The realization of multi-Weyl systems with the minimum nonzero number of Weyl points and the maximum charge number remains challenging in topology physics. In this work, based on first-principles calculations, we propose that ${\mathrm{BeH}}_2$ is thermodynamically, mechanically, and dynamically stable in a cubic crystal structure with the $P23$ space group. Importantly, this is the first work to report the appearance of single-pair multi-Weyl point phonons with the maximum charge number in $P23$-type ${\mathrm{BeH}}_2$. Furthermore, the number and charge of the Weyl points and the phononic surface modes can be tuned by applying $1\%$ and $2\%$ uniaxial strains along the [100] and [111] directions, respectively. Finally, we report that clean charge-two single-pair triple-point phonons appear in $P23$-type ${\mathrm{BeH}}_2$ and investigate the related chiral phonon transition under the uniaxial strains.

Metal-organic frameworks (MOFs) are crystalline and porous, molecular solids consisting of metal nodes and organic ligands. An interesting example is the MOF-2 system, where ${\mathrm{Cu}}^{2+}$ ions form antiferromagnetically coupled dimers to yield so-called paddlewheels. In the case of surface-anchored MOF-2 (SURMOF-2) systems the ${\mathrm{Cu}}^{2+}$ ions are connected via carboxylate and OH groups in a zipperlike fashion. This unusual coupling of the spin-1/2 ions within the resulting one-dimensional chains stabilizes a low-temperature ferromagnetic (FM) phase. In this study, the magnetic properties of two SURMOF-2 systems (Cu(bdc) and Cu(bpdc) with $\mathrm{bdc}=1, 4\text{-benzendicarboxylic}$ acid, $\mathrm{bpdc}=4$,4-biphenyldicarboxylic acid) were investigated using x-ray magnetic circular dichroism both in the absorption and in the scattering geometry. The presence of the FM phase in these SURMOF-2 systems is confirmed. Taking advantage of the element sensitivity of this technique. it was established that the magnetic signal originates from ${\mathrm{Cu}}^{2+}$ ions. After loading of SURMOF-2 with metallocene molecules, no remarkable changes of the magnetic properties of the host matrix were observed. However, the magnetic behavior of the guest molecules, as it turned out, is rather different. In the case of nickelocene loading, a polarization effect was found, resulting in ferromagnetic ordering of the guest molecules. However, in the case of manganocene derivatives, the polarization effect is not observed and these molecules remained in their paramagnetic state. The details of these effects are discussed.

The $S=1/2$ Heisenberg linear chain antiferromagnet is the simplest spin model; nevertheless it serves as a platform for various quantum many-body phenomena. Here, we report the magnetic behavior of a quasi-one-dimensional antiferromagnet ${\mathrm{KCuPO}}_4·{\mathrm{H}}_2\mathrm{O}$. A long-range commensurate antiferromagnetic order with ordered moment 0.31(1) ${\mu }_{\mathrm{B}}$ per spin occurs at $T_{\mathrm{N}}=11.7\left(1\right)$ K. Above $T_{\mathrm{N}}$, the inelastic neutron excitation is characterized by a two spinon continuum. The intrachain interaction $J$ and interchain interaction $|J^{\prime }|$ are estimated to be 172 and 4.25(4) K, respectively; thus the ratio of $|J^{\prime }|/J=0.0247\left(3\right)$. At lower energies, below $T_{\mathrm{N}}$, a spin gap is observed in the dispersive excitations. These results are consistent with characteristics observed in a weakly interacting $S=1/2$ Heisenberg chain system.

In recent times it has been observed that signatures of equilibrium quantum criticality surprisingly show up in many-body systems, which are manifestly far from equilibrium. We explore such scenarios in interacting spin systems subject to a quench and develop a robust method to systematically probe ground-state critical physics through nonequilibrium post-quench dynamics. Analyzing late-time behavior of finite string-like observables, we find emerging sharp signatures of equilibrium criticality. Specifically, these observables accurately detect equilibrium critical points and universal scaling exponents after long times following a quench. This happens despite the fact that the analyzed systems are strongly chaotic/ergodic and is interestingly due to a strong memory of the initial conditions retained by these observables after quench. We find that our results can also be used to explain critical signatures in post-quench domain formation, seen in a recent experiment with trapped ion quantum simulators.

Ionic conductors such as AgI with ultralow thermal conductivities $\left({\kappa }_l\right)$ are of increasing interest because of their excellent thermoelectric properties. However, the origin of their intrinsic low ${\kappa }_l$ values remain elusive. In this study, comprehensive theoretical calculations of the lattice dynamics and the thermal transport properties of $\gamma \text{−}\mathrm{AgI}$ (zinc-blende structure) and $\beta \text{−}\mathrm{AgI}$ (wurtzite structure) as functions of temperature were carried out based on many-body perturbation theory and phonon Boltzmann transport theory. First, the mean-squared displacements (MSDs) of ${\mathrm{Ag}}^{+}$ were significantly larger than those of ${\mathrm{I}}^{-}$ in both $\gamma \text{−}$ and β-phases below the order-disorder phase transition temperature $\left(T_{\mathrm{c}}\right)$, which led to a characteristic “rattling” feature and low-frequency, nearly flat local phonon vibrations. According to our previous work [Xie et al., Phys. Rev. Lett. 125, 245901 (2020)], such nondispersive flat phonon band structures are expected to give rise to four-phonon resonance and result in a dramatic increase in the four-phonon scattering over the conventional three-phonon scattering. For $\gamma \text{−}\mathrm{AgI}$, similar four-phonon resonance behavior was also discovered for the low-lying transverse acoustic phonon branches, and it was found that their four-phonon scattering rates were an order of magnitude larger than the corresponding three-phonon scattering rates. Considering the four-phonon scattering, the theoretical ${\kappa }_l$ of $\gamma \text{−}\mathrm{AgI}$ was predicted to be $\sim 0.32$ W/m K at 300 K, which was in good agreement with the value deduced from our experiments ($\sim 0.36$ W/m K at 300 K). Compared to $\gamma \text{−}\mathrm{AgI}$, the acoustic phonons in $\beta \text{−}\mathrm{AgI}$ were more dispersive, and they intertwined with low-energy optical phonons at the zone boundaries. It was found that three-phonon resonance became as important as four-phonon resonance for the nearly flat longitudinal phonon band. The theoretical ${\kappa }_l$ for $\beta \text{−}\mathrm{AgI}$ was determined to be around $\sim 0.32$ W/m K at room temperature, closely reproducing our measurement value $\sim 0.29$ W/m K. Our results for AgI demonstrate the strong quartic anharmonicity in materials characterized by the rattling of weak bonding atoms as well as dispersionless phonon band structures. It is believed that this intimate relationship between the low-${\kappa }_l$ and flat phonon dispersion can be employed as a good indicator when searching for material systems with ultralow ${\kappa }_l$ values, e.g., cagelike rattling structures, quasi-two-dimensional structures, and chainlike structures.

We address the competing superconducting and magnetic phases on the honeycomb lattice, in a field-theoretic approach suitable to yield a low-energy perturbative theory for the strong-coupling limit of the Hubbard model, both at half filling and in the low and high hole-doped regimes. The effective low-lying Hamiltonian is presented in terms of charge (Grassmann fields) and spin [SU(2) gauge fields] degrees of freedom. We analyze the competing phases by calculating the ground-state energy, electronic spectrum, and other observables associated with the $s$- and $d_{x^2-y^2}+i{d}_{xy}$-wave superconducting phases, doped antiferromagnetic, and doped ferromagnetic states. We find that, while the antiferromagnetic order has the lowest ground-state energy for low hole doping near half filling, a dominant superconducting state with chiral $d_{x^2-y^2}+i{d}_{xy}$-wave symmetry emerges in the vicinity of the Van Hove singularity in the high hole-doped regime, with the presence of a quantum first-order transition accompanied by spatial phase separation. We highlight that advances in the understanding of chiral superconducting states on the honeycomb lattice are relevant to a number of doped compounds including the graphene monolayer system.

Under temperature or pressure tuning, tetragonal ${\mathrm{EuPd}}_2{\mathrm{Si}}_2$ is known to undergo a valence transition from nearly divalent to nearly trivalent Eu accompanied by a volume reduction. Albeit intensive work, its microscopic origin is still being discussed. Here, we investigate the mechanism of the valence transition under volume compression by ab initio density functional theory (DFT) calculations. Our analysis of the electronic and magnetic properties of ${\mathrm{EuPd}}_2{\mathrm{Si}}_2$ when approaching the valence transition shows an enhanced $c\text{−}f$ hybridization between localized Eu $4f$ states and itinerant conduction states (Eu $5d$, Pd $4d$, and Si $3p$) where an electronic charge redistribution takes place. We observe that the change in the electronic structure is intimately related to the volume reduction where Eu-Pd(Si) bond lengths shorten and, for the transition to happen, we trace the delicate balance between electronic bandwidth, crystal field splitting, Coulomb repulsion, Hund's coupling and spin-orbit coupling. In a next step we compare and benchmark our DFT results to surface-sensitive photoemission data in which the mixed-valent properties of ${\mathrm{EuPd}}_2{\mathrm{Si}}_2$ are reflected in a simultaneous observation of divalent and trivalent signals from the Eu $4f$ shell. The study serves as well to explore the limits of density functional theory and the choice of exchange correlation functionals to describe such a phenomenon as a valence transition.

By employing the exact-diagonalization method, we revisit the ground-state phase diagram of the Haldane-Hubbard model on the honeycomb lattice with staggered sublattice potentials. The phase diagram includes the band insulator, Mott insulator, and two Chern insulator phases with Chern numbers $C=2$ and $C=1$, respectively. The character of transitions between different phases is studied by analyzing the lower-lying energy levels, excitation gaps, structure factors, and fidelity metric. We find that the $C=1$ phase can be continuously deformed into the $C=2$ phase without a gap closure in the periodic boundary condition, while a further analysis on the Berry curvatures indicates that the excitation gap closes at the phase boundary in a twisted boundary condition, accompanied by the discontinuities of structure factors. All the other phase transitions are found to be first-order ones as expected.

Green's functions of fermions are described by matrix-valued Herglotz-Nevanlinna functions. Since analytic continuation is fundamentally an ill-posed problem, the causal space described by the matrix-valued Herglotz-Nevanlinna structure can be instrumental in improving the accuracy and in enhancing the robustness with respect to noise. We demonstrate a three-pronged procedure for robust analytic continuation called PES: (1) projection of data to the causal space; (2) estimation of pole locations; and (3) semidefinite relaxation within the causal space. We compare the performance of PES with the recently developed Nevanlinna and Carathéodory continuation methods and find that PES is more robust in the presence of noise and does not require the usage of extended precision arithmetics. We also demonstrate that a causal projection improves the performance of the Nevanlinna and Carathéodory methods. The PES method is generalized to bosonic response functions, for which the Nevanlinna and Carathéodory continuation methods have not yet been developed. It is particularly useful for studying spectra with sharp features, as they occur in the study of molecules and band structures in solids.

We explore the electronic entropy per particle $s$ and Seebeck coefficient $\mathcal{S}$ in zigzag graphene ribbons. Pristine and edge-doped ribbons are considered using tight-binding models to inspect the role of edge states in the observed thermal transport properties. As a band gap opens when the ribbons are doped at one or both edges, due to asymmetric edge potentials, we find that $s$ and $\mathcal{S}$ signals are closely related to each other: both develop sharp dip-peak line shapes as the chemical potential lies in the gap, while the ratio $s/\mathcal{S}$ exhibits a near-constant value equal to the elementary charge $e$ at low temperatures. This constant ratio suggests that $\mathcal{S}$ can be seen as the transport differential entropy per charge, as suggested by some authors. Our calculations also indicate that measurement of $s$ and $\mathcal{S}$ may be useful as a spectroscopic probe of different electronic energy scales involved in such quantities in gapped materials.

Extensive studies of electron transport in Dirac materials have shown positive magnetoresistance (MR) and positive magnetothermopower (MTP) in a magnetic field perpendicular to the excitation current or thermal gradient. In contrast, measurements of electron transport often show a negative longitudinal MR and negative MTP for a magnetic field oriented along the excitation current or thermal gradient; this is attributed to the chiral anomaly in Dirac materials. Here, we report a very different magnetothermoelectric transport behavior in the massive Dirac material $\mathrm{Zr}{\mathrm{Te}}_5$. Although thin flakes show a commonly observed positive MR in a perpendicular magnetic field, distinct from other Dirac materials, we observe a sharp negative MTP. In a parallel magnetic field, we still observe a negative longitudinal MR, however, a remarkable positive MTP is observed for the fields parallel to the thermal gradients. Our theoretical calculations suggest that this anomalous magnetothermoelectric behavior can be attributed to the screened Coulomb scattering. This work demonstrates the significance of impurity scattering in the electron transport of topological materials and provides deep insight into the magnetotransport phenomena in Dirac materials.

A driven quantum system was recently studied in the context of nonequilibrium phase transitions and their responses. In particular, for a periodically driven system, its dynamics are described in terms of the multidimensional Floquet lattice with a lattice size depending on the number of driving frequencies and their rational or irrational ratio. So far, for a multifrequency driving system, the energy pumping between the sources of frequencies has been widely discussed as a signature of topologically nontrivial Floquet bands. However, the unique edge modes emerging in the Floquet lattice have not been explored yet. Here, we discuss how the edge modes in the Floquet lattice are controlled and result in the localization at particular frequencies, when multiple frequencies are present and their magnitudes are commensurate values. First, we construct the minimal model to exemplify our argument, focusing on a two-level system with two driving frequencies. For the strong frequency limit, one can describe the system as a quasi-one-dimensional Floquet lattice where the effective hopping between the neighboring sites depends on the relative magnitudes of the potential for two frequency modes. With multiple driving modes, nontrivial Floquet lattice boundaries always exist from controlling the frequencies, and this gives rise to states that are mostly localized at such Floquet lattice boundaries, i.e., particular frequencies. We suggest the time-dependent Creutz ladder model as a realization of our theoretical Hamiltonian and show the emergence of controllable Floquet edge modes.

Here, we analyze, in a noncontact fashion, charge-carrier mobility as a function of injection level and temperature in silicon by time-resolved terahertz spectroscopy (TRTS) and parametrize our data by the classical semiempirical models of Klaassen [Solid State Electron. 35, 953 (1992); Solid State Electron. 35, 961 (1992)] and Dorkel and Leturcq [Solid State Electron. 24, 821 (1981)]. Our experimental results are in very good agreement with the pioneering works of Krausse [Solid State Electron. 15, 1377 (1972)] and Dannhäuser [Solid State Electron. 15, 1371 (1972)], who analyzed these phenomena by employing contact-based methods. This agreement, that validates our methodology, can only be achieved by considering charge-carrier diffusion effects following above band gap near-surface pump photoexcitation of the sample. From our results, obtained over a large range of injection levels, we conclude that the model of Klaassen is the best at describing the collected data at room temperature. Furthermore, we analyze by TRTS the dependence of charge-carrier mobility with temperature for a fixed injection level. Once more, the parametrization made by the classical model of Klaassen describes our data appropriately even without the necessity of applying any fitting parameters (just with the charge-carrier density as an input). In this respect, our work supports the validity of the model and parametrization proposed by Klaassen and illustrates how TRTS can be reliably employed for the quantitative determination of mobility in semiconductors as a function of key parameters such as injection level and temperature.

Flat bands in twisted layered two-dimensional materials are the key to realizing the exotic phenomena related to electron correlation. The origin of the flat bands in various twisted two-dimensional materials remains elusive. In this work, we study the coexistence of flat bands driven by localization and interference in the twisted bilayer ${\mathrm{C}}_3\mathrm{N}$. One ultraflat band is induced by destructive interference in the kagome arrangement of localized states. Meanwhile, other flat bands induced by simple localization exist. The effective kagome lattice with parameters tuned by twist angle is deduced. The flat band induced by interference is more robust than that induced by simple localization under vertical strain. The kagome bands formed at the bottom of the conduction band provide a platform for studying the kagome Hamiltonian in twisted two-dimensional materials.

The phase diagram of a para-${\mathrm{H}}_2$ monolayer absorbed on an experimentally synthesized amorphous carbon sheet was calculated using a diffusion Monte Carlo technique. We found that the ground state of that system changed drastically from a perfectly flat substrate to a situation in which the carbon atoms were allowed a certain degree of disorder in the $z$ direction. In the first case, at zero pressure we have a glass of density $0.056\pm 0.003 {\text{Å}}^{-2}$ in equilibrium with an incommensurate solid of $0.068\pm 0.002 {\text{Å}}^{-2}$. At the equilibrium density, the glass was found to have a tiny, but non-negligible superfluid fraction of less than $1\%$ ($0.44\pm 0.05\%$). In the $z$-disordered substrate, we observe a significant enhancement of the superfluid fraction in the glass phase as well as a smaller but not zero value in the incommensurate crystal.

With conformal coordinate transformations, compacted dimensions might be realized in photonic systems. Here we show, with a one-dimensional (1D) photonic model system, that the essential topological nature of a two-dimensional (2D) nanoribbon is conserved in a mapping without conformal transformations. We take topological edge states as an example. They exist in physical systems of different dimensions, such as Su-Schrieffer-Heeger (SSH) model in 1D with dimerized polyacetylene, or a Haldane model in a 2D hexagonal lattice with spin-orbit coupling. In addition, the 2D graphene nanoribbon model also hosts topological edge states if the edge is of “zigzag” type with nontrivial Zak phase. In this Letter, we introduce a mapping formalism which establishes the correspondence between the momentum space of the nanoribbon and the parameter space of a 1D diatomic chain. It explicitly demonstrates that topological origin of the nanoribbon system can be reduced to the SSH model, which reveals the unification of topological nature across different dimensions. As an example, we reconstruct the 2D graphene nanoribbon band structure, including topological edge states, using 1D optical waveguide arrays. The coupling coefficients between waveguides are directly transformed from nanoribbons’ electron momenta. We believe that it is a powerful tool to connect physical phenomena in different dimensions and offers a new experimental methodology based on photonic platforms for condensed-matter research.

We investigate two concrete cases of phase transitions breaking a subsystem symmetry. The models are two classical compass models featuring line-flip and plane-flip symmetries and correspond to special limits of a Heisenberg-Kitaev Hamiltonian on a cubic lattice. We show that these models experience a hybrid symmetry breaking by which the system display distinct symmetry broken patterns in different submanifolds. For instance, the system may look magnetic within a chain or plane but nematic-like when observing from one dimensionality higher. We fully characterize the symmetry-broken phases by a set of subdimensional order parameters and confirm numerically both cases undergo a non-standard first-order phase transition. Our results provide new insights into phase transitions involving subsystem symmetries and generalize the notion of conventional spontaneous symmetry breaking.