Solid State Physics II
Contents
The course includes theory of electronic states in solids, Hartree, Hartree-Fock, and density-functional theory. Methods for calculation of band structures are discussed briefly, the linear muffin tin orbital (LMTO) in some detail. The effect of screening is described in terms of the Thomas-Fermi and Lindhard models. Phonons are treated in simple models as well as more realistic three dimensional schemes. Neutron scattering as a tool for measuring dispersion relations is discussed including calculation of Debye-Waller factors and simple melting models. Anharmonic effects, thermal expansion are also included. As a specific example we consider the temperature dependence of the thermal expansion of some tetrahedrally bonded semiconductors (silicon). The electron-phonon interaction and its influence on Fermi velocities as well as its role in conventional BCS theory of superconductivity is examined. Phenomenological theories of superconductivity are based on the London equations and the Ginzburg-Landau theory. The AC and DC Josephson effects are discussed as well as the application of weak links in magnetometers (SQUIDs). Magnetic properties of solids are described from simple models of a solid as an assembly of non-interacting magnetic ions. Cases where this picture breaks down are discussed, and finally itinerant magnetism, including a Stoner model, is described.
Fundamental electron transport theory, Boltzmann's transport equation, relaxation-time approximation as well as ways to go beyond this are included. The concepts are applied to description of methods for measuring Fermi surfaces, cyclotron resonance, dHvA effect, size effect, ultrasonic attenuation, time-of-flight measurements, anomalous skin effect. In connection with the latter, optical properties of metals are examined in the limit where interband transitions can be neglected. Also phonon transport is treated as well as kinetic (Onsager) coefficients. Basic subjects of semiconductor physics include effects of doping, the p-n junction and optical properties. Local-field effects, Lyddane-Sachs-Teller and Clausius-Mosotti relations are derived. Phase transitions, including review of thermodynamical potentials, are treated in a general and simple manner. As examples pyro- and ferroelectricity are considered, and applications are also made to superconductivity and magnetism.
The quantum-Hall effect is described in simple terms.
A substantial part of the course is devoted to application of group theory (symmetry groups) in solid state physics. All relevant theorems are derived, and no knowledge of the subject from previous mathematical courses is assumed. The role of symmetry groups, representation theory, construction and use of character tables, labelling of electronic, phonon, magnon states according to symmetry properties are trained. Selection rules (for optical transitions, for example) are derived and used in examples (e.g. optical properties of semiconductor superlattices).
Text-books
N.W. Ashcroft and N.D. Mermin: Solid State Physics. Special subjects are described in lecture notes distributed to the students during the course.
Evaluation
Pass/fail
ECTS-credits
10
Semester
Spring + fall