Program of the course "Quantum Solid State Physics"
Questions from the first
semester (included in the exam of the second semester)
1. The structure of periodically-ordered crystals.
2. The reciprocal lattice of periodically ordered crystals. Brillouin zone.
3. Methods for experimental determination of crystal structure.
4. Classification of Bravais lattices.
5. Incommensurably modulated crystals. Quasicrystals.
6. Liquid crystals and polymers; examples.
7. Substances in an amorphous state. Gels, airgels
and opals.
8. Effect of temperature on X-ray scattering; the Debye-Waller factor.
9. Specific heat of solids.
10.* Methods for determining the Debye temperature.
11. Normal modes of a monoatomic linear chain.
12. Normal modes of a diatomic linear chain; gap in the spectrum of vibrational
excitations.
13.* Normal vibrational modes of the Bravais lattice and lattices with a basis
in two-dimensional and three-dimensional cases.
14. Density of vibrational states.
15.* Number of independent components of the modulus tensor of elasticity of
crystals and amorphous media.
16. Interatomic interactions and coupling in solids.
17. Thermal conductivity. Its temperature dependence.
18. Phonon umklapp scattering processes.
19. Metals, semimetals, semiconductors, dielectrics. Understanding the graphs
of the band structure.
20.* The principle of operation of the simplest semiconductor devices: a diode, a photodiode, a solar battery, a laser, a transistor.
21. Dielectrics. Various contributions to the polarizability of dielectrics.
22. Frequency dependence of dielectric permittivity and susceptibility of
dielectrics. Its description with the help of forced oscillations.
23. Calculation of the orientation susceptibility.
24. Complex dielectric permittivity and its physical meaning.
25. Ferroelectrics and piezoelectrics
26. Various contributions to magnetic susceptibility of paramagnet and their temperature dependence.
27.* Adiabatic demagnetization as a cooling method.
28.* Nature of magnetic exchange interaction.
29. Ferromagnetism and antiferromagnetism in the mean-field approximation:
temperature dependence of their magnetic susceptibility and magnetization.
30. Spin waves in ferro- and antiferromagnets. Their dispersion law.
31. Temperature dependence of magnetization of ferromagnets.
Mean-field result, experimental, and theoretical with contribution from
magnons.
32. Magnon contribution to the temperature dependence of specific heat in
ferro- and antiferromagnets.
33. Frustrated magnets and spin glasses.
Main literature for home
reading: Introduction to Solid State
Physics , 8th Edition, by Charles Kittel
Questions new for the second
semester
34. Free electron gas and the Fermi surface
35. Theory of metals. Kinetic equation for electrons. Electric and thermal
conductivity of metals.
36. Thermoelectric phenomena.
37. Electronic properties of metals in a magnetic field: magnetoresistance
and quantum oscillations.
38. Skin effect.
39.* Defects in crystals.
40.* Hopping conductivity.
Superconductivity.
41. Basic properties of superconductors. Thermodynamics of superconductors (the jump in heat capacity at the superconducting transition temperature).
42. Phonon attraction between electrons in a metal. Formation of a Cooper pair. Cooper pair binding energy. Energy spectrum of quasiparticles in a superconductor according to BCS theory.
43. Ginzburg-Landau theory of a second-order phase transition. Temperature dependence of the order parameter near a second-order phase transition. Fundamental equations of the Ginzburg-Landau theory.
44. Limits of applicability of the Ginzburg-Landau theory, the Ginzburg-Levanyuk criterion.
Surface energy at the boundary between the normal and superconducting phases in the Ginzburg-Landau theory.
45. Correlation length and surface energy. Two types of superconductors.
Mixed state of type II superconductors in a magnetic field.
46. Magnetic properties of type II superconductors: Hc1 and Hc2 fields.
Abrikosov vortices. Concept of the Abrikosov vortex lattice.
* Motion of the Abrikosov vortex lattice with current flow. Pinning.
47. * Tunneling effect in metals. Single-particle current through a tunnel junction between two normal metals (qualitative description).
48. Josephson effect. Superconducting current flowing through a junction between two superconductors, its dependence on the phase difference.
Transient Josephson effect: frequency of Josephson current oscillations at a constant potential difference between the junction's terminals.
Dependence of current on the magnetic field flux through the junction. Practical applications of the Josephson effect. SQUID (qualitative description).
Main literature for home
reading: Introduction to Solid State
Physics , 8th Edition, by Charles Kittel
Additional literature for home
reading: Fundamentals of the Theory of Metals by A.A. Abrikosov and/or Principles of the Theory of Solids by J.M. Ziman
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