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Two novel properties, unique for semiconductors: a negative electron affinity [1-2], and a high p-type surface electrical conductivity [3-4], were discovered in diamond at the end of the last century. Both properties appear when the diamond surface is hydrogenated. A natural question arises: is the influence of the surface hydrogen on diamond limited only to the electrical properties? Here, we report the first observation of a transparency peak at 1328 cm-1 in IR absorption of hydrogen-terminated pure (undoped) nanodiamonds. This new optical property is ascribed to Fano-type destructive interference between zone-center phonons and free carriers (holes) appearing in the near-surface layer of hydrogenated nanodiamond. Our work opens the way to exploring the physics of electron-phonon coupling in undoped diamonds and promises the application of the H-terminated nanodiamonds as a new optical material with an induced transparency in IR optical range., Comment: 15 pages, 7 figures

We consider how electron-phonon interaction influences the insulator-metal transitions driven by doping in the strongly correlated system. Using the polaronic version of the generalized tight-binding method, we investigate a multiband two-dimensional model taking into account both Holstein and Su-Schrieffer-Heeger types of electron-lattice contributions. For adiabatic ratio of the hopping parameter and the phonon field energy, different types of band structure evolution are observed in a wide electron-phonon parameter range. We demonstrate the relationship between transition features and such properties of the system as the polaron and bipolaron crossovers, pseudogap behavior of various origin, orbital selectivity, and the redistribution of the spectral weight due to the electron-phonon interaction., Comment: 6 pages with 4 figures

Studying the tight binding model in an applied rational magnetic field (H) we show that in graphene there are very unusual Landau levels situated in the immediate vicinity of the saddle point (M-point) energy epsilon_M. Landau levels around $\epsilon_M$ are broadened into minibands (even in relatively weak magnetic fields ~40-53 T) with the maximal width reaching 0.4-0.5 of the energy separation between two neighboring Landau levels though at all other energies the width of Landau levels is practically zero. In terms of the semiclassical approach a broad Landau level or magnetic miniband at epsilon_M is a manifestation of the so called self-intersecting orbit signifying an abrupt transition from the semiclassical trajectories enclosing the $\Gamma$ point to the trajectories enclosing the K point in the momentum space. Remarkably, the saddle point virtually does not affect the diamagnetic response of graphene, which is caused mostly by electron states in the vicinity of the Fermi energy \epsilon_F. Experimentally, the effect of the broading of Landau levels can possibly be observed in twisted graphene where two saddle point singularities can be brought close to the Fermi energy.

Combining a precise ab initio electron band structure calculation of the TiO2 rutile structure with the temperature evolution of the Ti mean-square displacements, we reproduce a puzzling temperature increase of the electric field gradient at Ti sites in TiO2, observed experimentally. Our method employs a procedure of averaging two quadrupole electron density components (L = 2) inside a sphere vibrating with the Ti nucleus at its center, where the key factor introducing the temperature dependence is the square root of the Debye-Waller factor. Although the Debye-Waller factor always reduces the corresponding Fourier component, in TiO2 due to the interplay between terms of opposite signs, it results in a net increase of the whole sum with temperature, leading to the growth of the electric field gradient. Quantitatively, we find that the increase of electric field gradient is only half of the experimental value, which we ascribe to anharmonic effects or a strong oxygen position influence. In addition, our method reproduces the unusual temperature dependence of the asymmetry parameter eta, which first decreases with temperature, goes to zero and then increases., Comment: 9 pages, 7 figures, 1 Table

We explore an unusual nature of chemical bonding of the thorium atom with a ring of six carbon atoms (hexagon) in novel carbon materials. Our ab initio calculations of Th-based metallofullerenes (Th@C60, Th@C20) and Th bound to benzene or coronene at the Hartree-Fock level with the second order perturbation (MP2) correction accounting for the van der Waals interactions, demonstrate that the optimal position of the thorium atom is where it faces the center of a hexagon and is located at a distance of 2.01-2.07 A from the center. For Th encapsulated in C60 it is found at 2.01 A, whereas the other local energy minima are shifted to larger energies (0.22 eV and higher). Inside C60 the highest local minimum at 1.17 eV is observed when Th faces the center of the five member carbon ring (pentagon). Based on our calculations for Th with benzene and coronene where the global minimum for Th corresponds to its position at 2.05 A (benzene) or 2.02 A (coronene) from the hexagon center, we conclude that a well pronounced minimum is likely to present in graphene and in a single wall carbon nanotube. The ground state of Th is singlet, other high spin states (triplet and quintet) lie higher in energy (> 1.62 eV). We discuss a potential use of the carbon nanomaterials with the 229Th isotope having the nuclear transition of the optical range, for metrological purposes., Comment: 7 pages, 5 figures, 2 tables

We consider a Hamiltonian decomposition problem of partitioning a regular graph into edge-disjoint Hamiltonian cycles. It is known that verifying vertex non-adjacency in the 1-skeleton of the symmetric and asymmetric traveling salesperson polytopes is NP-complete. On the other hand, a sufficient condition for two vertices to be non-adjacent can be formulated as a combinatorial problem of finding a second Hamiltonian decomposition of a 4-regular multigraph. We present two backtracking algorithms for constructing a second Hamiltonian decomposition and verifying vertex non-adjacency: an algorithm based on a simple path extension and an algorithm based on the chain edge fixing procedure. Based on the results of computational experiments for undirected multigraphs, both backtracking algorithms lost to the known general variable neighborhood search heuristics. However, for directed multigraphs, the algorithm based on chain fixing of edges showed results comparable to heuristics on instances with an existing solution and better results on infeasible instances where the Hamiltonian decomposition does not exist., Comment: English translation

Within the multielectron model of magnetic insulator with spin crossover under high pressure we have studied the mean field phase diagrams in pressure temperature plane and dynamics of a sudden excited non equilibrium spin state. We obtain the different relaxation of the magnetization, high spin/low spin occupation numbers, and the metal oxygen bond length for different values of the external pressure. We found the long living oscillations of magnetization without pressure and at small external pressure. Close to crossover pressure the smooth relaxation is accompanied with a set of sharp strongly non linear oscillations of magnetization and HS/LS occupation numbers that are accompanied by the Franck Condon resonances.

The Shafarevich-Tate group $W (\mathscr{A})$ measures the failure of the Hasse principle for an abelian variety $\mathscr{A}$. Using a correspondence between the abelian varieties and the higher dimensional non-commutative tori, we prove that $W (\mathscr{A})\cong Cl~(\Lambda)\oplus Cl~(\Lambda)$ or $W (\mathscr{A})\cong \left(\mathbf{Z}/2^k\mathbf{Z}\right) \oplus Cl_{~\mathbf{odd}}~(\Lambda)\oplus Cl_{~\mathbf{odd}}~(\Lambda)$, where $Cl~(\Lambda)$ is the ideal class group of a ring $\Lambda$ associated to the K-theory of the non-commutative tori and $2^k $ divides the order of $Cl~(\Lambda)$. The case of elliptic curves with complex multiplication is considered in detail., Comment: 12 pages

The increasing importance of well-controlled ordered nanostructures on surfaces represents a challenge for existing metrology techniques. To develop such nanostructures and monitor complex processing constraints fabrication, both a dimensional reconstruction of nanostructures and a characterization (ideally a quantitative characterization) of their composition is required. In this work, we present a soft X-ray fluorescence-based methodology that allows both of these requirements to be addressed at the same time. By applying the grazing-incidence X-ray fluorescence technique and thus utilizing the X-ray standing wave field effect, nanostructures can be investigated with a high sensitivity with respect to their dimensional and compositional characteristics. By varying the incident angles of the exciting radiation, element-sensitive fluorescence radiation is emitted from different regions inside the nanoobjects. By applying an adequate modeling scheme, these datasets can be used to determine the nanostructure characteristics. We demonstrate these capabilities by performing an element-sensitive reconstruction of a lamellar grating made of Si$_3$N$_4$, where GIXRF data for the O-K$\alpha$ and N-K$\alpha$ fluorescence emission allows a thin oxide layer to be reconstructed on the surface of the grating structure. In addition, we employ the technique also to three dimensional nanostructures and derive both dimensional and compositional parameters in a quantitative manner., Comment: 7 pages, 7 figures

Electron-phonon coupling, diagonal in a real space formulation, leads to polaron paradigm of smoothly varying properties. However, fundamental changes, namely the singular behavior of polarons, occur if non-diagonal pairing is involved into consideration. The study of polaron transformations and related properties of matter is of particular interest for realistic models, since competition between diagonal and non-diagonal electron-phonon contributions in the presence of other strong interactions can result in unconventional behavior of the system. Here we consider the multiband pd-model of cuprate superconductors with electron-phonon interaction and analyze the features of the systems that are caused by the competition of diagonal and non-diagonal electron-phonon contributions in the limit of strong electron correlations. Using the polaronic version of the generalized tight-binding method, we describe the evolution of the band structure, Fermi surface, density of states at Fermi level, and phonon spectral function in the space of electron-phonon parameters ranging from weak to strong coupling strength of the adiabatic limit. On the phase diagram of polaron properties we reveal two quantum phase transitions and show how electron-phonon interaction gives rise to Fermi surface transformation (i) from hole pockets to Fermi arcs and (ii) from hole to electron type of conductivity. We also demonstrate the emergence of new states in the phonon spectral function of the polaron and discuss their origin., Comment: 14 pages, 7 figures

Based on ab initio band structure calculations we formulate a general theoretical method for description of the temperature dependence of electric field gradient in solids. The method employs a procedure of averaging multipole electron density component (l \neq 0) inside a sphere vibrating with the nucleus at its center. As a result of averaging each Fourier component (K \neq 0) on the sphere is effectively reduced by the square root of the Debye-Waller factor [exp(-W)]. The electric field gradient related to a sum of K-components most frequently decreases with temperature (T), but under certain conditions because of the interplay between terms of opposite signs it can also increase with T. The method is applied to calculations of the temperature evolution of the electric field gradients of pristine zinc and cadmium crystallized in the hexagonal lattice. For calculations within our model of crucial importance is the temperature dependence of mean-square displacements which can be taken from experiment or obtained from the phonon modes in the harmonic approximation. For the case of Zn we have used data obtained from single crystal x-ray diffraction. In addition, for Zn and Cd we have calculated mean-square displacements with the density functional perturbation treatment of the Quantum Espresso package. With the experimental data for displacements in Zn our calculations reproduce the temperature dependence of the electric field gradient very accurately. Within the harmonic approximation of the Quantum Espresso package the decrease of electric field gradients in Zn and Cd with temperature is overestimated. Our calculations indicate that the anharmonic effects are of considerable importance in the temperature dependence of electric field gradients., Comment: 13 pages, 11 figures

Following the recent demonstration of grazing-incidence X-ray fluorescence (GIXRF) based characterization of the 3D atomic distribution of different elements and dimensional parameters of periodic nanoscale structures, this work presents a new computational scheme for the simulation of the angular dependent fluorescence intensities from such periodic 2D and 3D nanoscale structures. The computational scheme is based on the dynamical diffraction theory in many-beam approximation, which allows to derive a semi-analytical solution to the Sherman equation in a linear-algebraic form. The computational scheme has been used to analyze recently published GIXRF data measured on 2D Si3N4 lamellar gratings, as well as on periodically structured 3D Cr nano pillars. Both the dimensional and structural parameters of these nanostructures have been reconstructed by fitting numeric simulations to the experimental GIXRF data. Obtained results show good agreement with nominal parameters used in the manufacturing of the structures, as well as with reconstructed parameters based on the previously published finite element method simulations, in case of the Si3N4 grating.