensional ferromagnet. Our data reveal the anisotropy gap of $\mathrm{\Delta }=80$ GHz at 2 K, which remarkably remains finite at $T_{\mathrm{C}}$ and vanishes only above $T_{\mathrm{\Delta }}\simeq 80$ K, i.e., for $T\gtrsim 1.3T_{\mathrm{C}}$. Concomitantly, anisotropic local magnetic fields are probed by a shift of the resonance lines in the same temperature regime. Well above $T_{\mathrm{C}}$, we detect short-range magnetic correlations up to 200 K. The observed changing nature of the short-range correlations at $T_{\mathrm{\Delta }}$ confirms the importance of spin-orbit coupling for the evolution of long-range ferromagnetism which develops from magnetically anisotropic short-range order. In addition, our analysis of the macroscopic magnetization enables to estimate the number of correlated spins well above $T_{\mathrm{C}}$ as well as the in-plane magnetic correlation length ${\xi }_{\mathrm{ab}}$.

We describe a unified classical approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. To fill the gap between experiment and theory, we also consider the influences of small circuit asymmetry and the finite length of the feedlines, and describe a procedure to correct their influences in typical experiments. We show that, similar to the transmission coefficient of a hanger-type resonator, the reflection coefficient of a necklace- or cross-type resonator also contains a so-called reference point that can be used to characterize the internal quality factor of the resonator. Our results provide a comprehensive understanding of superconducting microwave resonators from the design concepts to the characterization details.

We describe a unified quantum approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries, and demonstrate its consistency with the classical approach [Q.-M. Chen et al., Phys. Rev. B 106, 214505 (2022)]. We also generalize the result to a chain of resonators with time delays, and reveal several transport properties similar to a photonic crystal and can be used to design high-quality resonators. These results form a firm theoretical ground for analyzing the scattering coefficients of an arbitrary resonator network. They set a step forward to designing and characterizing superconducting microwave resonators in a complex superconducting quantum circuit.

The ground state of a free-fermionic chain with inhomogeneous hoppings at half-filling can be mapped into the Dirac vacuum on a static curved space-time, which presents exactly homogeneous occupations due to particle-hole symmetry. Yet, far from half-filling, we observe density modulations and depletion effects. The system can be described by a 1D Schrödinger equation on a different static space-time, with an effective potential, which accounts for the depleted regions. We provide a semiclassical expression for the single-particle modes and the density profiles associated to different hopping patterns and filling fractions. Moreover, we show that the depletion effects can be compensated for all filling fractions by adding a chemical potential proportional to the hoppings. Interestingly, we can obtain exactly the same density profiles on a homogeneous chain if we introduce a chemical potential, which is inverse to the hopping intensities, even though the ground state is different from the original one.

We present a theoretical study of the quantum dynamics of two magnetic fluxons trapped in Josephson junction parallel arrays (JJPAs) with large kinetic inductances. The Josephson phase distribution of two trapped magnetic fluxons satisfies a topological constraint, i.e., the total variation of Josephson phases along a JJPA is $4\pi$. In such JJPAs the characteristic length of the Josephson phase distribution (“the size” of magnetic fluxon) is drastically reduced to be less than a single cell size. Two extreme dynamic patterns will be distinguished: two weakly interacting and two merged magnetic fluxons, i.e., a $4\pi$ kink. Taking into account the repulsive interaction between two magnetic fluxons located in the same or adjacent cells, we obtain the energy band spectrum $E_{4\pi }\left(p\right)$ for a quantum $4\pi$ kink. The coherent quantum dynamics of $4\pi$ kinks demonstrates the quantum beats with the frequency and amplitude strongly deviating from those observed for two independent magnetic fluxons. In the presence of applied dc and ac bias currents of frequency $f$ a weakly incoherent quantum dynamics of a $4\pi$ kink results in the Bloch oscillations and the seminal current steps with values $I_{4\pi }^{\left(n\right)}=enf$ which are two times less than those for two independent magnetic fluxons.

Magic-angle twisted bilayer graphene displays at different fillings of the four flat bands lying around the charge neutrality point a wealth of notable phases that include magnetic Chern insulators, whose magnetization is mostly of an orbital nature and contiguous superconducting domes. Such a rich phase diagram is explained through the positive interplay of Coulomb repulsion and the electron coupling to a twofold optical mode that corresponds to Kekulé distortions localized into the small AA stacked regions of the moiré supercells. A static distortion stabilizes, at any integer filling of the flat bands, valence-bond insulators that carry finite Chern number away from charge neutrality. Similarly, a dynamic distortion that resonates between the two lattice vibrations leads to resonating-valence-bond topological insulators with built-in chiral d-wave pairs that have finite Chern number equal to the angular momentum, and thus are prone to turn superconducting upon doping away from integer filling.

The pseudofermion representation for $S=1/2$ quantum spins introduces unphysical states in the Hilbert space, which can be projected out using the Popov-Fedotov trick. However, state-of-the-art implementation of the functional renormalization group method for pseudofermions have so far omitted the Popov-Fedotov projection. Instead, restrictions to zero temperature were made and the absence of unphysical contributions to the ground state was assumed. We question this belief by exact diagonalization of several small-system counterexamples where unphysical states do contribute to the ground state. We then introduce Popov-Fedotov projection to pseudofermion functional renormalization, enabling finite-temperature computations with only minor technical modifications to the method. At large and intermediate temperatures, our results are perturbatively controlled and we confirm their accuracy in benchmark calculations. At lower temperatures, the accuracy degrades due to truncation errors in the hierarchy of flow equations. Interestingly, these problems cannot be alleviated by switching to the parquet approximation. We introduce the spin projection as a method-intrinsic quality check. We also show that finite-temperature magnetic-ordering transitions can be studied via finite-size scaling.

A wide band gap is one of the essential requirements for metal iodates to be used as nonlinear optical materials. Usually, the band gap of these materials decreases under the application of pressure. Herein, we introduce a case in which the band-gap energy of a hydrated metal iodate, namely $\mathrm{Ca}{\left({\mathrm{IO}}_3\right)}_2·{\mathrm{H}}_2\mathrm{O}$, has been successfully increased, from 4.52 to 4.92 eV, by applying external pressure without showing signs of saturation upon increasing pressure. The pressure-induced nonlinear band-gap opening correlates with the pressure-induced shortening of the I-O bond distances, as obtained from x-ray diffraction measurements. In addition, two pressure-induced isostructural phase transitions are observed in the pressure regions of 6.6–8.0 and 13.0–15.5 GPa. These two isostructural phase transitions cause a nonlinear pressure-induced evolution of the band-gap energy and crystal lattice parameters, as well as the occurrence of several extra peaks and peak splitting in Raman spectra.

We build a microscopic model to study the intralayer and interlayer superexchange due to electrons hopping in chromium trihalides ($\mathrm{Cr}{X}_3$, $X=$ Cl, Br, and I). In evaluating the superexchange, we identify the relevant intermediate excitations in the hopping. In our study, we find that the intermediate hole-pair excitations in the $p$ orbitals on $X$ ion play a crucial role in mediating various types of exchange interactions. In particular, the interlayer antiferromagnetic exchange may be realized by the hole-pair-mediated superexchange. Interestingly, we also find that these virtual hopping processes compete with each other, leading to weak intralayer ferromagnetic exchange. In addition, we also study the spin-orbit coupling effects on the superexchange and investigate the Dzyaloshinskii-Moriya interaction. Finally, we extract the microscopic model parameters from density functional theory for analyzing the exchange interactions in a monolayer ${\mathrm{CrI}}_3$.

We investigate the local moment formation in the half-filled $\mathrm{SU}(N$) Hubbard model under a staggered ionic potential. As the Hubbard $U$ increases, the charge fluctuations are suppressed and eventually frozen when $U$ is above a critical value $U_c$, marking the development of well-defined local moment with integer $m$ fermions on the A sublattice and $(N-m)$ fermions on the B sublattice, respectively. We obtain an analytical solution for $U_c$ for the paramagnetic ground state within the variational Gutzwiller approximation and renormalized mean field theory. For large $N$, $U_c$ is found to depend on $N$ linearly with fixed $m/N$, but sublinearly with fixed $m$. The local moment formation is accompanied by a peculiar phase transition from the band insulator to the Mott insulator, where the ionic potential and quasiparticle weight are renormalized to zero simultaneously. Inside the Mott phase, the low-energy physics is described by the $\mathrm{SU}(N$) Heisenberg model with conjugate representations, which is widely studied in the literature.

We calculate the surface dc conductivity of Weyl semimetals and show that it contains an anomalous contribution in addition to a Drude contribution from the Fermi arc. The anomalous part is independent of the surface scattering time, and appears at nonzero temperature and doping (away from the Weyl nodes), increasing quadratically with both with a universal ratio of coefficients. Microscopically, it results from the contribution of the gapless bulk to the surface conductivity. We argue that this can be interpreted as the conductivity of an effective interacting surface fluid that coexists with the Fermi arc metal. In a certain regime of low temperatures, the temperature dependence of the surface conductivity is dominated by the anomalous response, which can be probed experimentally to unravel the unusual behavior.

We analyze the dynamics of entanglement in a paradigmatic noninteracting system subject to continuous monitoring of the local excitation densities. Recently, it was conjectured that the evolution of quantum correlations in such system is described by a semiclassical theory, based on entangled pairs of ballistically propagating quasiparticles and inspired by the hydrodynamic approach to unitary (integrable) quantum systems. Here, however, we show that this conjecture does not fully capture the complex behavior of quantum correlations emerging from the interplay between coherent dynamics and continuous monitoring. We unveil the existence of multipartite quantum correlations which are inconsistent with an entangled-pair structure and which, within a quasiparticle picture, would require the presence of larger multiplets. We also observe that quantum information is highly delocalized, as it is shared in a collective nonredundant way among adjacent regions of the many-body system. Our results shed light onto the behavior of correlations in quantum stochastic dynamics and further show that these may be enhanced by a (weak) continuous monitoring process.

Light has a wavelength that is usually longer than the size of the unit cell of crystals. Hence, even intense light pulses are not expected to break the translation symmetry of materials. However, certain materials, including ${\mathrm{KTaO}}_3$, exhibit peaks in their Raman spectra corresponding to their Brillouin zone boundary phonons due to second-order Raman processes, which provide a mechanism to drive these phonons using intense midinfrared lasers. We investigated the possibility of breaking the translation symmetry of ${\mathrm{KTaO}}_3$ by driving its highest-frequency transverse optic mode $Q_{\text{HX}}$ at the $X(0,\frac{1}{2},0)$ point. Our first-principles calculations show that the energy curve of the transverse acoustic mode $Q_{\text{LZ}}$ at $X$ softens and develops a double-well shape as the value of the $Q_{\text{HX}}$ coordinate is increased, while that of the other transverse acoustic component $Q_{\text{LX}}$ hardens when the value of the $Q_{\text{HX}}$ coordinate is similarly varied. We performed similar total-energy calculations as a function of the $Q_{\text{HX}}$ coordinate and electric field to extract the nonlinear coupling between them. These were then used to construct the coupled equations of motion for the three phonon coordinates in the presence of an external pump term on the $Q_{\text{HX}}$ mode, which we numerically solved for a range of pump frequencies and amplitudes. We find that 465 MV/cm is the smallest pump amplitude that leads to an oscillation of the $Q_{\text{LZ}}$ mode at a displaced position while the $Q_{\text{HX}}$ mode is externally pumped, hence, transiently breaking the translation symmetry of the material. Such highly intense light pulses cannot be generated by currently available laser sources, and they have the possibility to damage the material. Nevertheless, our work shows that light can in principle be used to transiently break the translation symmetry of a material via nonlinear phononics.

Gapless edge states are the hallmark of a large class of topological states of matter. Recently, intensive research has been devoted to understanding the physical properties of the edge states at the quantum phase transitions of the bulk topological states. A higher-order symmetry-protected topological state is realized in a plaquette Heisenberg model on the square lattice. In its disordered phase, the lattice with an open boundary hosts either dangling corner states with spin-$1/2$ degeneracy characterizing the topological phase or nondangling corner states without degeneracy, which depends on the bond configuration near the corners. In this work, we study the critical behavior of these corner states at the quantum critical point (QCP) and find that the spin-$1/2$ corner state induces a new universality class of the corner critical behavior, which is distinct from the ordinary transition of the nondangling corners. In particular, we find that the dangling spin-$1/2$ corner state persists at the QCP despite its coupling to the critical spin fluctuations in the bulk. This shows the robustness of the corner state of the higher-order topological state.

The magnetism of double perovskites is a complex phenomenon, determined from intra- or interatomic magnetic moment interactions, and strongly influenced by geometry. We take advantage of the complementary length and timescales of the muon spin rotation, relaxation, and resonance (${\mu }^{+}\mathrm{SR}$) microscopic technique and bulk ac/dc magnetic susceptibility measurements to study the magnetic phases of the ${\mathrm{LaCaNiReO}}_6$ double perovskite. As a result, we are able to discern and report ferrimagnetic ordering below $T_{\mathrm{C}}=102\mathrm{K}$ and the formation of different magnetic domains above $T_{\mathrm{C}}$. Between $T_{\mathrm{C}}<T<270\mathrm{K}$, the following two magnetic environments appear, a dense spin region and a static-dilute spin region. The paramagnetic state is obtained only above $T>270\mathrm{K}$. An evolution of the interaction between Ni and Re magnetic sublattices, in this geometrically frustrated fcc perovskite structure, is revealed as a function of temperature through the critical behavior and thermal evolution of microscopic and macroscopic physical quantities.

This work reports a complete analysis of surface degradation in $\beta \text{−}\mathrm{FeSe}$ single crystals; which includes the dependence on aging and temperature of Raman spectra, electrical transport resistivity, and XPS depth profiling characterization. All measurements are consistent with the emergence of clusters of Se and the presence of ${\mathrm{FeO}}_x$ in the surface of the crystals. The vibrational modes of the Se clusters are coupled to the $\beta \text{−}\mathrm{FeSe}$ ones as seen in the structural transition. Moreover, this degraded surface can behave like a quasi-two-dimensional layer, as supported by a theoretical model and also consistent with Raman spectra. While the degradation of thin films of $\beta \text{−}\mathrm{FeSe}$ in air is widely known, with a corresponding loss of the superconducting properties, in single crystals with aged surfaces we observe an enhancement of the superconducting properties.