Solid State Physics - XP02FPL

Credits 4
Semesters Summer
Completion Exam
Language of teaching undefined
Extent of teaching 2P+2C
The course provides fundamentals of solid state physics at large.
Study targets
At the end of the course, the students will acquire basic knowledge on solid state physics.
Course outlines
1) Condensed matter, solids, their description; crystals; crystal as periodic lattice.
2) Wave diffraction and the reciprocal lattice. Scattering intensity. Structure factor and Atomic form factor.
3) Phonons; crystal vibrations as harmonic displacements; derivation of the secular equation for the dynamical matrix.
4) Thermal properties derived from phonons.
5) Free Electron: Brief overview of the Schrodinger equation for the free particle and a particle confined by infinite potentials. Fermi energy and Fermi level. Electronic density of states. Heat capacity of the electron gas.
6) Nearly free electron model; origin of the energy gap; magnitude of the energy gap; Bloch functions; Kronig-Penney model; the Bloch theorem; number of orbitals in a band; metals and insulators.
7) Band gap; equations of motion for the wave vector; holes; effective mass; physical interpretation of the effective mass; effective masses in semiconductors.
8) Fermi surfaces and metals; construction of Fermi surfaces; electron orbits, hole orbits and open orbits; physical origin and calculation of energy bands.
9) Dielectrics and Ferroelectrics; electric field of a permanent dipole; macroscopic electric field; depolarizatino field; local electric field at an atom; Lorentz Field; Field of dipoles inside a cavity.
10) Diamagnetism and paramagnetism; Langevin diamagnetism equation; quantum theory of diamagnetism of mononuclear systems; paramagnetism.
11) Ferromagnetism and Antiferromagnetism; ferromagnetic order; Curie point and the exchange integral; temperature dependence of the saturation magnetization; saturation magnetization at absolute zero; ferrimagnetic order; antiferromagnetic order; ferromagnetic domains.
12) Magnetic resonance; nuclear magnetic resonance; line width; hyperfine splitting; electron paramagnetic resonance.
13) Superconductivity; type I and type II superconductors; destruction of superconductivity by magnetic fields; Meissner effect; heat capacity; energy gap; thermodynamics of the superconducting transition; BCS theory.
14) Noncrystalline solids; diffraction pattern of noncrystalline solids; monoatomic amorphous materials; structure of vitreous silica SiO2; glasses, viscosity and the hopping rate; point defects; lattice vacancies; color centers; F centers; other centers in alkali halides.
Exercises outlines
1) Crystal structures; Problem: symmetries; Problem: copper oxide layer.
2) Fraunhofer diffraction and derivation of Bragg's law; Single-slit diffraction; two point sources; two slits with finite width (Young's slits); transmission diffraction grating.
3) Physical meaning of phonon eigendisplacements and eigenfrequencies. Explicit calculation of the phonon eigenvectors and eigenfrequencies for a simple system (e.g. isolated CO2 molecule).
4) Crystal binding and elastic constants. Van der Waals-London interactions; ionic crystals, the Madelung Energy; hydrogen bonds; elastic strain.
5) Electrical conductivity and Ohm's law. Experimental electrical resistivity of Metals. Motion in magnetic fields. The Hall effect.
6) Crystal momentum of an electron; Bloch theorem and solution of the central equation; aaproximate solution near a zone boundary.
7) Intrinsic carrier concentration; intrinsic mobility; impurity conductivity; donor and acceptor states; thermal ionization of donors and acceptors; semimetals.
8) Experimental methods in Fermi surface studies; quantization of orbits in a magnetic field; De Haas-van Alphen effect; Extremal orbits.
9) Dielectric constants and poalrizability; structural phase transitions; ferroelectric crystals; displacive transitions; Landau theory of the phase transition for ferroelectrics.
10) Quantum theory of paramagnetism; Hund rules; crystal field splitting; quenching of the orbital angular momentum; spectroscopic splitting factor; Van Vleck temperature-independent paramagnetism; paramagnetic susceptibility of conduction electrons.
11) Magnons; quantization of spin waves, thermal excitation of magnons; neutron magnetic scattering.
12) Electron paramagnetic resonance; ferromagnetic resonance; antiferromagnetic resonance.
13) Superconductivity; London equation; coherence length; flux quantization in a superconductive ring; single particle tunneling; Josephson superconductor tunneling.
14) Radial distribution function; diffusion.
Charles Kittel, Introduction to Solid State Physics, 8th edition, Wiley IPL, ISBN-13: 9788126535187
Lessons and tutorials attendance.