Condensed Matter Physics
Module program director: professor János Kertész


Solid-state physics III.
Credits: 5
Responsible for the course: Dr. Attila Virosztek
Abstract:
This is one of the fundamental courses of the condensed matter module, and its aim is to deepen and enrich the knowledge of the previous solid-state physics I. and II. courses for students who are particularly interested in solid-state physics. It gives an introduction to the second quantization, linear response theory and their application to interacting electron systems (ferromagnetism of metals, collective excitations, spin density waves) in the framework of mean-field approach.

Statistical physics II.
Credits: 3
Responsible for the course: Dr. János Kertész
Abstract:
Correlation- and response functions, fluctuation-dissipation theorem, Kubo formula, generalized hydrodynamics, broken symmetries, mode coupling, continuous phase transitions, the two dimensional Ising model, real-space renormalization group transformation, s4 model, basics of critical dynamics, first order phase transitions, nucleation, spinodial decomposition, disordered systems: percolation, fractals, localization, spin glasses, far from equilibrium systems, hydrodynamic instabilities, stability analysis, pattern formation, fundamentals of non-linear dynamics, turbulence models.

Many-body problem
Credits: 3
Responsible for the course: Dr. Alfréd Zawadowski
Abstract:
Correlation functions, definition and their measurement. Zero and finite temperature Green function technics Application in solid-state physics: superconductivity, plasmons, Kondo-effect, etc.

Lectures on the mathematical physics of one dimensional systems
Credits: 3
Responsible for the course: Dr. Ferenc Woynarovich
Abstract:
Real-space Bethe Ansatz for the 1D Heisenberg chain and 1D delta-gas. Solution of Bethe-Ansatz equation for the 1D Heisenberg chain, higher order Bethe-Ansatz equations, fully integrable finite temperature models, the algebraic Bethe-Ansatz, solution of impurity models using Bethe-Ansatz.

Magnetic theory of complex systems
Credits: 3
Responsible for the course: Dr. Alfréd Zawadowski
Abstract:
Ferri- meta- and super-magnetism, multilayers, spin glasses.

Dynamic systems
Credits: 2
Responsible for the course: Dr. Zoltan Noszticzius
Abstract:
The concept and types of the dynamic systems, chemical examples, examination of dynamical system described by ordinary differential equations, local stability analysis of non-linear dynamical systems, various types of stationary points, dissipative dynamic systems, mechanical and electrodynamical examples. Classification of attractors; point, periodic, quasiperiodic, strange attractors, chaos, bifurcations, stationary point and bifurcation of periodic attracts, Poincare cuts, one dimensional map as a dynamic system, logistic map.

Fractal structures
Credits: 3
Responsible for the course: Dr. János Kertész
Abstract:
Basics of fractal geometry, self-affinity, multifractals, random walks, linear polymers, percolation, structure of infinite clusters conductivity of percolation lattice, droplet theory of phase transition, growth phenomena, diffusion, diffusion limited aggregation, surface roughening, continuum theory, 1/f noise, self-organized criticality, scaling in exotic systems (biology, traffic, economy).

Theory of magnetism I.
Credits: 3
Responsible for the course: Dr. Patrik Fazekas
Abstract:
Classification of solids into metals and insulators. Mott insulators. Definition of the Hubbard model, and the simplest description of the Mott transition. Derivation of the antiferromagnetic Heisenberg model (kinetic exchange) and the ferromagnetic Heisenberg model (direct exchange with orthogonal orbits), non-orthogonal orbits, Wigner theorem for the ground states of two electrons, spin wave theory of the antiferromagnetic Heisenberg model, Holstein-Primakoff theorem, thermal properties, ground state and excitation spectrum of the antiferromagnetic Heisenberg model (spin wave theory), discussion of spontaneous symmetry breaking. Remark: this course includes homework assignments.

Theory of magnetism II.
Credits: 3
Responsible for the course: Dr. Patrik Fazekas
Abstract:
This course builds on the knowledge of the previous one and treats three topics: 1. Crystal field theory, 2. Magnetism of metals, 3. Some interesting examples of strongly correlated electron systems. Role of the symmetry in quantum mechanics, point groups, properties of weak, average and strong crystal fields, splitting of orbit degeneration, origin of magnetic anisotropy, Kramers theorem, Jan-Teller effect, magnetic effect on d and f electrons, magnetism in Hubbard model, mean field theory of spin waves, conditions of ferromagnetism, strong correlation in metallic, heavy-metalic ions, two band models, valence mixing, f electron systems, RKKY interaction, magnetism of rare-earth elements. Remark: this course also includes homework assignments.

Disordered systems
Credits: 3
Responsible for the course: Dr. János Kertész
Abstract:
The main goal of the course is to provide an introduction to disordered systems, especially to the statistical physics of spin glasses. Following the overview of some fundamental experiments about spin glasses, it treats theoretical methods (quenched averages, replica trick, ergodicity- and parity breaking , Parisi-theory, ultrametric property, loop expansion), application inside the physics (random ensembles) and outside (neuron network, combinatorial optimization) as well.

Order, diffusion and conductivity
Credits: 3
Responsible for the course: Dr. János Kertész
Superionic conductors, metallic hydrogen, alloys, surface monolayers, driven lattice gas model stochastic cellular automates.

Structure determination methods in solids
Credits: 3
Responsible for the course: Dr. György Mihály
Abstract:
Production X-rays, their properties and detection, diffraction type of local methods (EXAFS,XANES), exotic methods. (X-ray holography, Mössbauer diffraction)

Resonance methods
Credits: 3
Responsible for the course: Dr. András Jánossy
Abstract:
Fundamentals of the theory of spin and magnetic resonance. Equipments of spin resonance. Resonance in metals and insulators. Relaxation processes. Special applications.

Nuclear methods in solid-state research
Credits: 3
Responsible for the course: Dr. Sándor Kugler
Abstract:
Neutron sources, spectrometers, coherent and incoherent scattering, elastic and inelastic scattering, correlation functions, structure determination, measuring phonon spectrum with neutron scattering, neutron spin-echo method and applications, crystal diffraction, amorphous and liquid structures, Mössbauer spectroscopy, electromagnetic properties and transitions of nuclei, hyperfine interaction, resonance absorption and emission without phonon back-scattering, isomer shift, magnetic split, magnetic structures and phase transitions, examples and applications, outline of other methods and their comparison with Mössbauer spectroscopy.

Electron-microscopy
Credits: 3
Responsible for the course: Dr. János Kertész
Abstract:
Transmission electron-microscopy, electron diffraction LEED, RHEED, electro-microscopic mapping high-resolution, analytical and scanning tunnelling electro-microscopy, electron beam X-ray microanalysis.

Surface analytical methods
Credits: 3
Responsible for the course: Dr. János Kertész
Abstract:
Low-energy electron diffraction, experimental setup, two dimensional lattices, kinematic theory of LEED, dynamic theory of LEED, surface structures. Auger electron spectroscopy (AES), Auger-effect, experimental apparatus, explanation of spectras, concentration calculation, applications,  intrusive profiling . Microelectronic application. Metal physics. X-ray excitation, photo-electric spectroscopy: principles, instruments, concentration calculation, applications. Secondary-ion spectroscopy: principles, instruments, concentration calculation, applications.

Liquid crystals
Credits: 2
Responsible for the course: Dr. György Mihály
Abstract:
Liquid crystalline materials and properties, phase transitions in liquid crystals, electronic properties of liquid crystals, transport phenomena, optical properties of liquid crystals.

Band structure calculation I.
Credits: 3
Responsible for the course: Dr. Béla Vasvári
Abstract:
Reducing the many-body problem, Hohenberg-Kohn theorems, electron structures of metals, geometry of Fermi surface, electron structures of alloys, the method of coherent potentials, electron structures of amorphous metals.

Band structure calculation II.
Credits: 3
Responsible for the course: Dr. Béla Vasvári
Abstract:
Electron system of mesoscopic systems, clusters, fullerens, electron structure of carbon nanotubes, collective electron states, plasma oscillations in metals, fullerens and nanotubes.

Special laboratory I.
Credits: 6
Responsible for the course: Dr. György Mihály
Abstract:
The subject of the course is the experimental study and explanation some of the quantum phenomena in solids. Typical topics are:

  • Low dimensional electron gas instability in chain-structured calcogenides (TaS3, NbSe3)
  • Fundamental phenomena of superconductivity (Meissner effect, Josephson effect) in traditional (BCS-like), high temperature and C60 based superconductor materials.

  • During the laboratory work students should acquire the knowledge of the following methods: detecting, using computer controlled measurement technics, liquid helium based criotechnics and superconductor apparatus.

    Special laboratory II.
    Credits: 10
    Responsible for the course: Dr. György Mihály
    Abstract:
    The subject of the course is the experimental study and explanation some of quantum phenomena n solids Typical topics are:

  • Low dimensional electron gas instability in chain-structured calcogenides (TaS3, NbSe3)
  • Fundamental phenomena of superconductivity (Meissner effect, Josephson effect) in traditional (BCS-like), high temperature and C60 based superconductor materials.

  • During the laboratory work students should acquire the knowledge of the following method: detecting, using computer controlled measurement technics, liquid helium based criotechnics and superconductor apparatus.

    Selected lectures on theoretical physics I. II.
    Credit scores: 4+3
    Responsible for the course: Dr. Alfréd Zawadowski
    Abstract:
    The `` Selected lectures on theoretical physics I. II.'' courses have changing subjects. Their purpose is to give insight into some special fields based on the knowledge from fundamental courses. The following topics are some examples of the previous and future ones: Green-function technics, correlation functions, Van Hove-formula, Kubo-formula, superconductors, d-type superconductors, light scattering, point contacts, Josephson junctions.

    Selected lectures on experimental solid-state physics I.
    Credits: 3
    Responsible for the course: Dr. György Mihály
    Abstract:
    This course aims to give a year by year review of some topics of the modern experimental solid-state physics such as spin density waves, high temperature superconductors and C60. The subject is connected to the institute's current research topics.

    Selected lectures on experimental solid-state physics II.
    Credits: 3
    Responsible for the course: Dr. György Mihály
    Abstract:
    This course aims to give a year by year review of some topics of the modern experimental solid-state physics such as spin density waves, high temperature superconductors and C60. The subject is connected to the institute's current research topics.

    Seminars I. - IV.
    Credits: 2
    Responsible for the course: Dr. Alfréd Zawadowski
    Abstract:
    The purpose of the seminars is not only to broaden the knowledge but to improve the students' lecturing skills. Subject of the seminar is changing year by year, some examples are:

  • The topic is chosen by the students usually in connection with their term projects or M.Sc. theses.
  • Charge density waves.
  • Chapters of computational physics.
  • Chapters of application of physics in engineering.
  • Physics of metals (joint course with Material Science Module)
    Credits: 4
    Responsible for the course: Dr. Péter Deák
    Abstract:
    Structure of metals, periodic systems, electronic states in metals, methods for determining electron energies in metals, theory of metallic bonds, cohesion of metals, density of states, Fermi surface, methods of measuring the Fermi surface, calculation of dielectric constant, phonon spectra, Kohn anomaly, Friedel oscillations, optical, thermal and transport properties of metals (resistivity, specific heat, etc.) magnetic properties of metals (Pauli paramagnetism, itinerant  magnetism of the iron group, Stoner model, magnetism of rare earth elements) superconductivity.

    Physics of semiconductors (joint course with Material Science Module)
    Credits: 4
    Responsible for the course: Dr. Péter Deák
    Abstract:
    Structure of metals, periodic system, electron states in metals, methods for determining electron energies in metals, theory of metallic bonds, cohesion of metals, density of states, Fermi surface, methods of measuring the Fermi surface, calculation of dielectric constant, phonon spectra, Kohn anomaly, Friedel oscillations, optical, thermal and transport properties of metals (resistivity, specific heat, etc.) magnetic properties of metals (Pauli paramagnetism, itinerant magnetism of the iron group, Stoner model, magnetism of rare earth elements) superconductivity.

    Computer simulations in statistical physics
    Credit scores: 3
    Responsible for the course: Dr. János Kertész
    Abstract:
    Monte-Carlo methods (random number generators, time- and ensemble averages, importance sampling, finite size scaling, various ensembles, multi-spin coding, Swendsen-Wang cluster dynamics, Monte-Carlo renormalization group, relaxation problems). Molecular dynamics (solving the equations of motion, potentials and scales, stabilizing the temperature, calculation of time- and ensemble averages, measuring time dependent quantities, non-equilibrium molecular dynamics, Car-Parinello method) Simulation of fractals (Percolation model, spanning cluster analysis, large cell renormalization group for percolation, directed percolation, self- avoiding walk, Eden model, diffusion limited aggregation, methods for measuring the fractal dimension).

    Beyond the crystalline state
    Credits: 3
    Responsible for the course: Dr. György Mihály
    Abstract:
    Variety in structures: crystals, incommensurate and long period structures, quasicrystals, liquid crystals, glasses, systems with quasi long range order. Order out disorder: symmetry breaking, defects and fluctuations, Goldstone modes, generalized rigidity, orientation order vs. translational order. Landau theory: ordered atomic structures, amorphous structures, liquid crystals, defect mediated structures.

    Group theory in solid-state research
    Credits: 3
    Responsible for the course: Dr. György Kriza
    Abstract:
    Basics: symmetry groups, important theorems of finite groups, representation, character chart. Vibrational spectroscopy: normal coordinates,  selection rules, direct product representation, situs group, factor group. Electron transition: crystal space spallation, correlation diagrams. Molecule orbits: hybridization, chemical bonds, chemical reactions, Woodward-Hoffmann rules. Crystal lattice symmetries: space groups, crystallographic methods, international tables, band structure calculation.

    Interacting electronic systems
    Credit: 3
    Responsible for the course: Dr. György Mihály
    Abstract:
    Electronic states in a solid state. The success and the limits of the band picture. Mott insulator, Andersen localization. Extended and localized electronic states. Bloch and Wannier functions. Instability of low dimensional metals. Lindhard function, Kohn anomaly. Charge and spin density waves. Two dimensional electron gas. Quantum Hall effect, Wigner crystal.

    Charge and spin density waves I.
    Credits: 3
    Responsible for the course: Dr. György Mihály
    Abstract:
    Electron-electron interaction treated by perturbation theory. Lindhard function. The nesting properties of Fermi-surface, low-dimensional systems. Electron-phonon coupling. Peierls distortion, formation of charge density waves. Experimental indications of charge density waves. Incommensurate charge density waves, NMR experiments. Weak and strong pinning of charge density waves. Collective conductivity. Narrow-band noise, mode locking.

    Charge and spin density waves II.
    Credits: 3
    Responsible for the course: Dr. György Mihály
    Abstract:
    Excitation spectrum of charge density waves. Application of Kramers-Kronig relation. Microwave resonance, sum rule, effective mass. Dielectric constant, polarization relaxation. Linear response theory. Two-fluid model of charge density waves. AC conductivity, thermal voltage. Hall constant. Wide band noise, application of fluctuation-dissipation theorem. Low temperature charge density wave conductivity.

    Selected problems in the many-body theory
    Credits: 3
    Responsible for the course: Dr. Gergely Zaránd
    Abstract:
    The course aims to practice of the methods of many-body phenomena. Following a short review of the methods of many-body problems (Green function technics, formalism of second quantization) the lecturer can choose one from the topics listed below: Theory of localization, quantum impurity models, Bose condensation, quantized Hall effect, Cher-Simon gauge theories, path integral technics, one dimensional interacting electrons, renormalization group methods, bosonization.

    Physics of mesoscopic systems
    Credits: 3
    Responsible for the course: Dr. Gergely Zaránd
    Abstract: