Alessandro Toschi

Bio: Alessandro Toschi is an academic researcher from Vienna University of Technology. The author has contributed to research in topics: Hubbard model & Strongly correlated material. The author has an hindex of 41, co-authored 119 publications receiving 4396 citations. Previous affiliations of Alessandro Toschi include Sapienza University of Rome & Max Planck Society.

Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory

Abstract: Strong electronic correlations pose one of the biggest challenges to solid state theory. We review recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT). On top of this, non-local correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge-, magnetic-, and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. We provide an overview of the successes and results achieved---hitherto mainly for model Hamiltonians---and outline future prospects for realistic material calculations.

Dynamical vertex approximation : A step beyond dynamical mean-field theory

Abstract: We develop a diagrammatic approach with local and nonlocal self-energy diagrams, constructed from the local irreducible vertex. This approach includes the local correlations of dynamical mean-field theory and long-range correlations beyond. It allows us, for example, to describe (para)magnons and weak localization effects---in strongly correlated systems. As a first application, we study the interplay between nonlocal antiferromagnetic correlations and the strong local correlations emerging in the vicinity of a Mott-Hubbard transition.

Turning a nickelate Fermi surface into a cupratelike one through heterostructuring.

Abstract: Using the local density approximation and its combination with dynamical mean-field theory, we show that electronic correlations induce a single-sheet, cupratelike Fermi surface for hole-doped 1=1 LaNiO3=LaAlO3 heterostructures, even though both eg orbitals contribute to it. The Ni 3d 3z 2 � 1 orbital plays the role of the axial Cu 4s-like orbital in the cuprates. These two results indicate that ‘‘orbital engineering’’ by means of heterostructuring should be possible. As we also find strong antiferromagnetic correlations, the low-energy electronic and spin excitations in nickelate heterostructures resemble those of high-temperature cuprate superconductors. The discovery of high-temperature superconductivity (HTSC) in hole-doped cuprates [1] initiated the quest for finding related transition-metal oxides with comparable or even higher transition temperatures. In some systems, such as ruthenates [2] and cobaltates [3], superconductivity has been found. However, in these t2g systems superconductivity is very different from that in cuprates, and transition temperatures (Tc’s) are considerably lower. As it became possible to grow transition-metal oxides in heterostructures, this quest got a new direction: Novel effectively two-dimensional (2D) systems could be engineered. But which oxides, besides cuprates, are most promising for getting high Tc’s? The basic band structure of the hole-doped cuprates is that of a single 2D Cu 3d x 2 � y 2-like band which is less than half filled (configuration d 9� h ). In this situation, antiferromagnetic fluctuations prevail and are often believed to mediate the superconductivity. The Fermi surface (FS) from this x 2 � y 2 band has been observed in many overdoped cuprates and found to agree with the predictions of local density-functional (LDA) band theory. Recently the following idea for arriving at a cupratelike situation in nickelates was presented [4]: Bulk LaNiO3 (d 7 ) has one electron in two degenerate eg bands, but sandwiching a LaNiO3 layer between layers of an insulating oxide such as LaAlO3 will confine the 3z 2 � 1 orbital in the z direction and may remove this band from the Fermi level, thus leaving the electron in the x 2 � y 2 band. The possibility of finding bulk nickelates with an electronic structure analogous to that of cuprates was discarded awhile ago [5], but heterostructures offer new perspectives. Indeed, a major reconstruction of orbital states at oxide interfaces may recently have been observed [6], and this kind of phenomenon could lead to novel phases not present in the bulk. Extensive theoretical studies of mechanisms for orbital selection in correlated systems [7] have revealed the complexity of this problem, where details of the electronic structure and lattice distortions play decisive roles. It is therefore crucial to examine nickelate heterostructures by means of state-of-the-art theoretical methods and find the optimal conditions for x 2 � y 2 orbital selection. In this Letter we present results of electronic-structure calculations using the merger [8] of LDA band theory, which provides an ab initio description of the materials chemistry, and the dynamical mean-field theory (DMFT) [9], which includes electronic correlations. We find that the hopping between the x 2 � y 2 and 3z 2 � 1 orbitals substantially reduces the effects of correlations in the 3z 2 � 1 orbital. In this respect, eg electrons behave very differently than the t2g electrons, which have no interorbital hopping on a square lattice. Nevertheless, we do find that the correlations may sufficiently shift the bottom of the hybridizing e g bands relatively to each other to yield a FS with only one sheet. This sheet has predominantly x 2 � y 2 character and a shape like in the cuprates with the highest Tc max (Tc at optimum hole doping) [10], but even more extreme. Moreover, stretching the in-plane lattice constants by suitable choice of substrate reduces the correlation strength needed to produce a single-sheet FS. Since we also find strong antiferromagnetic fluctuations, somewhat larger than in the cuprates, nickelate heterostructures hold the basic ingredients for high-temperature superconductivity.

Local Electronic Correlation at the Two-Particle Level

Abstract: Electronic-correlated systems are often well described by dynamical mean field theory (DMFT). While DMFT studies have mainly focused hitherto on one-particle properties, valuable information is also enclosed into local two-particle Green's functions and vertices. They represent the main ingredient to compute momentum-dependent response functions at the DMFT level and to treat nonlocal spatial correlations at all length scales by means of diagrammatic extensions of DMFT. The aim of this paper is to present a DMFT analysis of the local reducible and irreducible two-particle vertex functions for the Hubbard model in the context of a unified diagrammatic formalism. An interpretation of the observed frequency structures is also given in terms of perturbation theory, of the comparison with the atomic limit, and of the mapping onto the attractive Hubbard model.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Phd by thesis

Abstract: Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Maximally-localized Wannier Functions: Theory and Applications

Abstract: The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized "Wannier functions" was introduced by Gregory Wannier in 1937. The connection between the Bloch and Wannier representations is realized by families of transformations in a continuous space of unitary matrices, carrying a large degree of arbitrariness. Since 1997, methods have been developed that allow one to iteratively transform the extended Bloch orbitals of a first-principles calculation into a unique set of maximally localized Wannier functions, accomplishing the solid-state equivalent of constructing localized molecular orbitals, or "Boys orbitals" as previously known from the chemistry literature. These developments are reviewed here, and a survey of the applications of these methods is presented. This latter includes a description of their use in analyzing the nature of chemical bonding, or as a local probe of phenomena related to electric polarization and orbital magnetization. Wannier interpolation schemes are also reviewed, by which quantities computed on a coarse reciprocal-space mesh can be used to interpolate onto much finer meshes at low cost, and applications in which Wannier functions are used as efficient basis functions are discussed. Finally the construction and use of Wannier functions outside the context of electronic-structure theory is presented, for cases that include phonon excitations, photonic crystals, and cold-atom optical lattices.

On the theory of superconductivity

Abstract: IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.