COURSE GOALS: The main goal of this course is to give an introduction into fundamental concepts of solid state physics, in particular: crystal structure and X-ray diffraction, interactions leading to cohesion of crystals, ellastic and thermal properties of crystal lattice, free electron gas and its thermal properties, Schroedinger equation for electron in periodic potential and electron energy bands, electronic and thermal transport and conductivity, dielectric response of materials to external electric field, properties of semiconductors, magnetic properties of materials (diamagnetism, paramagentism, ferromagnetism), basics of superconductivity. Students should acquire qualitative and quantitative knowledge in specified topics at the level of understanding the key concepts and relations between experimentally observed facts, as well as of the mathematical formalism used to describe and solve problems.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
1. KNOWLEDGE AND UNDERSTANDING
1.1. demonstrate a thorough knowledge and understanding of the fundamental laws of classical and modern physics
1.3. demonstrate a thorough knowledge and understanding of the most important physics theories (logical and mathematical structure, experimental support, described physical phenomena)
2. KNOWLEDGE AND UNDERSTANDING
2.1. identify and describe important aspects of a particular physical phenomenon or problem
2.4. recognize and follow the logic of arguments, evaluate the adequacy of arguments and construct well supported arguments
2.5. use mathematical methods to solve standard physics problems
3. MAKING JUDGMENTS
3.1. develop a critical scientific attitude towards research in general, and in particular by learning to critically evaluate arguments, assumptions, abstract concepts and data
4. COMMUNICATION SKILLS
4.2. present complex ideas clearly and concisely
4.3. present their own research results at education or scientific meetings
5. LEARNING SKILLS
5.1. search for and use professional literature as well as any other sources of relevant information
5.2. remain informed of new developments and methods in physics, chemistry and education
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
After finishing the course, the student will be capable to:
1. demonstrate qualitative knowledge of basic fields of solid state physics stated in the Course description, experimental phenomena and models related to them,
2. demonstrate qualitative and quantitative description of basic theoretical models within the framework of solid state physics: model of X-ray diffraction on crystal, model od crystal lattice vibrations (phonons), modelling of thermodynamical properties of crystal lattice, modelling of interatomic interactions leading to cohesion of crystals, Sommerfeld model of metals - free electron gas model and its thermodynamical properties, solving of Schroedinger equation for electron in the periodic potential and Bloch theorem within the framework of perturbation theory, tight binding approximation, Drude model of electrical conductivity, model of magnetoconductivity and Hall effect, model of thermal conductivity od the crystal and Wiedemann-Franz law, models of dielectric response of the electron gas, crystal lattice and atoms with respect to external electric field, model of action of masses in semiconductors, models of magnetism of matter (Langevine's diamagnetism and paramagnetism of atoms, Weiss theory of ferromagnetism, Landau diamagnetism and Pauli paramagnetism of free electron gas, ferromagnetism of interacting electron gas), model of electron-electron attractive interaction via phonon exchange and basics of BCS theory of superconductivity,
3. solve given problems related to models stated above,
4. demonstrate an overview upon the field in the sense of critical thinking on acquired models and relating the causally related phenomena from different subfields logically.
COURSE DESCRIPTION:
Lectures per weeks (15 weeks in total):
week 1: Crystal structure: introduction about the solid state physics, crystal symmetry classes, direct and reciprocal space, phenomenological and mathematical description of X-ray diffraction on crystal (Laue and Bragg law), defects in crystals
week 2-3: Dynamics of crystal lattice: concept and modelling of mechanical vibrations of crystal lattice with one and two atoms per unit cell - phonons (acoustical and optical), thermodynamical and thermal properties of crystal lattice (Planck distribution, Debye model, density of states, specific heat of crystal lattice, Dulong-Petit law), thermal expansion of crystal
week 4: Interatomic interactions in crystals: interatomic interactions leading to cohesion of crystals, concept of cohesive energy, covalent bond, ionic bond, van der Waals bond, hydrogen bond, metallic bond
week 5: Sommerfeld model of metals: free electron gas with its thermodynamical and thermal properties (Fermi-Dirac distribution, Fermi energy, Sommerfeld expansion, specific heat of free electron gas in metals), thermoelectric emission
week 6-7: Electron in the periodic potential: Schroedinger equation of electron in periodic potential, Bloch theorem, perturbation theory for degenerate states - electronic energy bands, concept of effective mass, tight binding approximation, density of states and van Hove singularities
week 8-9: Electrical and thermal transport: Drude model of electrical conductivity, concept of relaxation time, Matthiessen's and Nordheim's rule, phononic contribution to electric resistivity, Joule's heat, conductivity in time-dependent oscillating electric field, conductivity in magnetic field (the tensor of magnetoconductivity, Hall effect), thermal conductivity and Wiedemann-Franz law
week 10-11: Dielectric response: the concept of response function and susceptibility in particular with respect to external electric field, Maxwell equations within media, "jellium model" and response of electron gas within static (Thomas-Fermi approximation) and dynamic (electron plasma) limit, response of ionic crystal and infrared absorption (Clausius-Mossotti relation, Lyddane-Sacks-Teller relation, polaritons), atomic polarizability in dielectrics, index of refraction of light, susceptibility of interacting system
week 12: Semiconductors: concepts of intrinsic and doped semiconductor, law of mass action, electronic and hole conductivity
week 13-14: Magnetism: concept and origin of magnetism - Bohr-van Leeuwen theorem, Langevine atomic diamagnetism and paramagnetism, spin and orbital magnetic moment, Weiss theory of ferromagnetism, Landau diamagnetism and Pauli paramagnetism of free electron gas, ferromagnetism of interacting electron gas
week 15: Superconductivity: concept and phenomena in superconductivity (Meissner effect, isotope effect, type I and type II superconductors), basics of the theory of superconductivity: electron-phonon coupling, dielectric function of electron gas and ionic plasma, "overscreening" and electron-electron attraction - Cooper pair, BCS wave function, equations relating superconducting gap, critical temperature and electron-phonon coupling constant; Josephson effect
REQUIREMENTS FOR STUDENTS:
Students should attend lectures and exercises and solve the weekly homework. Signature requirements are attendance at at least 40% lectures/exercises with submission and successful elaboration of at least 40% of homework.
GRADING AND ASSESSING THE WORK OF STUDENTS:
Students that have attended at least 85% lectures/exercises and have successfully passed at least 85% homework elaborations, take just a final oral exam. Those that have not fulfilled these requirements, but have fulfilled the signature requirements, take a written exam before the final oral exam. The final grade is formed from: lectures/exercises attendance and activity (1 ECTS), the grades from homework elaborations / written exam (2 ECTS) and the final oral exam (3 ECTS).
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