General Prerequisites:
Course Term: Hilary
Course Lecture Information: 16 lectures
Course Weight: 1
Course Overview:
16 lectures.
Areas: CMT
Link to submit your homework to TA Matthew Steggles: https://cloud.maths.ox.ac.uk/index.php/s/x2G8A9QgRrsaFoJ
Areas: CMT
Link to submit your homework to TA Matthew Steggles: https://cloud.maths.ox.ac.uk/index.php/s/x2G8A9QgRrsaFoJ
Learning Outcomes:
Course Synopsis:
Intro to Superfluids and Superconductors
Two Fluid Model and Vortices
Landau Criterion and Intro to Charged Superfluids / London Theory
Superconducting Vortices / Type I and Type II Superconductors
Microscopic Theory / Second Quantization / Gross Pitaevskii and Bogoliubov Theory
Feynman Theory of Superfluidity
Ginzburg Landau Theory / Anderson Higgs Mechanism / Coherence Length / Vortex Structure
Interacting Fermions / Second Quantization / First Order Perturbation Theory / Hartree and Fock Terms
Hartree Fock Theory
Coulomb Interaction / Screening and Response
Linear Response Theory / Lindhard, Thomas Fermi, RPA / Plasmons
Landau Theory of Fermi Liquids part 1
Landau Theory of Fermi Liquids part 2
BCS theory part 1: Phonon Attraction Mechanism / Cooper Problem
BCS wavefunction
Bogoliubov Excitation Spectrum
plus if time permits
Quantum Hall Effect / Laughlin Gauge Invariance Argument
Chern Numbers / Quantum Spin Hall / Topological Insulators in 2 and 3 D
Fractional Quantum Hall Effect
Two Fluid Model and Vortices
Landau Criterion and Intro to Charged Superfluids / London Theory
Superconducting Vortices / Type I and Type II Superconductors
Microscopic Theory / Second Quantization / Gross Pitaevskii and Bogoliubov Theory
Feynman Theory of Superfluidity
Ginzburg Landau Theory / Anderson Higgs Mechanism / Coherence Length / Vortex Structure
Interacting Fermions / Second Quantization / First Order Perturbation Theory / Hartree and Fock Terms
Hartree Fock Theory
Coulomb Interaction / Screening and Response
Linear Response Theory / Lindhard, Thomas Fermi, RPA / Plasmons
Landau Theory of Fermi Liquids part 1
Landau Theory of Fermi Liquids part 2
BCS theory part 1: Phonon Attraction Mechanism / Cooper Problem
BCS wavefunction
Bogoliubov Excitation Spectrum
plus if time permits
Quantum Hall Effect / Laughlin Gauge Invariance Argument
Chern Numbers / Quantum Spin Hall / Topological Insulators in 2 and 3 D
Fractional Quantum Hall Effect