Shining light on quantum materials: lessons from optical spectroscopy
Abstract:
This course will focus on the optical properties of crystalline solids. The main question we will address is what we can learn about a material, by seeing how it interacts with light.
We will start by an easy introduction to energy bands in solids, covering the concepts of Bloch states, energy bands, and density of states. This will be illustrated on the example of a molecule made up of N atoms. We will look at the cases of a single or multiple bands. Next, we will calculate the general form of the conductivity tensor, using the linear response approach. Following our calculation, we will explore what one can obtain from the conductivity tensor. We will investigate the case of a single band in the presence of an electric and magnetic field, and will explain the Hall effect, cyclotron resonance, and related concepts. This approach will be generalized for transitions between multiple energy bands. We will investigate specific examples of conductivity, such as Dirac systems, or systems with Schrödinger-like electrons. Finally, we will address the theory of Landau levels, and how it relates to optical properties of a material in a magnetic field.
All of the above will be illustrated on experimental data. The students will be given simple programming tools to understand optical spectra. Familiarity with quantum physics will be necessary for this course. It is not required to have a background in solid state physics.