**Physics of Мetals**

*Prof. M.R.Trunin*

*The course embraces: early Drude-Sommerfeld theory, electron energy bands, Fermi surface and elementary calculation techniques; kinetic properties: electrical and galvanomagnetic effects; scattering processes; behavior of metals in high frequency fields; quantum conductivity effects; electromagnetic wave propagation in metals in presence of magnetic field. *

**Curriculum**

- General concepts of metal theory. Concept of free electron model, mean free path. Assumptions of Drude theory. Statistic electrical conduction in metals. High frequency conductivity. Thermal conduction of metals. Wiedemann-Franz law.
- Thermodynamic properties of free electron gas. Ground state. Application of Fermi-Dirac distribution. Thermal capacity of electron gas. Sommerfeld theory of metal conductivity.
- Crystal lattice. Unit cell. Reciprocal lattice. Brillouin bands. Normal modes and phonons. Thermal capacity of lattice. Debye and Einstein models. Thermal expansion of metals.
- Band theory. Periodic potential. Bloch theorem. General properties of electron energy spectrum in metals. Electrons in weak periodic potential.
- Strong coupling method. Diagrams of expanded, reduced and recurrent bands. Metals, semiconductors, dielectrics. Harrison plotting of Fermi surface.
- Quasiclassical model of electron dynamics. Equation of motion in electric and magnetic field. Electrons and holes. Effective mass. Cyclotron mass. Motion trajectory in magnetic field. Trajectory types.
- Kinetic equation. Collision integral. Relaxation time approximation. Conductivity in stationary electric field. Fermi surface shift.
- Scattering cross-section and mean free path. Scattering on neutral and charged impurities, dislocations, phonons. Electron-electron scattering. Combination of scattering processes.
- Magnetoresistance. Conductivity tensor in zero and first approximations. Resistance tensor. Hall effect. Magnetoresistance in two-band model. Effect of Fermi surface shape on electrical resistance. Open trajectory role.
- Density of states. Electrons in strong magnetic field. Quasiclassical quantization. Landau levels. Bloch electron level degeneracy. Oscillations of thermodynamic values. De Haas-van Alphen and Shubnikov-De Haas effects.
- Normal skin-effect. Leontovich boundary conditions and metal surface impedance. Abnormal skin-effect. Inefficiency concept. Chambers formula.
- Cyclotron resonance. Cyclotron resonance orbit cutoff. Rf size effects.
- Skip orbits. Magnetic surface levels. Interference effects in magnetic field. Conductivity quantum correction.
- Electromagnetic wave damping mechanisms in metals. Landau damping. Wave propagation in presence of magnetic field. Types of wave: helicon, Alfvén and cyclotron waves in metals.