Quantum mechanics was originally designed to describe the physics of one or a few atoms. We have since learnt that it can also dictate the physics of matter on a macroscopic scale. Superconductivity and superfluidity are perhaps the most dramatic manifestation of macroscopic quantum physics.
The electrical resistance of a metal decreases when the metal is cooled. For a superconductor, the resistance vanishes completely below a threshold temperature! The absence of dissipation has made superconductors useful in high-field magnets, e.g. in the LHC collider for high-energy physics or in a MRI machine in a hospital. A superconductor also expels magnetic fields, leading to applications such as magnetically levitated trains.
Superfluids, such as liquid helium and atomic Bose condensates, are the charge-neutral cousins of superconductors. Recent advances in quantum optics have led to an explosion of research activity on atomic condensates as a possible system for quantum information processing.
The key to the physics of these remarkable materials is the phenomenon of spontaneous broken symmetry. In this course, I will describe how this explains the macroscopic behaviour of superconductors and superfluids. This will be introduced in the framework of the Ginzburg-Landau theory of macroscopic phase coherence. This theory gives a detailed description of the signatures of superconductivity: magnetic flux expulsion (Meissner effect) and flux lines carrying the magnetic flux quantum (h/2e).
I will also introduce the microscopic (Bardeen-Cooper-Schrieffer) theory of electron pairing which leads to superconductivity. This part of the course will contain a self-contained introduction to techniques in quantum field theory, such as second quantization.
Quantum field theory has been an important tool in condensed matter physics in the last 50 years. Conversely, condensed matter physics has provided a fruitful testing ground for ideas in quantum field theory. We get a glimpse of this in the theory of flux expulsion in superconductors --- it is intimately related to (and pre-dates) the Higgs mechanism of mass generation in high-energy physics.
Throughout the course, systems of current research interest will be included to illustrate established theory and also to indicate where conventional understanding fails.
At the end of the course, you will have a basic understanding of superfluids and superconductors. From a wider perspective, you will have been exposed to key concepts and theoretical techniques in condensed matter physics.
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