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Lattice defects such as stacking faults may obscure electronic topological features of real materials. In fact, defects are a source of disorder that can enhance the density of states and conductivity of the bulk of the system and they break crystal symmetries that can protect the topological states. On the other hand, in recent years it has been shown that lattice defects can act as a source of nontrivial topology. Motivated by recent experiments on three-dimensional (3D) topological systems such as Bi$_2$TeI and Bi$_{14}$Rh$_3$I$_9$, we examine the effect of stacking faults on the electronic properties of weak topological insulators (WTIs). Working with a simple model consisting of a 3D WTI formed by weakly-coupled two-dimensional (2D) topological layers separated by trivial spacers, we find that 2D stacking faults can carry their own, topologically nontrivial gapless states. Depending on the WTI properties, as well as the way in which the stacking fault is realized, the latter can form a topologically protected 2D semimetal, but also a 2D topological insulator which is embedded in the higher-dimensional WTI bulk. This suggests the possibility of using stacking faults in real materials as a source of topologically nontrivial, symmetry-protected conducting states., Comment: 9 pages, 7 figures

We review the early works which were precursors of the Conceptual Density Functional Theory. Starting from Thomas–Fermi approximation and from the exact formulation of Density Functional Theory by Hohenberg and Kohn’s theorem, we will introduce electronegativity and the theory of hard and soft acids and bases. We will also present a general introduction to the Fukui functions, and their relation with nucleophilicity and electrophilicity, with an emphasis towards the importance of these concepts for chemical reactivity.

Leonardo è stato l'unico scienziato la cui ricerca non solo ha preso spunto da immagini, ma è avvenuta con immagini. Egli ha espresso le sue idee scientifiche non con parole o formule, ma con un linguaggio visivo. Leonardo è questa anomalia. Non si ripeterà nella storia della scienza una simile coincidenza fra scienza ed arte. Egli, inoltre, effettua una continua simbiosi tra diversi campi della scienza. Egli, ad esempio, trasferisce i suoi studi delle onde nell'acqua alle onde dell'aria o i suoi studi nell'ottica alla prospettiva nell'arte o le proprietà delle leve allo studio del moto degli arti. Leonardo è stato definito l'uomo più curioso che sia mai esistito, ed in effetti i suoi interessi spaziano tra tutti i saperi noti alla sua epoca: dalla pittura alla scultura, dalla meccanica all'idraulica, dall'architettura alla geologia, dall'anatomia alla zoologia, dalla fisiologia alla geografia, dalla matematica all'ottica, dalla statica all'astronomia ed alla botanica. In questa conferenza si accenna ad alcune delle più importanti scoperte di Leonardo, sottolineando il carattere di rottura che esse hanno rispetto alle idee dominanti nella scienza del suo tempo.

Complex phenomena, as those involving many particles, may still exhibit simple patterns, usually expressed by simple relations among relevant quantities. We briefly recount how Professor Norman March led our way through superconducting experiments for several material classes, including the high-\(T_c\) cuprates and the heavy-Fermion materials, in the unending quest for simple paths among intricated data.

Fingerprints of antiaromaticity in the negative ion (Li$_3$Al$_4$)$^-$, this species being realizable via a laser vaporization technique, are revealed by means of an \emph{ab initio} quantum-chemical investigation. First, the ground-state equilibrium geometry of this ion is predicted. Also, for the corresponding inhomogeneous electron liquid, the characteristics of the HOMO are studied, both for the square and the rectangular Al$_4$ geometry in two low-lying isomers of the negative ion. There is no particular sensitivity to the change in geometry of the Al$_4$ configuration. Therefore, we have calculated theoretically chemical shifts (NICS), which contain remarkable fingerprints of antiaromaticity. As to future directions, some comments are added in relation to the Shannon entropy., Phys. Chem. Liquids (to appear in vol. 52, 2014)

The relationship between science and religion is not a well-posed question, at least over the last decades. Indeed, it was long ago when scientists such as Boyle or Newton endeavoured to justify in which way their faith could be reconciled with their own scientific discoveries. Nowadays, most scientists seem to share the conviction that region has been and still is a hindrance towards scientific progress. On the other hand, most theologians seem to consider scientists as bold and incapable to understand that, beyond their experiments and calculations, there exists a deeper word on the human being.

For many years , the epistemological debate in Italy has been polarized between ‘internists’ and ‘externists’. That is, between those who think that the scientific ‘progress’ should be explained by means of criteria internal to science itself (and these are related to Popper), and those who think that scientific revolutions could be understood only in connection with economical, political, and social revolutions.

Tuning structural properties, e.g., by means of external pressure or applied uniaxial strain, can significantly modify the electronic properties of several solid systems, thereby influencing, or even inducing, several electronic instabilities. We specifically analyze the effect of pressure or strain on several superconducting materials, including the high-\(T_c\) cuprates , some organic salts, and magnesium diboride, on the light alkalis, where pressure can even destroy metallicity, and graphene , whose remarkable electronic and transport properties can be tailored by applied strain.

Among Ettore Majorana’s (1906–1938) earliest works, there is a brief memory on the Thomas–Fermi model , and a paper on the chemical bond in the helium molecular ion. Here, we emphasize Majorana’s hypercritical attitude even towards his own work. Besides describing Majorana’s contributions to the Thomas–Fermi model and to the understanding of the molecular bond, we argue that some of Majorana’s seminal contributions in molecular physics already prelude to the idea of exchange interactions (or Heisenberg–Majorana forces) in his later works on theoretical nuclear physics . In all his papers, he tended to emphasize the symmetries at the basis of a physical problem, as well as the limitations, rather than the advantages, of the approximations of the method employed.

This year [2015] is the centennial of the publication of Einstein’s paper (1915) on general relativity (Einstein, Sitzungsber K Preuss Akad Wiss Phys Math Kl 1915 (part 1):315, 1915, [1], Einstein, Sitzungsber. K. Preuss. Akad. Wiss Phys Math Kl 1915 (part 2):778, 1915, [2], Einstein, Sitzungsber K Preuss Akad Wiss Phys Math Kl 1915 (part 2):831, 1915, [3], Einstein, Sitzungsber K Preuss Akad Wiss Phys Math Kl 1915 (part 2):844, 1915, [4], Einstein, Sitzungsber K Preuss Akad Wiss Phys Math Kl 1915 (part 1):688, 1916, [5]). Among the numerous celebrations of Einstein’s life and works, we will here remind a probably less emphasized aspect of his activity: the quest for peace in the world.

We study the dependence on the strength and orientation of applied uniaxial strain of the Drude weight in the conductivity of graphene. We find a nonmonotonic dependence on strain, which may be related to the proximity to several strain-induced electronic topological transitions. Given the relation between the Drude weight and the long-wavelength plasmon frequency, such a strain dependence can be evidenced by infrared spectroscopy measurements., High Press. Res., to appear

The possibility of intrinsic superconductivity in alkali-coated graphene monolayers has been recently suggested theoretically. Here, we derive the possible pairing symmetries of a carbon honeycomb lattice and discuss their phase diagram. We also evaluate the superconducting local density of states (LDOS) around an isolated impurity. This is directly related to scanning tunneling microscopy experiments, and may evidence the occurrence of unconventional superconductivity in graphene., Eur. Phys. J. B, to appear

Using a proposed generalization of the pair distribution function for a gas of non-interacting particles obeying fractional exclusion statistics in arbitrary dimensionality, we derive the statistical correlations in the asymptotic limit of vanishing or low temperature. While Friedel-like oscillations are present in nearly all non-bosonic cases at T=0, they are characterized by exponential damping at low temperature. We discuss the dependence of these features on dimensionality and on the value of the statistical parameter alpha., Comment: to appear in Phys. Chem. Liquids

Ab initio calculations including electron correlation are still extremely costly except for the smallest atoms and molecules. Therefore, our purpose in the present study is to employ a bond-order correlation approach to obtain, via equilibrium molecular energies, molecular dissociation energies and heats of formation for some 20 molecules containing C, H, and O atoms, with a maximum number of electrons around 40. Finally, basis set choice is shown to be important in the proposed procedure to include electron correlation effects in determining thermodynamic properties. With the optimum choice of basis set, the average percentage error for some 20 molecules is approximately 20% for heats of formation. For molecular dissociation energies the average error is much smaller: ~0.4., Mol. Phys., to be published

We argue that an ionic lattice surrounded by a Fermi liquid changes phase several times under pressure, oscillating between the symmetric phase and a low-symmetry dimerized structure, as a consequence of Friedel oscillations in the pair potential. Phase oscillations explain the tendency towards dimerization which has been recently reported for the light alkali metals under high pressure. Moreover, a restoring of the symmetric phase is predicted for such elements at an even higher density., accepted in Eur. Phys. J. B

We propose a Ginzburg-Landau phenomenological model for the dependence of the critical temperature on microscopic strain in tetragonal high-[Formula: See Text] cuprates. Such a model is in agreement with the experimental results for LSCO under epitaxial strain, as well as with the hydrostatic pressure dependence of [Formula: See Text] in most cuprates. In particular, a nonmonotonic dependence of [Formula: See Text] on hydrostatic pressure, as well as on in-plane or apical microstrain, is derived. From a microscopic point of view, such results can be understood as due to the proximity to an electronic topological transition (ETT). In the case of LSCO, we argue that such an ETT can be driven by a strain-induced modification of the band structure, at constant hole content, at variance with a doping-induced ETT, as is usually assumed.

Three solvable models are set out in some detail in reviewing different types of phase transitions. Two of these relate directly to emergent critical phenomena, viz. melting and magnetic transitions in heavy rare-earth metals, and secondly, via the 3d Ising model, to critical behavior in an insulating ferromagnet such as CrBr3. The final "transition", however, concerns ionization of an electron in an isoelectronic series with N electrons as the atomic number Z is reduced below that of the neutral atom. These solvable models are, throughout, brought into contact either with experiment, or with very precise numerical modeling on real materials.

Egelstaff, March, and McGill (1973) proposed the extraction of electron correlation functions in liquids from scattering data. Here, we appeal to computer simulation by de Wijs et al. (1995) on the partial structure factor [GRAPHICS] between ions (i) and valence electrons (v) for liquid Mg near freezing, to write the valence-valence partial structure factor [GRAPHICS] in terms of [GRAPHICS] and the neutron structure factor [GRAPHICS] , to high accuracy.

We propose a Ginzburg-Landau phenomenological model for the dependence of the critical temperature on microscopic strain in tetragonal high-Tc cuprates. Such a model is in agreement with the experimental results for LSCO under epitaxial strain, as well as with the hydrostatic pressure dependence of Tc in most cuprates. In particular, a nonmonotonic dependence of Tc on hydrostatic pressure, as well as on in-plane or apical microstrain, is derived. From a microscopic point of view, such results can be understood as due to the proximity to an electronic topological transition (ETT). In the case of LSCO, we argue that such an ETT can be driven by a strain-induced modification of the band structure, at constant hole content, at variance with a doping-induced ETT, as is usually assumed.

Krueger some years ago proposed a cluster LiBeBCNOF, now called periodane. His ground-state isomer proposal has recently been refined by Bera et al. using DFT. Here, we take the approach of molecules in such a cluster as starting point. We first study therefore the triangular molecule LiOB by coupled cluster theory (CCSD) and thereby specify accurately its equilibrium geometry in free space. The second fragment we consider is FBeCN, but treated now by restricted Hartree-Fock (RHF) theory. This four-center species is found to be linear, and the bond lengths are obtained from both RHF and CCSD calculations. Finally, we bring these two entities together and find that while LiOB remains largely intact, FBeCN becomes bent by the interaction with LiOB. Hartree-Fock and CCSD theories then predict precisely the same lowest isomer found by Bera et al. solely on the basis of DFT., to appear in Phys. Lett. A

Three solvable models are set out in some detail in reviewing different types of phase transitions. Two of these relate directly to emergent critical phenomena, viz. melting and magnetic transitions in heavy rare-earth metals, and secondly, via the $3d$ Ising model, to critical behaviour in an insulating ferromagnet such as CrBr$_3$. The final `transition', however, concerns ionization of an electron in an isoelectronic series with $N$ electrons as the atomic number $Z$ is reduced below that of the neutral atom. These solvable models are, throughout, brought into contact either with experiment, or with very precise numerical modelling on real materials., Comment: to appear in Int. J. Mod. Phys. B

Three aspects of low-order density matrix (DM) theory will be reviewed, following some brief comments on analogies with, and differences from, density functional theory (DFT). First, the local energy equation, involving first-to-third order DMs, will be set out and applied exactly to model spin-compensated two-electron atoms. Explicit relations known between low-order DMs for harmonic confinement and arbitrary interparticle interactions will be reported for such model atoms. Second, the March-Young proposal for use variationally, satisfying N-representability, will be set out for spin-free systems such as a four-electron model in the quintet state. Third, the equation of motion for the correlated 1DM is summarised, and brief comments are made on its application to (a) the He atom and (b) crystalline Si. Finally, a model two-electron atom with Coulomb confinement plus an s-wave Coulomb repulsion modified by a δ-function radial correlation is reported as an exactly solvable example. © 2013 Copyright Taylor and Francis Group, LLC.

Uniaxial strain is known to modify significantly the electronic properties of graphene, a carbon single layer of atomic width. Here, we study the effect of applied strain on the composite excitations arising from the coupling of charge carriers and plasmons in graphene, i.e. the plasmarons. Specifically, we predict that the plasmaron energy dispersion, which has been recently observed experimentally in unstrained graphene, is shifted and broadened by applied uniaxial strain. Thus, strain constitutes an additional parameter which may be useful to tune graphene properties in plasmaronic devices., Invited oral lecture at the 23rd AIRAPT International Conference on "High Pressure Science and Technology", Mumbai (India), September 25-30, 2011. To be published in J. Phys.: Conf. Series (2012)

Quantum-chemical calculations are first reported on the building block Li2C2. Two low-lying isomers are predicted, and hence the equilibrium ground-state geometry by the coupled cluster method (CCSD). The ground-state is non-linear, contrasting with the other planar isomer. The dimer (Li2C2)(2) is then examined by the Hartree-Fock plus second-order Moller-Plesset (HF+MP2) method. The ground-state geometry is predicted to have C-4 on a linear chain. As to the trimer, the C-6 atoms are predicted at the same ab initio level to lie on a hexagon. But the Li atoms prefer each to bond to two C atoms, rather than reproduce the geometry of benzene. Finally, some contact is made with a recent density functional theory study of solid lithium carbide under pressure.

We study the effect of uniaxial strain on the transmission and the conductivity across a strain-induced barrier in graphene. At variance with conventional studies, which consider sharp barriers, we consider a more realistic, smooth barrier, characterized by a nonuniform, continuous strain profile. Our results are instrumental towards a better understanding of the transport properties in corrugated graphene., High Press. Res., to appear

Un’ottimo riassunto dei principali risultati di teoria, numerosi esercizi anche svolti e numerosi complementi sono forniti da (1975). Qui mi limito a dare le tracce di svolgimento ed i risultati di alcuni temi d’esame (alcuni sono pertinenti anche al Cap. 5 sulle trasformate di Fourier) e complementi su alcune funzioni speciali (Lebedev e Silverman, 1972).

Per questo capitolo, fare riferimento a (1980) per quanto riguarda la teoria dell’analisi funzionale, in generale, ancora a (1976) per i primi cenni relativi alla serie di Fourier, ed a (1989) per alcuni esempi ed applicazioni.

Per la teoria, cfr. (1980). La maggioranza degli esercizi e tratta da (1977). Alcuni esercizi sono tratti da (1994) e da (1997).

Il testo richiama i principali concetti, definizioni e teoremi relativi agli spazi vettoriali, agli sviluppi in serie di Fourier, alle equazioni alle derivate parziali, alle trasformate integrali di Laplace e di Fourier, ad alcune classi di equazioni integrali (con specifico riferimento alla funzione di Green). Si danno altresi' cenni di funzioni di variabile complessa, di teoria dei gruppi, e di spazi funzionali. Di ciascun argomento vengono ampiamente discusse le motivazioni e le applicazioni nel campo della fisica e, talora, di altre discipline scientifiche. Tali argomenti vengono approfonditi da esercizi (perlopiu' svolti, o con soluzione), spesso tratti da effettivi temi d'esame del corso di Metodi matematici per la fisica del corso di laurea in Fisica (Catania).