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Heat Transport
The aim is to provide a fundamental framework for appreciating the success of the quantum theory of solids in describing the transport coefficients of any solid subject to a temperature gradient and/or electric field. The solids in question range from semiconductors to superconductors passing through metals including those hosting strongly correlated or non-trivially topological electrons. The transport coefficients range from the most familiar (electrical conductivity) to most exotic (the Nernst effect or the thermal Hall effect). The hope is to show at the end of the course that while many mysteries have been solved, others persist, giving rise to a research area loosely called `quantum materials’, in which the focus is to understand what remains beyond this standard transport picture.
Syllabus
1) Introduction to dichotomies (Electrons & nuclei; crystals & glasses, metals & insulators)
2) Boltzmann equation for phonons: different regimes of thermal conduction in insulators
3) Onsager reciprocity, extended thermodynamics and thermoelectricity
4) Boltzmann equation for electrons: the Wiedemann-Franz law and the Mott formula
5) The Landauer picture of conduction as transmission, quanta of conduction, equivalency between Boltzmann and Landauer pictures, Kubo formula
6) Transport in a magnetic field: magnetoresistance, Hall and Nernst effects
7) Landau quantization: quantum oscillations, Fermi surface geometry & topology, the Fermi liquid and beyond
8) Collective quantum phenomena- I: Heat transport in superconductors
9) Collective quantum phenomena- II: Anomalous and topological transverse (Hall, Nernst, and thermal Hall response in magnets
Prerequisites
Examination
Oral examination (to be specified)