Physics 155.

Physics 155:  (50% midterms and final. 50% homework, participation and special projects*)
* Special projects typically involve working a problem for this class a presenting your work in a blog post.

0. Crystal structure. Crystals are spatially periodic. There is a basic unit, like an atom or small molecule. A crystal is a collection of many of these basic units are arranged in a regular pattern. A good way to learn about crystals is through examples. Graphene is a 2-dimensional structure, made by arranging a basic unit consisting of 2 carbon atoms at the vertices of a triangular lattice. A one-dimensional chain of atoms is an uncomplicated example.

1. Quantum review. We will look at the quantum eigenstates (wave-functions) of simple atoms and square wells. Going from one square well to several square wells is a good first step toward understanding electron states in crystals.

2. Quantum states of electrons in crystals.
     Most of solid state physics deals with quantum states of electrons in crystals. What are they? How are quantum states of electrons in crystals related to states of electrons in atoms? This is a natural starting point for the study of solid state physics. It leads to something called “band theory” which includes states called “Bloch states”. We will explore the nature of “Bloch states”. These provide the quintessential starting point for the understanding of solid state physics.

3. Fermi energy
     Fermi statistics and the Pauli exclusion principle play a huge role in the physics of crystals. Most Bloch states of quantum energy below the Fermi energy are occupied by electrons, while most states above the Fermi energy are not occupied. Electrons very near the Fermi energy play a major role in phenomena such as: magnetism and superconductivity as well as characteristics such as conductivity, specific heat and magnetic susceptibility. (Electrons near the Fermi energy in crystals are roughly  analogous to valence electrons in atoms.)

4. Semiconductor physics
    For semiconductors the Fermi energy is in a gap between two bands. Additionally, it can be manipulated by doping. Semiconductor structures often involve sp2 or sp3 bonding. (This is the same type of bonding that connects carbon atoms graphene as well as in biological systems.)

5. Metal physics.
     Metals have a Fermi energy within a band so that there are lots of states very near the Fermi energy. Understanding what happens around the Fermi energy in metals is key to understanding electrical conductivity and superconductivity. Magnetism, superconductivity and other interesting and exotic phenomena. Sometimes a Fermi surface may be unstable and interesting things happen.

6. Disorder.
     A crystal is a mathematically perfect thing (at least in our models) but what happens when it is not? How does disorder effect conductivity? This turns out to be pretty interesting. It leads to “localization” and was the subject of a Nobel prize in about 1977. This subject lends itself to learning a matrix formulation of quantum mechanics and can be explored via computer simulations.

7. Magnetism.
    A lot of popular literature is confusing with regard to the fundamental nature and origin of magnetism. Magnetism comes from electron-electron repulsion and its relationship to spin via the Pauli exclusion principle.

8. Superconductivity.
     Electrons form pairs which act as Bosons, form a Bose condensate and conduct electricity with no resistance. How strange is that? Superconductivity was discovered empirically in about 1908 however there was no real theoretical understanding of superconductivity until about 1958. The difficulty and nature of the theory helped motivate ideas underlying the more is different paradigm.

9. More is different.
     Understanding electrons, protons and neutrons and their interactions does not necessarily mean we can understanding the nature and phenomena of systems of many electrons, protons and neutrons. Some phenomena in metals, biological systems and other complex interacting systems seems to elude an understanding starting from the Schrodinger or Dirac equation.

Outline:
Week 1. Brief discussion of crystal structure. Review of key quantum concepts and wave functions including low energy bound states of finite square wells in 1 dimension (1D). Also, hydrogen atom ground and first-excited states and a brief intro to sp2 hybridization and bonding. Thinking about constructing crystal states, as well as states of 2, 3, or 4 wells in 1D. Bloch state construction and quantum energies of Bloch states.

Week 2. More on Bloch states. States of electrons in crystals.

Week 3. Semiconductor theory

Week 4. Semiconductor theory and semiconductor device physics

Week 5. Metal physics

Week 7. Metal physics 2

Week 8. Magnetism

Week 9. Superconductivity