PHY238A: Condensed Matter Physics, Fall 2014

PHY238A: Condensed Matter Physics, Fall 2014

Course Information:

Instructor: Sid Parameswaran, Assistant Professor

310J Rowland Hall, sidp_at_uci.edu

Lectures: Tuesday/Thursday 9:30AM - 10:50 AM, Rowland 192.

Office Hours: Tuesdays/Thursdays, 11:00AM-12:00PM, Rowland 310J.

Overview:

This is the first in a three-course graduate sequence on condensed matter physics. Roughly, this quarter we will learn about the structure of matter, chemical bonding, and crystal structures, apply that knowledge to understand lattice vibrations in solids and the electronic properties of materials via Bloch's theorem, and learn basic elements of the theory of metals, insulators and semiconductors. Throughout, we will use tools from quantum mechanics and statistical mechanics to explain basic phenomena of the solid state. Modern topics that may be covered if time permits include topological insulators, quasicrystals, and the basics of the quantum Hall effect.

Prerequisites:

As this is an upper-level graduate course, you are expected and will need to be familiar with quantum and statistical mechanics and electrodynamics at the level of our own first-year coursework. If you have not taken these courses, or are taking them concurrently, but still would like to attend the lectures or sign up for the class, please contact me beforehand. As in all courses and particularly advanced ones, you will get as much out of this class as you put in to it - so keep up with the homework and readings!

Textbook(s):

Condensed matter is a vast subject and there are many books that do a reasonably good job of presenting the basics. The course will more or less follow The Oxford Solid State Basics by Steve Simon - i.e., this is the required text. Although the book is slightly less advanced than is ideal (it is intended for an advanced undergraduate course at Oxford), it more than makes up for this in humor, modernity, and above all, style. The lectures may therefore be a little more advanced to compensate, and I may supplement the basic material with suggested reading.

I strongly recommend purchasing or otherwise having access to the now-classic Solid State Physics by N.W. Ashcroft and N.D. Mermin; this is a canonical textbook that often proves to be useful beyond the classroom. Previous versions of 238A used M.P. Marder's Condensed Matter Physics, so you might want to have that handy as well. Finally, there are older books that you might find illuminating: Principles of the Theory of Solids by J.M. Ziman, and Quantum Theory of Solids by C. Kittel. Steve Simon's book also contains a brief list of other texts with comments on their pros and cons, which you might find useful.

Lecture Notes and Course Outline:

I will post my handwritten notes whenever possible and appropriate, but I suggest that you take notes in class - particularly as this is an advanced course, I hope there will be a fair amount of discussion in 'real time' that you might like to have a record of. I will post a rough outline of the lectures one week before classes start; this will be updated to reflect what is actually covered.

Here is a rough schedule of topics to be covered. Some topics may bleed into subsequent lectures.

Warning: this is subject to change without notice as the class progresses.

These notes are organized by topic rather than by the actual lecture; so some span multiple lectures, or vice-versa.

Brief primer on basic statistical mechanics (from Feynman's book).

Pines & Laughlin's article on emergence.

Course Overview

  1. Specific Heat of Solids
  2. Electrons in Metals (Ashcroft & Mermin Appendix on the Sommerfeld expansion)
  3. Basic Chemistry of the Solid State
  4. Types of Matter
  5. Toy Models of Solids in d=1
  6. Electrons in d=1, tight-binding, Peierls distortion
  7. Geometry of solids; crystal structure
  8. Reciprocal lattice, Brillouin zones, waves in crystals
  9. Neutron and X-Ray Diffraction
  10. Electrons in Periodic Potentials I: Nearly Free Electrons
  11. Electrons in Periodic Potentials II: Bloch's Theorem
  12. Graphene Basics
  13. Semiconductor Physics & Devices
  14. Semiclassical Electron Dynamics
    1. 'Quantum Oscillations'
    2. Landau Levels and the (Integer) Quantum Hall Effect
  15. Topology in Solids: An Introduction

If you prefer a single large file with all the lectures, here is the combined PDF (warning, 195 pages, file size~25MB).

Oct. 2: Overview ; Specific heat of Solids, Einstein and Debye models.

Oct. 7: Finish Debye model. Electrons in metals: Drude Model.

Oct. 9: Electrons in Metals: Sommerfeld theory. PS#1 Due.

Oct. 14: Periodic Table, Chemical Bonding, Types of Matter.

Oct. 16: Toy Models of Solids in d=1; simple models of compressibility, expansion, melting. PS#2 Due.

Oct. 21: Vibrations of a 1D Monoatomic Chain: a first look at phonons. 1D Diatomic chain, Acoustic/optical modes.

Oct. 23: Tight-binding models: a first look. PS#3 Due.

Oct. 28: Crystal structure.

Oct. 30: Reciprocal Lattice and Brillouin zones; Start Neutron/X-Ray Diffraction.. Ps#4 Due -- extension until Monday, Nov. 3.

Nov. 4: Finish Neutron/X-Ray Diffraction; start nearly free electrons.

Nov. 6: Finish nearly free electrons; Bloch's theorem. PS#5 Due.

Nov. 10: Take-home midterm posted on website/emailed out.

Nov. 11: Veteran's Day, no class

Nov. 13: Take-home review; band structure and thermodynamics of graphene; Take home mid-term exam due in class.

Nov. 18: Semiconductor Physics.

Nov. 20: Semiconductor Devices.

Nov. 25: Semiclassical electron dynamics. PS#6 Due.

Nov. 27: Thanksgiving, no class.

Dec. 2: Measuring the Fermi surface; Shubnikov-de Haas and de Haas-van Alphen oscillations.

Dec. 4: Electrons in magnetic fields: Landau levels and the Quantum Hall Effect.

-- also on Dec. 4, Steve Simon (author of the textbook) will give the department colloquium!

Dec. 9: Topological effects on semiclassical dynamics: Berry's phase in crystals. Chern insulators. PS#7 Due.

Dec. 11: Course summary. Final write-ups due via e-mail; final presentations I. 2-5pm (location TBD)

Dec 18: final presentations II (in lieu of final exam, 8:00-10:00 AM. in Rowland 192)

In the interests of fairness, the order of presentation will be decided by drawing lots on the day - so you will need to be ready by Dec. 12!

Problem Sets:

There will be one problem set a week except for the week of the mid-term. Problem sets will be posted by Tuesday, and will be due the following Thursday, by noon. You may hand them in during class, or place them in my mailbox in FRH 4129, where they will be picked up when the departmental office reopens after lunch. The late policy is simple: if you provide a reasonable excuse beforehand, I'm willing to accept late submissions on a case-by-case basis. In the absence of information to the contrary, however, I will assume that you are not turning in an assignment and you will not receive a grade for that set. You are free to discuss problems with each other and collaborate on solving them, but you must write up solutions independently. This is a graduate class, so expect the problem sets to involve work!

(See the most recent edition of this course for the PDF problem sets)

Final project topics

Grading:

Your grade will be based on the problem sets (50%), a mid-term exam (25%) and a 10-minute presentation (Powerpoint or blackboard) and 4-5 page write-up (preferably in LaTeX format) on a condensed matter topic (25%). The topic of the presentation must be discussed with me beforehand; ideally, by Thanksgiving. I will post a list of suggested topics by the beginning of November, but you can come up with your own as well.

As discussed, the mid-term will be a take-home exam.