Solid State Physics

Garant předmětu:

Antonio Cammarata

Lecturer:

Antonio Cammarata

Tutor:

Antonio Cammarata

Supervisor:

Department of Physics

Synopsis:

The course provides fundamentals of solid state physics at large.

Requirements:

Lessons and tutorials attendance.

Syllabus of lectures:

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.

Syllabus of tutorials:

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.

Study Objective:

At the end of the course, the students will acquire basic knowledge on solid state physics.

Study materials:

Charles Kittel, Introduction to Solid State Physics, 8th edition, Wiley IPL, ISBN-13: 9788126535187

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: