Overview of Solid State Physics Starting from the Drude Model

1. The Drude Model A. Assumptions 1) Free Electron Model 2) Independent Electron Model 3) Relaxation Time Approximation 4) Maxwell Boltzmann Statistics - Elementary kinetic theory - Equation of motion

1. The Drude Model B. Main Results 1) DC Conductivity ( ) - mean free path at RT 2) Hall Coefficient ( ) 3) AC Conductivity ( ) - plasma frequency

1. The Drude Model B. Main Results 4) Thermal Conductivity ( ) - Wiedemann-Franz law = 5) Thermopower ( ) =

2. The Sommerfeld Model Electrons are fermions. - Ground state: Fermi sphere, - Distribution function Modification of the Drude model - the mean free path - the Wiedemann-Frantz law - the thermopower

3. Bloch Electrons Electrons are subject to a periodic crystal potential. Crystal structure = lattice + basis 14 Bravais lattices include sc, bcc, fcc (cubic) and simple hexagonal (hexagonal). Some common crystal structures are sodium chloride structure, cesium chloride structure, hexagonal close packed structure, diamond structure, zinc blende structure and wurtzite structure.

3. Bloch Electrons The crystal structure is studied by the x-ray diffraction. Diffraction condition (by lattice) - Bragg formulation - von Laue formation, = reciprocal lattice vector (geometrical interpretation) - Ewald construction - Brillouin zone boundary Geometrical structure factor (by basis) Atomic form factor

3. Bloch Electrons The Schrodinger equation for Bloch electrons with the Born-von Karman BC, Bloch theorem or Schrodinger equation in the momentum space

4. Beyond Relaxation Time Approximation Boltzmann equation RTA -> Main scattering mechanisms - impurities and crystal defects (dominant at low T) - phonons (dominant at high T) Matthiessen’s rule

4. Beyond Relaxation Time Approximation Classical theory of lattice vibrations - Harmonic approximation + Adiabatic approximation - Dispersion relation of the normal modes 3 acoustic modes [1 LA, 2 TA] 3(p-1) optical modes [(p-1) LO, 2(p-1) TO] Quantum theory – Phonons - Debye and Einstein model for lattice specific heat

5. Beyond Independent Electron Approximation N electron system Hartree approximation Exchange: Hartree-Fock approximation minimization of with in Slater determinant form Screening Fermi liquid theory of Landau