Quantum Theory of Matter:
Superfluids & Superconductors
Course Plan 2005 [ 26 lectures ]
- Overview [ 1 lecture ]
- broken symmetry in condensed matter physics
- examples: BEC, superfluids, superconductors, magnetism
- macroscopic quantum effects: SQUIDs
- new materials: cuprate superconductors
- Bose-Einstein condensation [ 1 lecture ]
- revision: periodic conditions, counting states
- ideal Bose gas
- macroscopic occupation of single-particle state
- degeneracy temperature
- phase transition: vanishing chemical potential
- Superfluidity & the condensed state [ 2 lectures ]
- condensate wavefunction
- momentum distribution of a condensed state
- current and velocity
- Landau criterion for superfluidity
- pathologies of an ideal Bose gas
- Interacting Bose fluids [ 3 lectures ]
- liquid helium: condensate fraction, excitation spectrum
- variational approach: nonlinear Schrodinger equation
- characteristic scales: Hartree energy and healing length
- London theory: smooth phase and density variations
- condensate phase & the superfluid velocity
- effective Hamiltonian: number-phase representation
- dynamics: sound waves; Goldstone theorem
- Vortices [ 2 lectures ]
- circulation quantisation
- vortices as topological singularities
- vortex energy
- superfluid in rotation
- Superconductors: macroscopic quantum effects [ 5 lectures ]
- Phenomenology of condensate phase: London equations
- Meissner effect: penetration depth (Higgs mechanism)
- Hidden order: phase coherence & the Josephson effect
- Type II superconductors: flux quantisation
- Abrikosov flux lattice: flux flow & dissipation
- Second quantisation [ 3 lectures ]
- boson creation & annihilation operators
- quantisation of normal modes: from waves to particles
- example: one-dimensional phonons
- fermions: creation & annihilation operators
- Superfluids: microscopics [ 3 lectures ]
- second quantisation of interacting Bose fluid
- number-phase uncertainty
- condensate depletion
- Superconductors: microscopics [ 6 lectures ]
- phonon-mediated electron attraction
- Cooper pairing: Fermi sea on the edge of an instability
- Bardeen-Cooper-Schrieffer (BCS) trial wavefunction
- BCS Hamiltonian: energy gap, excitations
- pairing symmetry and spin