In this paper the results of numerical simulation of graphene effective field theory in external magnetic field are presented. The numerical simulation is performed using noncompact ($3+1$)-dimensional Abelian lattice gauge fields and ($2+1$)-dimensional staggered lattice fermions. The dependences of fermion condensate and conductivity on the dielectric permittivity of the substrate for different values of external magnetic field are calculated. It is found that magnetic field shifts insulator-semimetal phase transition to larger values of the dielectric permittivity of the substrate. The phase diagram of graphene in external magnetic field is drawn.

A systematic study on the anharmonicity of phonons is made for single-crystal type-I clathrates: n-type ${\text{Ba}}_8$${\text{Ga}}_{16}$${\text{Ge}}_{30}$ (n-BGG), p-type ${\text{Ba}}_8$${\text{Ga}}_{16}$${\text{Ge}}_{30}$ (p-BGG), n-type ${\text{Sr}}_8$${\text{Ga}}_{16}$${\text{Ge}}_{30}$ (n-SGG), n-type ${\text{K}}_8$${\text{Ga}}_{16}$${\text{Sn}}_{30}$ (n-KGSn), and n-type ${\text{Ba}}_8$${\text{Ga}}_{16}$${\text{Sn}}_{30}$ (n-BGSn), based on their heat capacity $C_p$ at low temperatures (T) down to 360 mK. The low-T linear terms ${}^{obs}\gamma T$ of $C_p$, including the tunneling term of the atoms accommodated in the host cages (${\gamma }_{ph}T=\alpha T$) and the Sommerfeld itinerant-electron term (${\gamma }_{e}T$), are successfully separated through careful measurements of single crystals with various carrier concentrations. The values of the minimum density of anharmonic potentials are deduced from $\alpha$ to be $0.12\pm 0.24$ for n-KGSn, $0.47\pm 0.24$ for n-BGG, $1.9\pm 0.8$ for p-BGG, $6.0\pm 0.9$ for n-SGG, and $10.9\pm 0.7$ for n-BGSn in units of $\times$10${}^{15}$ cm${}^{-3}$. The effective mass ($m^{*}/m_0$) is determined from ${\gamma }_e$ to be $1.01\pm 0.25$ for n-BGG, $1.20\pm 0.19$ for p-BGG, $1.68\pm 0.24$ for n-SGG, $1.86\pm 0.54$ for n-KGSn, and 2.05$\pm$0.48 for n-BGSn in units of free electron mass $m_0$, and the electron-phonon interaction strength can be evaluated from these values. It is shown that both the thermal conductivity ($\kappa$) and the electron-phonon interaction strength ($\lambda$) agree well with the $\alpha$ parameters deduced from $C_p$. The differences in $\kappa$ known between n- and p-BGGs are ascribed to the influence of defects at the crystallographic 6c sites, which are clearly indicated by magnetic susceptibility measurements. This is very different from the situation in the other clathrates.

An open question in the behavior of metals subjected to shock is the nature of the deformation that couples to the phase transformation process. Experiments to date cannot discriminate between the role of known deformation processes such as twinning or dislocations accompanying a phase change, and modes that can become active only in extreme environments. We show that a deformation mode not present in static conditions plays a dominant role in mediating plastic behavior in hcp metals and determines the course of the transformation. Our molecular dynamics simulations for titanium demonstrate that the transformation is preceded by a 90° lattice reorientation of the parent, and the growth of the reoriented domains is accompanied by the collective action of dislocations and deformation twins. We suggest how diffraction and transmission electron microscopy experiments may validate our findings.

We study dynamics of the electron spin of a nitrogen-vacancy (NV) center subjected to a strong driving field with periodically reversed direction (train of rotary echoes). We use analytical and numerical tools to analyze in detail the form and time scales of decay of the rotary echo train by modeling the decohering spin environment as a random magnetic field. We demonstrate that the problem can be exactly mapped onto a model of spin 1 coupled to a single bosonic mode with imaginary frequency. This mapping allows comprehensive analytical investigation beyond the standard Bloch-Redfield-type approaches. We explore the decay of the rotary echo train under assumption of strong driving and identify the most important regimes of the decay. The analytical results are compared with the direct numerical simulations to confirm quantitative accuracy of our study. We present the results for realistic environment of substitutional nitrogen atoms (P1 centers) and provide a simplified but accurate description for the decay of the rotary echo train of the NV center's spin. The approach presented here can also be used to study decoherence and longitudinal relaxation of other spin systems under conditions of strong driving.

We study the ${\mathbb{Z}}_2$ topologically ordered surface state of three-dimensional bosonic SPT phases with the discrete symmetries ${\mathrm{G}}_1\times {\mathrm{G}}_2$. It has been argued that the topologically ordered state cannot be realized on a purely two-dimensional lattice model. We carefully examine the statement and show that the surface state should break ${\mathrm{G}}_2$ if the symmetry ${\mathrm{G}}_1$ is gauged on the surface. This manifests the conflict of the symmetry ${\mathrm{G}}_1$ and ${\mathrm{G}}_2$ on the surface of the three-dimensional SPT phase. Given that there is no such phenomena in the purely two-dimensional model, it signals that the symmetries are encoded anomalously on the surface of the three-dimensional SPT phases and that the surface state can never be realized on the purely two-dimensional models.

Semiconductor superlattices may display dispersions that are degenerate either at the zone center or zone boundary [G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures, Monographies de Physique (Les Éditions de Physique, Les Ulis, 1988); C. Sirtori, F. Capasso, D. L. Sivco, and A. Y. Cho, Appl. Phys. Lett. 64, 2982 (1994)]. We show that they are linear upon the wave vector in the vicinity of the crossing point. This establishes a realisation of massless Dirac bands within semiconductor materials. We show that the eigenstates and the corresponding Wannier functions of these superlattices have peculiar symmetry properties. We discuss the stability of the properties of such superlattices versus the electron in-plane motion. As a distinct fingerprint, the inter-sub-band magnetoabsorption spectrum for such superlattices is discussed.

We report on a remarkable effect of pseudospin precession on the collective motion of exciton-polaritons in a microresonator coherently driven by a linearly polarized pump. In particular, we show that hexagonal patterns can undergo a spontaneous symmetry breaking of their polarization and start a uniform motion in the plane of the resonator. Similar to the optical spin Hall effect, this becomes possible due to a spin-orbit interaction induced by a longitudinal-transverse splitting (TE-TM splitting) of the photonic resonator mode. We derive a simple analytical expression for the drift velocity of the patterns.

Efficient second-harmonic generation may be induced based on the anomalous tunneling properties of double zero-permittivity narrow cross-slit nonlinear channels. Ideal phase matching conditions, large coherence length, combined with uniform field enhancement entail the ideal conditions to achieve giant second-harmonic conversion efficiencies for backward and forward signals. It is shown that these conditions are particularly well suited to enhance nonlinear effects over a wide range of frequencies, leading to efficient electromagnetic wave mixers and parametric amplifiers.

We have investigated the formation of a dislocation network that develops at the interface of a Ag film on $\mathrm{Pt}\mathrm{(111)}$ and its evolution with film thickness at 600 K and above. This system is commonly considered to be representative of a surface-confined alloy, and we have studied the structure and topography of the films' surfaces up to thicknesses of 35 ML using high-resolution low-energy electron diffraction. The network is formed during the growth of the second layer and is fully developed already for films only a few layers thick. The spacing of the network varies between 5.8 and 6.6 nm when grown at 600 and 800 K, respectively. This dependence on the growth temperature is attributed to a temperature-dependent material mixing in the first (few) layers of the film. This mixing is irreversibly set by the deposition temperature and even persists during prolonged annealing at a temperature close to the desorption of Ag from $\mathrm{Pt}\mathrm{(111)}$.

We investigate crystal plane stacking in InP nanowires with marked wurtzite/zinc-blende phase mixing. We measure the length distributions of hexagonal and cubic segments and the frequencies of all short sequences of monolayers. This reveals spatial correlations extending over several monolayers, which we describe in terms of conditional probabilities. Results can be modeled by considering the energy barriers for nucleation on top of all types of preexisting stacking. A quantitative agreement is obtained only if the interaction with the underlying layers involves the edge energy of the nucleus.

Homogenization of metamaterials based on the analysis of their reflection and transmission spectra often leads to nonphysical values of the effective permittivity and permeability. Here we address this challenge by analyzing the scattering spectra in terms of perfectly emitting and absorbing modes considering nonlocal constitutive relations. The decomposition of the scattering spectra into even and odd modes permits us to quantify the nonlocal contributions and provides explicit formulas for the effective permittivity and permeability which always satisfy the passivity and causality constraints.

Negatively charged nitrogen-vacancy (NV${}^{-}$) centers in diamond have generated much recent interest for their use in sensing. The sensitivity improves when the NV ground-state microwave transitions are narrow, but these transitions suffer from inhomogeneous broadening, especially in high-density NV ensembles. To better understand and remove the sources of broadening, we demonstrate room-temperature spectral “hole burning” of the NV ground-state transitions. We find that hole burning removes the broadening caused by magnetic fields from ${}^{13}$C nuclei and demonstrate that it can be used for magnetic-field-insensitive thermometry.

A theoretical investigation of the single-particle polariton properties for a microcavity embedding a charged quantum well is presented. The electron-gas optical susceptibility is calculated numerically using the method devised by Combescot and Nozières [J. Phys. (Paris) 32, 913 (1971)]. The role of many-body effects, such as the Fermi edge singularity and Anderson orthogonality catastrophe, in the polariton formation is elucidated. By tuning the light-matter coupling the short-time behavior of the electron-gas response function is probed, and comparisons with earlier results only using the long-time response are made. Various single-particle polariton properties such as the Rabi splitting, line shape, Hopfield coefficients, and effective mass are discussed. These are experimentally accessible quantities and thus allow for a comparison with the presented theory.

We have combined magneto-optical Kerr effect, scanning tunneling microscopy, and x-ray magnetic circular dichroism to study the magnetic properties and the morphology of Fe nanoparticles grown on 2 ML thick ${\text{Al}}_2$${\text{O}}_3$/${\text{Ni}}_3\mathrm{Al}\mathrm{(111)}$-$(\sqrt{67}\times \sqrt{67})\mathrm{R}12.2^{\circ }$ with and without Pd seeding. The ${\text{Ni}}_3\mathrm{Al}\mathrm{(111)}$ substrate is ferromagnetic and shows two transition temperatures. The first, $T_{{\mathrm{C}}_1}=81\pm 3$ K, is attributed to a 20–30 nm thick slightly Ni enriched region; the second, $T_{{\mathrm{C}}_2}=240\pm 12$ K, is attributed to a much thinner and more strongly Ni enriched near interface region that contains Ni clusters embedded in the alloy matrix. The magnetic properties of the Fe cluster superlattice are strongly influenced by the superexchange coupling between Fe clusters and the underlying Ni clusters in that near interface region. Since the Ni clusters are at different distances from the oxide/metal interface, this coupling oscillates between ferro- and antiferromagnetic such that the overall magnetic moment is not increased by the Fe clusters. Pd seeding does not influence the magnetic properties of the system. The intrinsic Fe cluster properties, such as Curie temperature and easy magnetization axis, are accessed for $T>T_{{\mathrm{C}}_2}$. We find out-of-plane easy magnetization axes and $T_{\mathrm{C}}\approx$ 300 K for cluster sizes above 440 atoms.

The phase transition from ice VII to ice X under extreme pressures is an example where quantum proton delocalization coexists with classical thermal fluctuations. We investigate this transition, including quantum effects on the nuclear motion through adapted Langevin dynamics. This approach, which allows us to follow the semiclassical trajectories of protons, provides excellent agreement with experimental vibrational spectra indicating a transition pressure of about 65 GPa. Furthermore, we map the full dynamical problem onto a pressure-dependent, one-dimensional mean-field potential for the proton. By solving exactly the corresponding Schrödinger equation, we disentangle tunneling and quantum delocalization from classical thermal effects and identify the transition through the topological changes of the proton ground state and its susceptibility. The process is dominated by quantum effects even at ambient temperature and can be considered to be a paradigmatic case of a quantum-driven phase transition.

The antipolar and antiferrodistortive (AFD) components of the antiferroelectric (AFE) transition in ${\mathrm{PbZr}}_{1-x}{\mathrm{Ti}}_x{\mathrm{O}}_3$ ($x\le 0.054$) can occur separately and with different kinetics, depending on the sample history, and are accompanied by elastic softening and stiffening, respectively. Together with the softening that accompanies octahedral tilting in the fraction of phase that is not yet transformed into AFE, they give rise to a variety of shapes of the curves of the elastic compliance versus temperature. All such anomalies found in samples with $x=0.046$ and 0.054, in addition to those already studied at $x=0.050$, can be fitted consistently with a phenomenological model based on the simple hypothesis that each of the polar and AFD transitions produces a step in the elastic modulus, whose position in temperature and width reflect the progress of each transition. The slowing of the kinetics of the transformations is correlated with the formation of defect structures during aging in the ferroelectric or AFE state, which are also responsible for a progressive softening of the lattice with time and thermal cycling, until annealing at high temperature recovers the initial conditions.

We report the magnetic characterization of the frustrated transition metal pyrochlore ${\text{NaCaCo}}_2{\mathrm{F}}_7$. This material has high spin Co${}^{2+}$ in CoF${}_6$ octahedra in a pyrochlore lattice and disordered nonmagnetic Na and Ca on the large-atom sites in the structure. Large crystals grown by the floating zone method were studied. The magnetic susceptibility is isotropic; the Co moment is larger than the spin-only value; and in spite of the large Curie Weiss theta (−140 K), freezing of the spin system, as characterized by peaks in the ac and dc susceptibility and specific heat, does not occur until around 2.4 K. This yields a frustration index of $f=-{\theta }_{\mathrm{CW}}/T_f\approx 56$, an indication that the system is highly frustrated. The observed entropy loss at the freezing transition is low, indicating that magnetic entropy remains present in the system at 0.6 K. The compound may be the realization of a frustrated pyrochlore antiferromagnet with weak bond disorder. The high magnetic interaction strength, strong frustration, and the availability of large single crystals makes ${\text{NaCaCo}}_2{\mathrm{F}}_7$ an interesting alternative to rare earth oxide pyrochlores for the study of geometric magnetic frustration in pyrochlore lattices.

Three-magnon effects are known to be important for nonlinear processes in magnetic thin films. In such a process, for example, the uniform mode at a frequency ω can decay into two modes at a lower frequency ω/2. In magnetic nanoelements, there are additional concerns which do not occur in films. First, in small elements, the excitation wave vectors become a set of discrete values. This limits the availability of final states. Second, localized modes are important in nanoelements. Our study is based on micromagnetic calculations using the Landau-Lifshitz equations. We use an oscillating magnetic field at frequency ω to drive the system and to study the response over a wide range of frequencies and for a wide set of input powers. In nanoelements, the typical response occurs not exactly at ω/2 but for several frequencies which are symmetrically spaced around ω/2. This is explained by the two considerations introduced above. We study the response both as a function of the amplitude of the driving field and as a function of the driving frequency. In this way, we can study the system response both at resonance and outside of resonance.

We study the dc Josephson effect in a clean noncentrosymmetric superconductor/ferromagnet/noncentro-symmetric superconductor junction within the quasiclassical theory of superconductivity. By considering charge and spin currents, we show that in such junctions an exotic Josephson effect can take place, depending on the superconducting pairing state and spin polarization direction. We focus on the importance of spin-triplet/spin-singlet gaps ratio in such systems showing that its value is related to the existence of even and odd high-order harmonics in the charge and spin current-phase relations, and to the possibility of 0-$\pi$ transitions.

We use ultrafast resonant x-ray diffraction to study the magnetic order in CuO under conditions of high electronic excitation. By measuring changes in the spectral shape of the ${\mathrm{Cu}}^{2+}$ magnetic (1/2 0 −1/2) reflection we investigate how an intense optical pump pulse perturbs the electronic and magnetic states. We observe an energy shift in the magnetic resonance at short times after the pump pulse. This shift is compared with expectations from band structure calculations at different electronic temperatures. This spectral line shift indicates that although the electrons are heated to effective electron temperatures far above $T_{\mathrm{N}}$ on a time scale faster than the experimental resolution, magnetic order persists in this highly excited state for several hundred femtoseconds.