§1 Translational symmetry and reciprocal lattice

§2 Properties of the reciprocal lattice

§3 Bloch's theorem

3.1 Non-degenerate case

April 16-18

3.2 Degenerate case

§4 Reduction to the Brillouine zone

§5 Boundary conditions: counting the available states

Chapter 2, Dynamic properties of the lattice

§1 Lattice oscillations

1.1 Lattice waves and eigenmodes

1.2 Examples. Properties of the lattice waves

April 23-25

§2 Specific heat of the lattice

2.1 Bravais lattice case

2.2 Lattice with basis

§3 Diffraction on the lattice. Phonons

3.1 The perfect crystal case (T=0)

3.2 Diffraction in presence of oscillations (finite T)

April 30 - May 2

3.3 Phonons

3.4 Debye-Waller factor

3.5 Beyond harmonic approximation. Phonon-phonon interaction

Chapter 3, Electrons in solids

1.1 Drude theory of metals

May 7-9

1.2 Sommerfeld theory of metals

§2 Electron diffraction on the lattice

May 14-16

§3 Band structure calculation methods

3.1 Nearly free electrons (NFE) model

3.2 Tight binding model (TBM)

3.3 Linear combination of atomic orbitals (LCAO) method

3.4 Orthogonalised plane waves (OPW) method

3.5 Augmented plane waves (APW)

3.6 Green's function method

May 21-23

§4 Band structure and conductance properties

§5 Electrons in semiconductors

5.1 "Clean" case (intrinsic semiconductors)

5.2 Doped semiconductors

§6 Electron-electron interactions

6.1 Hartree-Fock approximation

May 28-30

6.2 Static screening. Thomas-Fermi approximation

6.3 Dynamical screening. RPA approximation

6.4 Screening singularities. Friedel oscillations and sum rule

June 4-6

6.5 Basic principles of the Fermi liquid theory

6.6 Interacting fermions in 1D: Tomonaga-Luttinger model

June 11-13

1.1 Boltzmann equation

1.2 DC conductivity

1.3 Residual resistivity

June 18-20

1.4 Phonon contribution to resistivity

1.5 Kinetic coefficients

§2 Solids in magnetic fields

2.1 Hall effect

June 25-27

2.2 Energy quantisation in finite magnetic field

2.3 Integer quantum Hall effect

2.4 Fractional quantum Hall effect

§3 Magnetization and magnetic susceptibility

3.1 Atomic contribution

July 2-4

3.2 Conductance band contribution

1.1 Exchange interaction

1.2 Heisenberg model within the MFA

1.3 Ising model and its solutions

July 9-11

§2 Superconductivity

2.1 Role of electron-phonon coupling

2.2 Cooper instability

2.3 BCS groundstate, energy spectrum

July 16-18

2.4 Thermodynamic properties

2.5 Physical properties of superconductors

2.6 Tunnelling between superconductors. Josephson effect

2.7 High-T

Conclusions