Quantum information stored in local operators spreads over other degrees of freedom of the system during time evolution, known as scrambling. This process is conveniently characterized by the out-of-time-order commutator (OTOC), the time dependence of which reveals salient aspects of the system's dynamics. Here we study the spatially local spin-correlation function, i.e., the expectation value of the spin commutator and the corresponding OTOC of Dirac-Weyl systems in one, two, and three spatial dimensions. The OTOC can be written as the square of the expectation value of the commutator and the variance of the commutator. In principle, the problem features two energy scales, the chemical potential and the high-energy cutoff. We find that only the latter is dominant, therefore the time evolution is separated into only two different regions. The spin-correlation function grows linearly with time initially and decays as $t^{-2}$ for late times. The OTOC reveals a universal $t^2$ initial growth from both the commutator and the variance while its late time decay $t^{-2}$ originates from the variance of the commutator. This late time decay is identified as a characteristic signature of Dirac-Weyl fermions. These features remain present also at finite temperatures. Our results indicate that Dirac-Weyl systems are slow information scramblers and are essential when additional channels for scrambling, i.e., interaction and disorder, are analyzed.

Stacking layered materials revealed to be a very powerful method to tailor their electronic properties. It has indeed been theoretically and experimentally shown that twisted bilayers of graphene (tBLG) with a rotation angle $\theta$, forming a Moiré pattern, confine electrons in a tunable way as a function of $\theta$. Here, we study electronic structure and transport in tBLG using tight-binding numerical calculations in commensurate twisted bilayer structures and a pertubative continuous theory, which is valid for not-too-small angles ($\theta >\sim 2^{\circ }$). These two approaches allow us to understand the effect of $\theta$ on the local density of states, the electron lifetime due to disorder, the DC conductivity, and the conductivity quantum correction due to multiple scattering effects. We distinguish the cases where disorder is equally distributed over two layers or only one layer. When only one layer is disordered, diffusion properties depend strongly on $\theta$, thus showing the effect of Moiré electronic localization at intermediate angles $\theta , \sim 2^{\circ }<\theta <\sim {20}^{\circ }$.

Fermi level dependence of ultrafast optical responses of single-layer graphene has been investigated using sub-10-fs pump-probe spectroscopy under bias voltages. We observe the ultrafast thermalization of photoexcited carriers, whose dynamics can be modulated via bias-induced change of the Fermi level. The relaxation time and the amplitude of the electronic response are maximized when the Fermi level reaches approximately half of the excitation photon energy. From the analysis of the pump-pulse-induced optical conductivity change, we find that the bias-induced blocking of the relaxation pathways and the pump-induced change of the electronic temperature and the Fermi level significantly contribute to the observed ultrafast optical modulation. The results demonstrate the controllability of the ultrafast optical responses in single-layer graphene, which could be useful for future ultrafast electro-optic graphene devices.

Spectral degeneracies of quantum magnets are often described as diabolical points or magnetic Weyl points, which carry topological charge. Here, we study a simple, yet experimentally relevant, quantum magnet: two localized interacting electrons subject to spin-orbit coupling. In this setting, the degeneracies are not necessarily isolated points, but can also form a line or a surface. We identify 10 different possible geometrical patterns formed by these degeneracy points, and study their stability under small perturbations of the Hamiltonian. Stable structures are found to depend on the relative sign $\mathcal{S}$ of the determinants of the two $g$ tensors. Both for $\mathcal{S}=+1$ and $-1$, two stable configurations are found, and three out of these four configurations are formed by pairs of Weyl points. These stable regions are separated by a surface of almost stable configurations, with a structure akin to codimension-one bifurcations. These properties of magnetic degeneracy points can be practically important for control and readout of spin-based quantum bits.

Structural transformations at high pressure in $\mathrm{NaAlG}{\mathrm{e}}_3{\mathrm{O}}_8$ glass were investigated by means of x-ray absorption spectroscopy at the Ge $K$ edge in combination with a diamond anvil cell. The obtained results provide a detailed picture of the local structural behavior of Ge in a chemically complex glass under compression. First and second shell bond distances ($R_{\text{Ge-O}}$ and $R_{\mathrm{Ge}...\mathrm{Ge}}$) were extracted assuming contributions of two scattering paths (Ge-O and Ge…Ge). We observed a significant extension of the Ge-O distance from 1.73 to 1.82 Å between 3 and $\sim 26\mathrm{GPa}$, accompanied by an increase of the fitted number of nearest neighbors from $\sim 4$ to $\sim 6$. These observations can be attributed to the change from tetrahedral to octahedral Ge coordination. Second shell bond distances Ge…Ge are also consistent with this structural transformation. Between 34 and 131 GPa, the evolution of the fitted Ge-O distance implies a gradual volume reduction of the Ge octahedra. At the highest probed pressure of 131 GPa a Ge-O distance of 1.73 Å was found, which is similar to the one obtained at ambient conditions for Ge in fourfold coordination. The compressibility of the Ge-O octahedron in $\mathrm{NaAlG}{\mathrm{e}}_3{\mathrm{O}}_8$ beyond 34 GPa is considerably higher than the one reported for amorphous $\mathrm{Ge}{\mathrm{O}}_2$ from x-ray diffraction analysis but it is similar to the one reported for the Ge octahedron in crystalline rutile-type $\mathrm{Ge}{\mathrm{O}}_2$. We attribute the high compressibility of the Ge-O bond in $\mathrm{NaAlG}{\mathrm{e}}_3{\mathrm{O}}_8$ glass to the presence of Al and Na that increase the system's complexity and therefore its degrees of freedom. Beyond 110 GPa the data on $\mathrm{NaAlG}{\mathrm{e}}_3{\mathrm{O}}_8$ glass indicate the onset of polyhedral distortion. The performed study provides insights into the structural changes of complex and polymerized germanate glasses or melts at extreme pressure conditions.

The correlation between structure and glass formability in glassy systems is a long-standing puzzle. To solve this puzzle, many descriptors based on the short-range order (SRO) have been proposed. Here we show that the SRO, however, offers little help in explaining the glass formability and stability; instead it is the formation of medium-range order that stabilizes the glass against crystallization by suppressing the atomic rearrangement and compositional change. Our results provide a perspective for understanding the correlation between structure and stability in glasses.

The vibrational frequency of hydrogen molecules has been observed to increase strongly with He concentration in helium-hydrogen fluid mixtures. This has been associated with He-H interactions, either directly through chemical bonding [Lim and Yoo, Phys. Rev. Lett. 120, 165301 (2018)] or indirectly through increased local pressure [Loubeyre et al., Phys. Rev. B 32, 07611 (1985)]. Here, we demonstrate that the increase in the Raman frequency of the hydrogen molecule vibron is due to the number of ${\mathrm{H}}_2$ molecules participating in the mode. There is no chemical bonding between He and ${\mathrm{H}}_2$; helium acts only to separate the molecules. The variety of possible environments for ${\mathrm{H}}_2$ gives rise to many Raman-active modes, which causes broadening of the vibron band. As the Raman-active modes tend to be the lower-frequency vibrons, these effects work together to produce the majority of the shift seen in experiment. We used density functional theory (DFT) methods in both solid and fluid phases to demonstrate this effect. DFT also reveals that the pressure in these ${\mathrm{H}}_2$-He mixtures is primarily due to quantum nuclear effects; again, the weak chemical bonding makes it a secondary effect.

We performed inelastic neutron scattering measurements on a polycrystalline sample of a classical kagome antiferromagnet ${\mathrm{NaBa}}_2{\mathrm{Mn}}_3{\mathrm{F}}_{11}$ to investigate the possibility of a dispersionless zero-energy excitation associated with rotation of spins along the chains. The observed spectra indeed exhibit such an excitation with strong intensity at low energy, as well as dispersive excitations with weak intensity at high energy. Combining the measurements with calculations from linear spin-wave theory reveals that ${\mathrm{NaBa}}_2{\mathrm{Mn}}_3{\mathrm{F}}_{11}$ is a good realization of the classical kagome antiferromagnet which exhibits a dispersionless mode lifted by the magnetic dipole-dipole interaction.

A recent theory [Metlov and Michels, Phys. Rev. B 91, 054404 (2015)] predicts a qualitative effect in the magnetic small-angle neutron scattering (SANS) cross section of statistically isotropic disordered ferromagnetic media. The effect is due to the third-order terms in the amplitude of the inhomogeneities. Here, its existence is demonstrated both numerically via large-scale micromagnetic simulations and analyzed experimentally in a two-phase iron-based nanocomposite. The previous model is extended to an arbitrary spatial defect profile, which allows us to describe the experimental field dependence of the third-order SANS effect quantitatively.

High-precision radio-frequency magnetic susceptibility measurements were performed on single crystals of fully deuterated $\kappa \text{−}{\left(\mathrm{ET}\right)}_2\mathrm{Cu}\left[\mathrm{N}{\left(\mathrm{CN}\right)}_2\right]\mathrm{Br}$, hereafter designated as $\kappa \text{−}{\left(\mathrm{D}8\mathrm{ET}\right)}_2\mathrm{Cu}\left[\mathrm{N}{\left(\mathrm{CN}\right)}_2\right]\mathrm{Br}$. This material phase separates into superconducting and antiferromagnetic regions, the degree of which depends strongly upon the cooling rate. We show that the screening fraction ${\eta }_{\text{sc}}$ varies logarithmically with the cooling rate over nearly five decades. The average size of superconducting regions is estimated to vary from 5 to $40\mu \mathrm{m}$, depending upon cooling rate, consistent with previous infrared microscopy measurements. In the region $T\lesssim T_c/3$, the effective magnetic penetration depth exhibits power-law behavior $\lambda \left(T\right)-\lambda \left(0\right)\sim T^n$ with $n=1.6$, independent of the cooling rate. Changes in cooling rate and the consequent phase separation evidently do not introduce the kind of disorder that would alter the exponent $n$ in a $d$-wave superconductor. The exponent remains close to $n=$ 1.5, reported in single crystals of $\kappa \text{−}{\left(\mathrm{ET}\right)}_2\mathrm{Cu}\left[\mathrm{N}{\left(\mathrm{CN}\right)}_2\right]\mathrm{Br}$ and $\kappa \text{−}{\left(\mathrm{ET}\right)}_2\mathrm{Cu}{\left(\mathrm{NCS}\right)}_2$ [A. Carrington et al., Phys. Rev. Lett 83, 4172 (1999)]. The transition temperature fell linearly with $1-{\eta }_{\text{sc}}$. Measurements were also made on $\kappa \text{−}{\left(\mathrm{ET}\right)}_2\mathrm{Cu}\left[\mathrm{N}{\left(\mathrm{CN}\right)}_2\right]\mathrm{Cl}$ of normal isotopic abundance in which a very small amount of superconducting phase ${\eta }_{\text{sc}}\approx {10}^{-4}$ developed, presumably through the strain-induced sample mounting. This material showed a power-law exponent of $n=1.64$, independent of the cooling rate.

The three-band d-p model is investigated by means of a variational Monte Carlo (VMC) method with the BCS-like wave-function supplemented by the Gutzwiller and Jastrow correlators. The VMC optimization leads to a $d\text{−}\mathit{wave}$ superconducting state with a characteristic domelike shape of the order parameter for hole doping $\delta \lesssim 0.4$, in good agreement with the experimental observations. Also, the off-diagonal pair-pair correlation functions, calculated within VMC, vindicates the results obtained very recently within the diagrammatic expansion of the Gutzwiller wave function method [cf. Zegrodnik, Biborski, Fidrysiak, and Spałek, Phys. Rev. B 99, 104511 (2019)]. Subsequently, the nature of the $d\text{−}\mathit{wave}$ pairing is investigated by means of recently proposed minimal-size real-space d-wave pairing operators [Moreo and Dagotto, Phys. Rev. B 100, 214502 (2019)]. An emergence of the long-range superconducting ordering for both $d$ and $p$ orbitals is reported by analyzing the corresponding off-diagonal pair-pair correlation functions. The dominant character of d-wave pairing on $d$ orbitals is confirmed. Additionally, the trial wave function is used to investigate the magnetic properties of the system. The analysis of spin-spin correlation functions is carried out and shows antiferromagnetic $\mathbf{q}=(\pi ,\pi )$, short-range order, as expected. For the sake of completeness, the charge gap has been estimated, which for the parent compound takes the value ${\mathrm{\Delta }}_{\text{CG}}\approx 1.78\pm 0.51\text{eV}$, and agrees with values reported experimentally for the cuprates.

Owing to their structural complexity and wide range of possible chemical combinations, perovskite oxides exhibit many technically important physical properties. Pressure is a thermodynamic parameter which is useful for tuning physical properties; however, the response of the complex crystal structure to high pressure has not been thoroughly studied and rationalized. This study focuses on in situ high-pressure x-ray diffraction of the orthorhombic perovskite oxides $A^{3+}{B}^{3+}{\mathrm{O}}_3$, commonly found for the rare-earth transition-metal oxides of the $RM{\mathrm{O}}_3$ formula. Each of the four families of $RM{\mathrm{O}}_3$ ($M=\mathrm{Ti}$, Cr, Mn, Fe) perovskites in this study all crystallize in the same orthorhombic perovskite structure with the Pbnm space group. The lanthanide contraction in these materials leads to varying degrees of orthorhombic distortions that are primarily associated with octahedral site rotations. The pressure-induced change of the lattice parameters demonstrates an evolution from a suppression to an enlargement of the orthorhombic distortion for substitution of the rare-earth element from $R=\mathrm{La}$ to Lu in $RM{\mathrm{O}}_3$ perovskites. This unusual crossover of the lattice parameters’ dependence on pressure contradict the results from first-principles calculation but can be rationalized by the intrinsic distortion of the perovskite structure.

The ground-state structure of ${\mathrm{BaZrO}}_3$ is experimentally known to be cubic down to absolute zero. However, there exist several measured properties and experimental characterizations that earlier computational works have failed to accurately describe and explain within this cubic symmetry. Among these properties and observations are the dielectric constant and the parallel mean-squared relative displacement value that tracks the fluctuations in distance for Ba-O atom pairs. Previous density-functional theory (DFT) studies have resolved the issue by assuming that ${\mathrm{BaZrO}}_3$ undergoes a phase transition from cubic to tetragonal $I4/mcm$ symmetry, possibly while forming a glasslike state that reflects cubic symmetry on average. In this paper, we show that the set of experimental results can indeed be satisfactorily explained by DFT entirely within the cubic symmetry. We find that past theory limitations arose from the choice of exchange-correlation-functional approximations and that the inclusion of Fock exchange in hybrids significantly improves the DFT performance. We also find that the inclusion of nonlocal correlation effects is beneficial. We conclude by making a prediction for the phase-transition pressure for the transition from cubic to tetragonal symmetry at zero kelvin.

The low lattice thermal conductivity in inorganic clathrates has been shown recently to be related to the low-energy range of optical phonons dominated by motions of guest atoms trapped in a network of host covalent cages. A promising route to further reduce the heat conduction, and increase the material efficiency for thermoelectric heat waste conversion, is then to lower the energy of these guest-weighted optical phonons. In the present work, the effect of the host cage geometry is explored. The lattice dynamics of the binary type-IX clathrate, $\mathrm{B}{\mathrm{a}}_{24}\mathrm{S}{\mathrm{i}}_{100}$, has been investigated experimentally by means of inelastic neutron scattering as a function of temperature between 5 and 280 K, and computed by ab initio density functional techniques. It is compared with the lattice dynamics of $\mathrm{B}{\mathrm{a}}_8\mathrm{S}{\mathrm{i}}_{46}$, the simplest representative of the well-known type-I clathrate structure. The binary $\mathrm{B}{\mathrm{a}}_8\mathrm{S}{\mathrm{i}}_{46}$ and $\mathrm{B}{\mathrm{a}}_{24}\mathrm{S}{\mathrm{i}}_{100}$ materials have both a cubic unit cell made of different Si cages. The energies, the degree of anharmonicity as well as the anisotropy of the optical phonon modes weighted by Ba motions are found to depend strongly on the size and shape of the cages. The lowest optical phonon energies in $\mathrm{B}{\mathrm{a}}_{24}\mathrm{S}{\mathrm{i}}_{100}$ are found around 2.5–4 meV, while those in $\mathrm{B}{\mathrm{a}}_8\mathrm{S}{\mathrm{i}}_{46}$ have higher energies around 7–9 meV. The low-lying optical phonons in $\mathrm{B}{\mathrm{a}}_{24}\mathrm{S}{\mathrm{i}}_{100}$ are mainly weighted by the motion of Ba in the opened $\mathrm{S}{\mathrm{i}}_{20}$ cage, which does not exist in $\mathrm{B}{\mathrm{a}}_8\mathrm{S}{\mathrm{i}}_{46}$. Moreover, the Ba vibrations within the opened $\mathrm{S}{\mathrm{i}}_{20}$ cages are found intrinsically anisotropic, strongly dispersionless in some directions, and exhibit a significant anharmonicity, which is not observed for any optical phonon modes in $\mathrm{B}{\mathrm{a}}_8\mathrm{S}{\mathrm{i}}_{46}$.

Current-induced effective magnetic fields provide efficient methods to electrically control the magnetization switching in ultrathin magnetic films. It is getting clearer that the two terms of spin-orbit torque (SOT), i.e., the dampinglike SOT and the fieldlike SOT, play different roles during the magnetization switching process. Fast and direct estimation of both effective fields are crucial for highly efficient magnetization switching. Methods to extract the amplitudes of the effective fields have been intensively investigated, but they are either complex or require multiparameter fitting, especially for the fieldlike field. We introduce the direct detection of SOT effective fields using hysteresis-loop shift through the magneto-optical Kerr effect in the out-of-plane Pt/Co/W and in-plane Pt/Fe/MgO trilayer systems. The results show strong agreement with transport measurements. Benefiting from noncontact optical detection, our approach in the detection of the spin-orbit effective field has great advantages in the simplified device fabrication processing, and it is suitable not only for metallic systems but also for insulating systems, which paves the way to direct detection of SOT effective fields.

We introduce a phenomenological model for a pairwise repulsive interaction potential of vortices in a type-II superconductor, consisting of superimposed sixfold and twelvefold anisotropies. Using numerical simulations we study how the vortex lattice configuration varies as the magnitudes of the two anisotropic interaction terms change. A triangular lattice appears for all values, and rotates through ${30}^{\circ }$ as the ratio of the sixfold and twlevefold anisotropy amplitudes is varied, in agreement with experimental results. The transition causes the vortex lattice to split into domains that have rotated clockwise or counterclockwise, with grain boundaries that are “decorated” by dislocations consisting of fivefold and sevenfold coordinated vortices. We also find intradomain dislocations and defects, and characterize them in terms of their energy cost. We discuss how this model could be generalized to other particle-based systems with anisotropic interactions, such as colloids, and consider the limit of very large anisotropy where it is possible to create cluster crystal states.

We numerically investigate the effect of an edge indentation on the threshold field of thermomagnetic instabilities in superconducting films subjected to a ramping magnetic field, applied perpendicular to the plane of the film. In particular, we are able to address the question on whether edge indentations promote magnetic flux avalanches. For the magnetic field-independent critical current density model, the triggering of the first magnetic flux avalanche systematically occurs at the edge indentation. In contrast to that, for the more realistic field-dependent critical current density model the first flux avalanche can take place either at or away from the indentation. This selective triggering of magnetic flux avalanches is shown to result from two effects. Namely, (i) the variation of the threshold magnetic field for the first flux avalanche triggered at the indentation and (ii) the reduction of the critical current density by large local magnetic fields at the tip of the indentation which translates in a lower power density dissipated near the tip. We demonstrate that this interplay can be tuned by varying the indentation size, ramp rate of applied field ${\dot{H}}_a$, and working temperature $T_0$. We build up a phase diagram in the ${\mu }_0{\dot{H}}_a-T_0$ plane with well-defined boundaries separating three distinct regimes of thermomagnetic instability.

Weyl semimetals in a magnetic field give rise to interesting nonlocal electronic orbits: the ballistic transport through the bulk enabled by the chiral Landau levels is combined with a momentum-space sliding along the surface Fermi-arc driven by the Lorentz force. Bulk chiral Landau levels can also be induced by axial fields whose sign depends on the chirality of the Weyl point. However, the microscopic perturbations that give rise to them can be described in terms of gauge fields only in the low-energy sectors around the Weyl points. In addition, since pseudofields are intrinsic, there is no apparent reason for a Lorentz force that causes sliding along the Fermi arcs. Therefore, the existence of nonlocal orbits driven exclusively by pseudofields is not obvious. Here we show that for systems with at least four Weyl points in the bulk spectrum, nonlocal orbits can be induced by axial fields alone. We discuss the underlying mechanisms by a combination of analytical semiclassical theory, the microscopic numerical study of wave-packet dynamics, and a surface Green's function analysis.

The coupling between fermionic matter and gauge fields plays a fundamental role in our understanding of nature, while at the same time posing a challenging problem for theoretical modeling. In this situation, controlled information can be gained by combining different complementary approaches. Here, we study a confinement transition in a system of $N_{\mathrm{f}}$ flavors of interacting Dirac fermions charged under a U(1) gauge field in $2+1$ dimensions. Using quantum Monte Carlo simulations, we investigate a lattice model that exhibits a continuous transition at zero temperature between a gapless deconfined phase, described by three-dimensional quantum electrodynamics, and a gapped confined phase, in which the system develops valence-bond-solid order. We argue that the quantum critical point is in the universality class of the ${\mathrm{QED}}_3$-Gross-Neveu-XY model. We study this field theory within a $1/N_{\mathrm{f}}$ expansion in fixed dimension as well as a renormalization group analysis in $4-\epsilon$ space-time dimensions. The consistency between numerical and analytical results is revealed from large to intermediate flavor number.