PH-719 Topics in Condensed Matter Physics.

  1. Scattering from ordered structures: General Theory of scattering from a crystal. X-ray, neutron and electron scattering. Magnetic and small angle scattering.
  2. Electron Transport Phenomenon in bands: Motion of electrons in bands. Boltzmann transport equation, relaxation time approximation. Onsager relations and reciprocity. Electrical conductivity, generalized treatment of conductivity in bands. Thermoelectric phenomenon (Seebeck and Peltier effects.) Introduction to Fermi liquid theory.
  3. Dielectric and Optical Properties:General background: Maxwell equations, dielectric functions, Kramers–Kronig relations. Absorption of electromagnetic radiation; Optical properties of semiconductors, direct and indirect transitions, excitons. Optical properties of insulators. Longitudinal amd transverse normal modes, local field, Polarization, and polarization catastrophe, Ferroelectrics and ferroelctricty. Optical modes in ionic crystals, coupling of electromagnetic and lattice modes (polarons and polaritons), point defects and color centers. Optical properties of metals, plasma frequency, metals at low frequencies, plasmons, Brillouin scattering.
  4. Electrons in low dimensional systems: Electronic states in bands: review of free, nearly free and tightly bound electrons. Confined states in zero, one and two dimensions. Effects of confinement on band structures and optical properties: band gap variations and surface plasmon effects.  Density of states in quantum wells, wires and dots.  Quantum Hall effect.  semiconductor laser action. Single electron tunneling. Tunneling structures and devices.
  5. Critical phenomenon and phase transitions: Molecular field theory and application to simple systems e.g. ferromagnetism or Van der Waals equation of state. Generalized theory of phase transitions (Landau theory), order parameter, Free energy, equilibrium behavior, temperature dependence of order parameter and generalized susceptibilities, coherence lengths, specific heats. Application to different examples e.g. ferromagnetic, ferroelectrics, superconductors(Ginzburg-Landau theory). Basic ideas of fluctuations and of critical exponents.


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