Advanced solid state physics

• Define and discuss the concept of the density response function of a system of interacting electrons and its relation to the elementary electronic excitations in the system.
• Formulate and derive the analytic properties of general response functions including the Kramer-Kronig relations between the real- and imaginary parts.
• Discuss and characterize the various types of elementary electronic excitations in a solid state system including collective excitations, bound electron-hole, and single-particle excitations.
• Explain the key features of the density response function of the homogeneous electron gas.
• Describe the connection between the microscopic dielectric function and the density response function.
• Relate the microscopic dielectric function to the macroscopic optical constants of a solid such as the absorption coefficient and reflectivity, and discuss the role of local field effect.
• Define the single-particle Green function and the self-energy, and discuss its relation to the band structure of a solid.
• Discuss the GW approximation as a method to obtain the band structure
• Discuss the Bethe-Salpeter equation as a method to calculate optical excitations
• Explain the Hydrogenic model for calculating excitons
• Explain the Berry phase and relate it to topological insulators.

The density response functions and its relation to the dielectric function. A quantum expression for the response function; static and dynamical screening within the random phase approximation (RPA); plasmons and plasmon-polaritons; electronic band structures and quasi-particles; the single-particle Green’s functions and the concept of the self-energy; quasiparticle excitations and the GW approximation and the quasiparticle equation; excitons and the Bethe-Salpeter equation for optical excitations; Berry’s phase, topological insulators.

10317/10112, Knowledge of solid state physics and quantum mechanics. Advanced quantum mechanics is desirable, but the course can be followed without by the ambitious student.

Lectures, group work, exercises

This is a continuation of the introductory course on solid state physics.