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

DayTopicReadingSummaryAssignments
M 9/30PHYSICS COMP EXAM No class
1W 10/2Sommerfield modelA&M Ch 2-3, Kittel Ch 6day1.pdf: Gas of free electrons trapped in a 3d potential. Fermi Energy. Orders of magnitude. Introduce periodic potential.HW #1
2F 10/4Occupation functionA&M Ch 8 & Ch 12day2.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.
DayTopicReadingSummaryAssignments
3M 10/7Phonon scattering A&M Ch 13day3_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
4W 10/9Phonon scatteringA&M Ch 13day4_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.
5F 10/11Ballistic TransportKittel 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
DayTopicReadingSummaryAssignments
6M 10/14Adding scatteringKittel 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
7W 10/16Adding scatteringKittel 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.
8F 10/18Variable range hopping. Mott InsulatorsMott's txt bk, A&M p340 & 542day8_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
DayTopicReadingSummaryAssignments
9M 10/21Electrons in B-fieldFeynman Lecture on AB effect day9_2013.pdf: Topological phenomena in electron transport. Electrons in B-field: Hall effect, Aharanov-Bohm effect. HW #4
10W 10/23Quantum Hall EffectArticle 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.
11F 10/25Tunneling devicesTunneling (wikipedia)day11_2013b.pdf: Importance of tunneling device in technology. Calculating I_tunnel. Examples: STM microscopy, STM spectroscopy, tunnel magnetoresistance, tunnel diodes.hw4solns.pdf
DayTopicReadingSummaryAssignments
12M 10/28SuperconductivityIbach chapterday12_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
13W 10/30SuperconductivityIbach chapterday13_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.
14F 11/1 hw5soln.pdf

review session and final

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