Seminar 1 impurity in the tomonaga-luttinger model:a functional integral approach

This chapter explains a functional integral approach about impurity in the Tomonaga–Luttinger model. The Tomonaga–Luttinger model of one-dimensional (1D) strongly correlates electrons gives a striking example of non-Fermi-liquid behavior. For simplicity, the chapter considers only a single-mode Tomonaga–Luttinger model, with one species of right- and left-moving electrons, thus, omitting spin indices and considering eventually the simplest linearized model of a single-valley parabolic electron band. The standard operator bosonization is one of the most elegant methods developed in theoretical physics. The main advantage of the bosonization, either in standard or functional form, is that including the quadric electron–electron interaction does not substantially change the free action. The chapter demonstrates the way to develop the formalism of bosonization based on the functional integral representation of observable quantities within the Keldysh formalism.

High-frequency conductivity of optically excited charge carriers in hydrogenated nanocrystalline silicon investigated by spectroscopic femtosecond pump-probe reflectivity measurements

We report an investigation into the high-frequency conductivity of optically excited charge carriers far from equilibrium with the lattice. The investigated samples consist of hydrogenated nanocrystalline silicon films grown on a thin film of silicon oxide on top of a silicon substrate. For the investigation, we used an optical femtosecond pump-probe setup to measure the reflectance change of a probe beam. The pump beam ranged between 580 and 820nm, whereas the probe wavelength spanned 770 to 810nm. The pump fluence was fixed at 0.6mJ/cm2. We show that at a fixed delay time of 300fs, the conductivity of the excited electron-hole plasma is described well by a classical conductivity model of a hot charge carrier gas found at Maxwell-Boltzmann distribution, while Fermi-Dirac statics is not suitable. This is corroborated by values retrieved from pump-probe reflectance measurements of the conductivity and its dependence on the excitation wavelength and carrier temperature. The conductivity decreases monotonically as a function of the excitation wavelength, as expected for a nondegenerate charge carrier gas.

Bosonisation as The Hubbard-Stratonovich transformation

The problem of strongly correlated electrons in one dimension attracted attention of condensed matter physicists since early 50’s. After the seminal paper of Tomonaga [1] who suggested the first soluble model in 1950, there were essential achievements reflected in papers by Luttinger [2] (1963) and Mattis and Lieb [3] (1963). A considerable contribution to the understanding of generic properties of the 1D electron liquid has been made by Dzyaloshinskii and Larkin [4] (1973) and Efetov and Larkin [5] (1976). Despite the fact that the main features of the 1D electron liquid were captured and described by the end of 70’s, the investigators felt dissatisfied with the rigour of the theoretical description. The most famous example is the paper by Haldane [6] (1981) where the author developed the fundamentals of a modern bosonisation technique, known as the operator approach. This paper became famous because the author has rigourously shown how to construct the Fermi creation/anihilation operators out of the Bose ones. The most recent example of such a dissatisfaction is the review by von Delft and Schoeller [7] (1998) who revised the approach to the bosonisation and came up with what they called constructive bosonisation.

Dynamical Resonances and SSF Singularities for a Magnetic Schrödinger Operator

We consider the Hamiltonian H of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator H has infinitely many eigenvalues of infinite multiplicity embedded in its continuous spectrum. We perturb H by appropriate scalar potentials V and investigate the transformation of these embedded eigenvalues into resonances. First, we assume that the electric potentials are dilation-analytic with respect to the variable along the magnetic field, and obtain an asymptotic expansion of the resonances as the coupling constant ϰ of the perturbation tends to zero. Further, under the assumption that the Fermi Golden Rule holds true, we deduce estimates for the time evolution of the resonance states with and without analyticity assumptions; in the second case we obtain these results as a corollary of suitable Mourre estimates and a recent article of Cattaneo, Graf and Hunziker [11]. Next, we describe sets of perturbations V for which the Fermi Golden Rule is valid at each embedded eigenvalue of H; these sets turn out to be dense in various suitable topologies. Finally, we assume that V decays fast enough at infinity and is of definite sign, introduce the Krein spectral shift function for the operator pair (H+V, H), and study its singularities at the energies which coincide with eigenvalues of infinite multiplicity of the unperturbed operator H.

The correlation of structure and electronic properties near the surface of transition metal oxides

The strong couplings between different degrees of freedom are believed to be responsible for novel and complex phenomena discovered in transition metal oxides (TMOs). The physical complexity is directly responsible for their tunability. Creating surfaces/interfaces add an additional ' man-made' twist, approaching the quantum phenomena of correlated materials. ^ The dissertation focused on the structural and electronic properties in proximity of surface of three prototype TMO compounds by using three complementary techniques: scanning tunneling microscopy, angle-resolved photoelectron spectroscopy and low energy electron diffraction, particularly emphasized the effects of broken symmetry and imperfections like defects on the coupling between charge and lattice degrees of freedom. ^ Ca1.5Sr0.5RuO4 is a layered ruthenate with square lattice and at the boundary of magnetic/orbital instability in Ca2-xSrxRuO4. That the substitution of Sr 2+ with Ca2+ causing RuO6 rotation narrows the dxy band width and changes the Fermi surface topology. Particularly, the γ(dxy) Fermi surface sheet exhibited hole-like in Ca1.5Sr0.5RuO4 in contrast to electron-like in Sr2RuO4, showing a strong charge-lattice coupling. ^ Na0.75CoO2 is a layered cobaltite with triangular lattice exhibiting extraordinary thermoelectric properties. The well-ordered CoO2-terminated surface with random Na distribution was observed. However, lattice constants of the surface are smaller than that in bulk. The surface density of states (DOS) showed strong temperature dependence. Especially, an unusual shift of the minimum DOS occurs below 230 K, clearly indicating a local charging effect on the surface. ^ Cd2Re2O7 is the first known pyrochlore oxide superconductor (Tc ∼ 1K). It exhibited an unusual second-order phase transition occurring at TS1 = 200 K and a controversial first-order transition at TS2 = 120 K. While bulk properties display large anomalies at TS1 but rather subtle and sample-dependent changes at TS2, the surface DOS near the EF show no change at T s1 but a substantial increase below TS2---a complete reversal as the signature for the transitions. We argued that crystal imperfections, mainly defects, which were considerably enhanced at the surface, resulted in the transition at TS2. ^

Carbon nanostructure based electrodes for high efficiency dye sensitized solar cell

Synthesis and functionalization of large-area graphene and its structural, electrical and electrochemical properties has been investigated. First, the graphene films, grown by thermal chemical vapor deposition (CVD), contain three to five atomic layers of graphene, as confirmed by Raman spectroscopy and high-resolution transmission electron microscopy. Furthermore, the graphene film is treated with CF4 reactive-ion plasma to dope fluorine ions into graphene lattice as confirmed by X-ray photoelectron spectroscopy (XPS) and UV-photoemission spectroscopy (UPS). Electrochemical characterization reveals that the catalytic activity of graphene for iodine reduction enhanced with increasing plasma treatment time, which is attributed to increase in catalytic sites of graphene for charge transfer. The fluorinated graphene is characterized as a counter-electrode (CE) in a dye-sensitized solar cell (DSSC) which shows ~ 2.56% photon to electron conversion efficiency with ~11 mAcm−2 current density. Second, the large scale graphene film is covalently functionalized with HNO3 for high efficiency electro-catalytic electrode for DSSC. The XPS and UPS confirm the covalent attachment of C-OH, C(O)OH and NO3- moieties with carbon atoms through sp2-sp3 hybridization and Fermi level shift of graphene occurs under different doping concentrations, respectively. Finally, CoS-implanted graphene (G-CoS) film was prepared using CVD followed by SILAR method. The G-CoS electro-catalytic electrodes are characterized in a DSSC CE and is found to be highly electro-catalytic towards iodine reduction with low charge transfer resistance (Rct ~5.05 Ωcm 2) and high exchange current density (J0~2.50 mAcm -2). The improved performance compared to the pristine graphene is attributed to the increased number of active catalytic sites of G-CoS and highly conducting path of graphene. We also studied the synthesis and characterization of graphene-carbon nanotube (CNT) hybrid film consisting of graphene supported by vertical CNTs on a Si substrate. The hybrid film is inverted and transferred to flexible substrates for its application in flexible electronics, demonstrating a distinguishable variation of electrical conductivity for both tension and compression. Furthermore, both turn-on field and total emission current was found to depend strongly on the bending radius of the film and were found to vary in ranges of 0.8 - 3.1 V/μm and 4.2 - 0.4 mA, respectively.

Interações magnéticas e elétricas em GaMnAs

In this paper, we will address together the magnetic and electrical properties of a particular semiconductor, the GaMnAs. The treatment will be done analytically in the first part of the work, according to the computational method for simulation of physical systems through the implementation of the expressions obtained in the first part. All study of magnetic contribution will be made using an interaction Kondo type, using an approach by Green functions. The electrical part, which consists of the Coulomb interactions between carriers and Mn ions, will be treated within the approach of multiple scattering. The implementation of the proposed method will calculate the Green functions converged as multiple scattering solution and use them as a starting point for the calculation of the effective magnetic interactions between Mn ions mediated charge carriers. The concentration parameters were varied for Mn ions and carriers as well. The combination of these two parameters can lead to insulating, metal samples with carriers in Fermi level to low or high mobility. As a result a correlation between the obtained carrier mobility and the strength of magnetic interaction. The greater mobility, the greater the intensity of the interaction.

Una propuesta didáctica para contribuir al desarrollo de la expresión de ideas, vivencias y sentimientos de los alumnos de secundaria a través de la educación artística

Esta tesis es el resultado de una investigación llevada a cabo con alumnos de Educación Secundaria Obligatoria (ESO), en la asignatura de Educación Plástica y Visual durante más de diez años. Según la legislación vigente uno de los objetivos de la Educación Secundaria Obligatoria consiste en utilizar el lenguaje plástico para representar emociones y sentimientos, vivencias e ideas, contribuyendo a la comunicación, reflexión crítica y respeto entre las personas. Aunque la Ley lo expresa claramente, no lo desarrolla suficientemente en sus contenidos, con lo cual pretendemos dar respuesta a este objetivo. Por ello hemos elaborado una unidad didáctica específica por cada nivel educativo, dentro del área de Educación Plástica y Visual que ayuden a conseguir que los alumnos desarrollen la capacidad de representar emociones y sentimientos, vivencias e ideas. Teniendo en cuenta que esta propuesta se pondrá en práctica con alumnos adolescentes, será imprescindible conocer las características específicas de la adolescencia, por lo que consideramos importante promover actividades programadas para ellos, en las que se activen y promuevan mecanismos de reflexión y preocupación por los temas específicos de su edad. El lenguaje visual y las actividades propuestas deben ayudar al adolescente a exteriorizar todo lo que tiene en su interior. Utilizaremos la expresión artística como acelerador emocional, para ayudarles a sacar recuerdos y sentimientos que, seguramente, no podrían manifestar fácilmente de otro modo...

Gamma-ray and neutrino fluxes from Heavy Dark Matter in the Galactic Center

We present a study of the Galactic Center region as a possible source of both secondary gamma-ray and neutrino fluxes from annihilating dark matter. We have studied the gamma-ray flux observed by the High Energy Stereoscopic System (HESS) from the J1745-290 Galactic Center source. The data are well fitted as annihilating dark matter in combination with an astrophysical background. The analysis was performed by means of simulated gamma spectra produced by Monte Carlo event generators packages. We analyze the differences in the spectra obtained by the various Monte Carlo codes developed so far in particle physics. We show that, within some uncertainty, the HESS data can be fitted as a signal from a heavy dark matter density distribution peaked at the Galactic Center, with a power-law for the background with a spectral index which is compatible with the Fermi-Large Area Telescope (LAT) data from the same region. If this kind of dark matter distribution generates the gamma-ray flux observed by HESS, we also expect to observe a neutrino flux. We show prospective results for the observation of secondary neutrinos with the Astronomy with a Neutrino Telescope and Abyss environmental RESearch project (ANTARES), Ice Cube Neutrino Observatory (Ice Cube) and the Cubic Kilometer Neutrino Telescope (KM3NeT). Prospects solely depend on the device resolution angle when its effective area and the minimum energy threshold are fixed.

Magnetic properties of paramagnetic systems : density functional studies

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Magnetic properties of paramagnetic systems : density functional studies

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Efficient simulations with electronic open boundaries

We present a reformulation of the hairy-probe method for introducing electronic open boundaries that is appropriate for steady-state calculations involving nonorthogonal atomic basis sets. As a check on the correctness of the method we investigate a perfect atomic wire of Cu atoms and a perfect nonorthogonal chain of H atoms. For both atom chains we find that the conductance has a value of exactly one quantum unit and that this is rather insensitive to the strength of coupling of the probes to the system, provided values of the coupling are of the same order as the mean interlevel spacing of the system without probes. For the Cu atom chain we find in addition that away from the regions with probes attached, the potential in the wire is uniform, while within them it follows a predicted exponential variation with position. We then apply the method to an initial investigation of the suitability of graphene as a contact material for molecular electronics. We perform calculations on a carbon nanoribbon to determine the correct coupling strength of the probes to the graphene and obtain a conductance of about two quantum units corresponding to two bands crossing the Fermi surface. We then compute the current through a benzene molecule attached to two graphene contacts and find only a very weak current because of the disruption of the π conjugation by the covalent bond between the benzene and the graphene. In all cases we find that very strong or weak probe couplings suppress the current.

Multiscale Analysis for Field-Effect Penetration through Two-Dimensional Materials

Gate-tunable two-dimensional (2D) materials-based quantum capacitors (QCs) and van der Waals heterostructures involve tuning transport or optoelectronic characteristics by the field effect. Recent studies have attributed the observed gate-tunable characteristics to the change of the Fermi level in the first 2D layer adjacent to the dielectrics, whereas the penetration of the field effect through the one-molecule-thick material is often ignored or oversimplified. Here, we present a multiscale theoretical approach that combines first-principles electronic structure calculations and the Poisson–Boltzmann equation methods to model penetration of the field effect through graphene in a metal–oxide–graphene–semiconductor (MOGS) QC, including quantifying the degree of “transparency” for graphene two-dimensional electron gas (2DEG) to an electric displacement field. We find that the space charge density in the semiconductor layer can be modulated by gating in a nonlinear manner, forming an accumulation or inversion layer at the semiconductor/graphene interface. The degree of transparency is determined by the combined effect of graphene quantum capacitance and the semiconductor capacitance, which allows us to predict the ranking for a variety of monolayer 2D materials according to their transparency to an electric displacement field as follows: graphene > silicene > germanene > WS2 > WTe2 > WSe2 > MoS2 > phosphorene > MoSe2 > MoTe2, when the majority carrier is electron. Our findings reveal a general picture of operation modes and design rules for the 2D-materials-based QCs.

Dielectric screening in atomically thin boron nitride nanosheets

Two-dimensional (2D) hexagonal boron nitride (BN) nanosheets are excellent dielectric substrate for graphene, molybdenum disulfide, and many other 2D nanomaterial-based electronic and photonic devices. To optimize the performance of these 2D devices, it is essential to understand the dielectric screening properties of BN nanosheets as a function of the thickness. Here, electric force microscopy along with theoretical calculations based on both state-of-the-art first-principles calculations with van der Waals interactions under consideration, and nonlinear Thomas-Fermi theory models are used to investigate the dielectric screening in high-quality BN nanosheets of different thicknesses. It is found that atomically thin BN nanosheets are less effective in electric field screening, but the screening capability of BN shows a relatively weak dependence on the layer thickness.

Manifestation of Colossal Thermoelectric Power by Charge Ordered Small and Intermediate Bandwidth Manganites

Thermoelectric materials are revisited for various applications including power generation. The direct conversion of temperature differences into electric voltage and vice versa is known as thermoelectric effect. Possible applications of thermoelectric materials are in eco-friendly refrigeration, electric power generation from waste heat, infrared sensors, temperature controlled-seats and portable picnic coolers. Thermoelectric materials are also extensively researched upon as an alternative to compression based refrigeration. This utilizes the principle of Peltier cooling. The performance characteristic of a thermoelectric material, termed as figure of merit (ZT) is a function of several transport coefficients such as electrical conductivity (σ), thermal conductivity (κ) and Seebeck coefficient of the material (S). ZT is expressed asκσTZTS2=, where T is the temperature in degree absolute. A large value of Seebeck coefficient, high electrical conductivity and low thermal conductivity are necessary to realize a high performance thermoelectric material. The best known thermoelectric materials are phonon-glass electron – crystal (PGEC) system where the phonons are scattered within the unit cell by the rattling structure and electrons are scattered less as in crystals to obtain a high electrical conductivity. A survey of literature reveals that correlated semiconductors and Kondo insulators containing rare earth or transition metal ions are found to be potential thermoelectric materials. The structural magnetic and charge transport properties in manganese oxides having the general formula of RE1−xAExMnO3 (RE = rare earth, AE= Ca, Sr, Ba) are solely determined by the mixed valence (3+/4+) state of Mn ions. In strongly correlated electron systems, magnetism and charge transport properties are strongly correlated. Within the area of strongly correlated electron systems the study of manganese oxides, widely known as manganites exhibit unique magneto electric transport properties, is an active area of research.Strongly correlated systems like perovskite manganites, characterized by their narrow localized band and hoping conduction, were found to be good candidates for thermoelectric applications. Manganites represent a highly correlated electron system and exhibit a variety of phenomena such as charge, orbital and magnetic ordering, colossal magneto resistance and Jahn-Teller effect. The strong inter-dependence between the magnetic order parameters and the transport coefficients in manganites has generated much research interest in the thermoelectric properties of manganites. Here, large thermal motion or rattling of rare earth atoms with localized magnetic moments is believed to be responsible for low thermal conductivity of these compounds. The 4f levels in these compounds, lying near the Fermi energy, create large density of states at the Fermi level and hence they are likely to exhibit a fairly large value of Seebeck coefficient.