### Table of Contents

# PH671: Solid State Physics - Electron Transport Module

# Fall 2013

PH671 is a two-credit graduate course taught by the Department of Physics at Oregon State University.

In 2013 the course is being taught Weeks 1 - 5 of Fall Quarter by Prof. Ethan Minot. The module is offered biyearly.

## Calendar

Day | Topic | Reading | Summary | Assignments | |
---|---|---|---|---|---|

M 9/30 | PHYSICS COMP EXAM | No class | |||

1 | W 10/2 | Sommerfield model | A&M Ch 2-3, Kittel Ch 6 | day1.pdf: Gas of free electrons trapped in a 3d potential. Fermi Energy. Orders of magnitude. Introduce periodic potential. | HW #1 |

2 | F 10/4 | Occupation function | A&M Ch 8 & Ch 12 | day2.pdf: Drawing the occupation function in k-space, Bloch's theorem, free electron gas at T = 0, electron velocity, electron response to E-field, relaxation time, calculating a current. | |

Day | Topic | Reading | Summary | Assignments | |

3 | M 10/7 | Phonon scattering | A&M Ch 13 | day3_2013.pdf: Drude result for calculating current density. Phonon review, ph575 notes24. Fermi Golden Rule for scattering probability. Transition matrix element for electron-phonon interaction. Conservation of momentum/energy. Scattering probability. | HW #2 |

4 | W 10/9 | Phonon scattering | A&M Ch 13 | day4_2013.pdf: Temperature dependent resistivity in metals predicted by phonon scattering matrix elements. Highest energy phonon sets important energy scale. Estimation of highest energy phonon. Introduction to electron transport in ballastic systems. | |

5 | F 10/11 | Ballistic Transport | Kittel Ch 18 (Nanostructures) | day5_2013.pdf: Comparison with diffusive transport. CNT example. Calculating the conductance quantum. Definitions of 1d channels. Systems with multiple 1d channels. | hw2solns.pdf |

Day | Topic | Reading | Summary | Assignments | |

6 | M 10/14 | Adding scattering | Kittel Ch 18 (Nanostructures) | day6_2013.pdf: Add scattering to a ballistic system. One scattering site reduces current by transmission probability. Two scattering sites, transmission depends on wave interference. | HW #3 |

7 | W 10/16 | Adding scattering | Kittel Ch 18 (Nanostructures) | day7_2013.pdf: Pair of inelastic scattering sites. See hw#3 for many inelastic scattering sites. Many elastic scattering sites. Anderson localization. Review of what we've covered so far. Temperature-dependent conductivity of lightly doped semiconductors. Gate-voltage-dependent conductivity of lightly doped semiconductors. | |

8 | F 10/18 | Variable range hopping. Mott Insulators | Mott's txt bk, A&M p340 & 542 | day8_2013.pdf: Disordered semiconducting materials: conductance vs. temperature predicted by variable range hopping theory. Introduction to Mott insulator state. Calculation of critical lattice constant for metal-insulator transition. Little a limit: Thomas-Fermi screening depends on the electron concentration. Big a limit: polarizability depends on the distance to neighboring dipoles. | hw3solns.pdf |

Day | Topic | Reading | Summary | Assignments | |

9 | M 10/21 | Electrons in B-field | Feynman Lecture on AB effect | day9_2013.pdf: Topological phenomena in electron transport. Electrons in B-field: Hall effect, Aharanov-Bohm effect. | HW #4 |

10 | W 10/23 | Quantum Hall Effect | Article 1, Article 2 | day10_2013.pdf: Aharanov-Bohm effect. QM description of cyclotron orbits. Landau levels. Fluctuation in electron density (constant chemical potential). The QHE experiment. Animation. QHE explanation based on ExB drift velocity. | |

11 | F 10/25 | Tunneling devices | Tunneling (wikipedia) | day11_2013b.pdf: Importance of tunneling device in technology. Calculating I_tunnel. Examples: STM microscopy, STM spectroscopy, tunnel magnetoresistance, tunnel diodes. | hw4solns.pdf |

Day | Topic | Reading | Summary | Assignments | |

12 | M 10/28 | Superconductivity | Ibach chapter | day12_2013.pdf: The experimental observations. Note about Type I vs. Type II. Composite bosons. Ionic lattice can be deformed: trail of deformation. Size scale for attractive interaction. The Cooper pair wavefunction. The Cooper pair binding energy at T = 0. The number density of Cooper pairs. Temperature dependence of Cooper pair binding energy. | HW #5 |

13 | W 10/30 | Superconductivity | Ibach chapter | day13_2013.pdf: Center of mass motion of Copper pairs. Critical current density. London equation. London penetration depth. Solenoid field generated by a solid cylinder of superconductor. Critical B field for Type I superconductor. Explaining the difference between Type I and Type II superconductors. | |

14 | F 11/1 | hw5soln.pdf |

## Syllabus

Fundamentals of bandstructure

- Bloch theorem
- Semiclassical dynamics

Boltzman transport equation

- motion in constant E field → Drude result
- diffusion
- phonon scattering mechanism

Quantum transport

- elastic vs inelastic scattering
- 1d wire no scattering (nano module?)
- Landauer formalism

Quantum to classical crossover

- Transmission probabilities
- Resonant tunneling
- Incoherent scattering

Transport in magnetic field

- Vector potential and electron phase
- Example: AB effect

Localization

- Feynman path integrals in solid state
- Anderson localization in different dimensions
- Testing with B-field

Metal-Insulator transition

- Difference between Mott insulator and Anderson localization (not covered in 2009)
- Thomas-Fermi screening
- Bohr radius overlap

Tunneling

- WKB approx
- STM (nano module?)
- Fermi golden rule
- Coulomb blockade (nano module?)

Superconductivity

- curl A = 0 inside superconductor
- consequences

### Archive

Webpages from previous years