### Course Description

# Condensed Matter Theory

## Program

Nanosciences and Nanotechnologies, second-level study programme## Lecturers:

prof. dr. Viktor Kabanov## Goals:

Students will gain an overview of theoretical techniques for studying physics of solid state. They will gain a basic understanding of theory of electron systems, band theory and electrical, magnetic and superconducting properties of materials and nanomaterials. They will learn the fundamentals of density-functional-theory: a first principles method for the calculation of the electronic structure of solids.

## Content:

1 Introduction

2 Elements of group theory. Irreducible representations.

3 Lattice vibrations in crystalline solids. Mode classifications.

4 Electrons in crystals. Tight-binding and weak coupling approximations.

5 Density-Functional-Theory: a practical first-principle method for the calculation of electronic structure

6 Classification of solids: covalent, molecular, ionic, H-bonded crystals and metals

7 Localized electrons in solids. Excitons. Polarons.

8Thermodynamic properties of solids.

9 Magnetic properties. Pauli paramagnetizm, Landau diamagnetism. Quantum effects.

10 Optical properties of solids. Dielectric function.

11 Kinetic properties of metals and semiconductors. Kinetic equation.

12. Scattering processes. Impurity scattering, scattering by phonons.

13 Kinetic processes in magnetic field. Hall effect, magnetoresistance.

14 Theory of phase transition. Ising model, Landau theory of phase transition. Kinetics of phase transitions.

15. Superconductivity. Cooper pairs. Ginzburg-Landau theory. Critical current and critical field. Quantum effects.

16 From 3D to lower dimensions: surfaces, molecules, and heterogeneous catalysis

## Course literature:

N.W. Ashcroft N.D. Mermin Solid State Physics, Holt-Saunders 1976.

A.A. Abrikosov, Fundamentals of the theory of metals, North-Holland,1988.

P.G. de Gennes, Superconductivity of Metals and Alloys, Perseus books, 1989.

L.D. Landau and E.M. Lifshitz Statistical Physics, Pergamon Press 1980.

E.M. Lifshitz and L.P. Pitaevskii Statistical Physics, Pergamon Press 1980.

Charles Kittel Introduction to Solid State, J. Wiley 1996.

R.M. Martin Electronic structure: basic theory and practical methods, Cambridge University Press, 2004.

## Significant publications and references:

ALEXANDROV, A. S., KABANOV, V. V., RAY, D. K. From electron to small polaron : an exact cluster solution. Phys. rev., B, Condens. matter, 1994, vol. 49, str. 9915-9923.

ALEXANDROV, A. S., KABANOV, V.V., MOTT, N. F. Coherent ab and c transport theory of high-T[sub]c cuprates. Phys. rev. lett., 1996, vol. 77, str. 4796-4799.

KABANOV, V. V. Zeros of the order parameter of the d-superconducting film in the presence of uniform current. Phys. rev., B, Condens. matter mater. phys., 2004, vol. 69, str. 052503-1-052503-3

MERTELJ, T., KABANOV, V. V., MIHAILOVIĆ, D. Charged particles on a two-dimensional lattice subject to anisotropic Jahn-Teller interactions. Phys. rev. lett., 2005, vol. 94, str. 147003-1-147003-4.

KOKALJ, A, DOMINKO, R., MALI, G., MEDEN, A., GABERŠČEK, M., JAMNIK, J. Beyond one-electron reaction in Li cathode materials : designing Li2MnxFe1-xSiO4. Chem. mater., 2007, vol. 19, no. 15, str. 3633-3640.

KOKALJ, A., BONINI, N., de GIRONCOLI, S., SBRACCIA, C., FRATESI, G., BARONI, S. Methane dehydrogenation on Rh@Cu(111) : a first-principles study of a model catalyst. J. Am. Chem. Soc., 2006, vol. 128, str. 12448-12454.

KOKALJ, A., KOBAL, I., MATSUSHIMA, T. A DFT study of the structures of N2O adsorbed on the Pd(110) surface. J. phys. chem., B Condens. mater. surf. interfaces biophys., 2003, vol. 107, str. 2741-2747.

KOKALJ, A. XCrySDen - a new program for displaying crystalline structures and electron densities. J. mol. graph. model., 1999, vol. 17, str. 176-179.

## Examination:

Written and oral examination.

## Students obligations:

Written and oral examination.