Physics 170 Condensed Matter

Description: 
Crystal structure; mechanical, thermal, electric, and magnetic properties of solids; band theory of solids; metals, insulators, and semiconductors; lattice vibrations; imperfections; superconductivity and superfluidity.
Faculty: 
Francis Paraan
References: 
Kittel, Ashcroft & Mermin
Schedule: 
R201, WFR (WF 8:30AM-10:00AM)

Corequisite:
Physics 142 (2014)

Announcements:

Please submit your PS2 and NB2 requirements here: 
https://forms.gle/zj2dXM5ZUZTbgHXK6

RFID access required for R201. Please inform me if you need an RFID.
Please upload proof of satisfying corequisite here: Corequisite proof submission link

Notebook checklist items for previous semesters:

Week 13 (Dec 13)
Kittel ISSP Chapter 8, Semiconductors: Carriers and transport

Week 12 (Dec 6)
Kittel ISSP Chapter 8, Semiconductors

- Briefly discuss how band structure in semiconductors affect transport properties in the scattering time approximation.

Week 11 (Nov 29-Dec 1)
Kittel ISSP Chapter 7, Nearly free electrons

  • Describe the Kronig-Penney model and summarize how it approximates the periodic potential in a crystal.
  • Work on Problem Set 2, especially Problem II.
  • Download Problem Set 2 here.

Week 10 (Nov 22-24)
Kittel ISSP Chapter 7, Energy bands I

  • Briefly explain why the Bragg reflection of electron waves due to a periodic potential can cause band gaps to form at the boundaries of the Brillouin zone.
  • Discuss how the presence or absence of band gaps give rise to insulating and conducting materials. 
  • Consider a 1D crystal with lattice spacing a so that the potential also has period a. Use the Bloch theorem to write down the functional form of the eigenfunction solutions to the Schrodinger equation.  

Week 9 (Nov 15-17)
Kittel ISSP Chapter 6, A&M Chapters 1,3 Drude model for electron transport

  • Provide a brief description of the Drude model of electron transport and the core assumptions needed for it to hold.
  • Give the Drude model expression for Ohm's law and describe each of the quantities appearing in the Drude conductivity.
  • Explain how a Hall effect experiment may be used to determine the charge and density of current carriers in a material.

Week 8 (Nov 8-10)
Kittel ISSP Chapter 6 Free electron gas

  • Describe how a Fermi sphere forms in a 3D free electron gas at zero temperature due to Pauli exclusion.
  • Obtain the Fermi energy of a free electron gas with density N/V.
  • Make a sketch and describe the qualitative features of the Fermi distribution at low temperatures.
  • Give a simple argument for why the specific heat of the electron gas is proportional to temperature at low temperatures. 

Week 7 (Oct 25-27)
Catch up week.

Week 6 (Oct 20)
Kittel ISSP Chapter 5 Crystal phonons

  • Derive the leading temperature dependence of the phonon heat capacity in the Debye approximation at low temperatures (temperatures much lower than the Debye temperature).

Week 5 (Oct 9)
Kittel ISSP Chapter 4 Crystal vibrations

  • Derive the dispersion relation for elastic waves in a one-dimensional monoatomic crystal.
  • Explain why dispersion relations are typically reported only for wavevectors in the first Brillouin zone.
  • Show how phonon momentum is accounted for in inelastic scattering processes.

Week 4 (Oct 4-6)
Kittel ISSP Chapter 3 Crystal binding and linear elastic response

  • Summarize in a table the important features of the four types of crystal binding mechanisms discussed in class. You may use a sketch or cartoon to illustrate. Mention the quantum mechanical highlights.
  • Briefly describe linear elastic response theory (one paragraph only). The theory can be summarized elegantly in a single tensor equation (and its inverse).