Prerequisites

It is assumed that students taking this course will have also done Advanced Quantum Condensed Matter Physics.

Learning Outcomes and Assessment

The course presents a unified treatment of superconductivity, superfluidity and Bose-Einstein condensation as an introduction to the general problem of quantum coherence.

Synopsis

Introduction to Superconductivity:  Historical overview; superconducting materials; macroscopic properties; Meissner effect and levitation; type-I and type-II states; Landau theory; critical field Bc.

Ginzburg-Landau Theory:  The Ginzburg-Landau free energy and Ginzburg-Landau equations; London equations; penetration depth and coherence length; gauge transformations and gauge symmetry breaking (broken symmetry in internal space).

Vortex Matter:  Flux quantization; vortex lines and vortex lattice; the critical fields Bc1 and Bc2, type-I and type-II superconductivity; vortex pinning and critical currents; vortex liquid state.

Josephson Effect and SQUIDs:  DC and AC Josephson effects; gauge invariant phase; quantum interference for weak links; the DC SQUID; applications.

Superfluidity:  Phenomenology; superfluid wavefunction; two-fluid model and the fountain effect; flow quantization and vortices; first and second sound; rotons; Landau’s critical velocity.

Bose-Einstein Condensation (BEC):  Ultra-cold atomic gases; BEC with weak interactions; coherent states and second quantization; the Bogoliubov Theory and connection to the phenomenological Ginzurg-Landau Theory.

The Bardeen-Cooper-Schrieffer (BCS) Theory:  BEC to BCS cross-over; Cooper pairs; the BCS wavefunction; the Bogoliubov quasiparticles and the energy gap; experimental evidence for the validity of the BCS theory; order parameter and the Ginzburg-Landau coherence length.

Current Problems in Superfluidity and Superconductivity:  Unconventional forms of quantum order; p-wave spin-triplet superfluidity in 3He; spin-triplet superconductivity in Sr2RuO4 and UGe2; d-wave superconductivity in the high Tc cuprates; phase-sensitive measurements of the gap anisotropy; the pseudo-gap state; unconventional mechanisms for superconductivity; collective modes in superfluids and superconductors; the Anderson-Higgs mechanism and superconductivity.

References

BOOKS

Superconductivity, Superfluids and Condensates, Annett J F  (Oxford University Press, 2004)

Superconductivity of Metals and Cuprates, Waldram J R  (Institute of Physics Publishing, 1996)

Also:

Bose-Einstein Condensation in Dilute Gases, Pethick C J and Smith H  (Cambridge University Press, 2002)

Introduction to Superconductivity, Tinkham M  (McGraw-Hill, 1996)