Last lectures…

I seem to have some difficulties in keeping up constant blogging. Now after three more lectures (on Coulomb blockade, on superconducting junctions, and on graphene), I have reached already Chapter 10 in the book. I skipped Ch. 8 on quantum dots in order to be able to cover the other chapters on time, and I have skipped also some sections in each of the other chapters as well: I did not talk about cross correlations, full counting statistics or heat current noise related to Chapter 6, skipped dynamical Coulomb blockade in Chapter 7, SINIS physics in Chapter 9, and multilayer graphene and nanoribbons in Chapter 10. On some other years I will probably make some other choices. Anyway, I tried to motivate supercurrent in the superconducting junctions as a dual effect to the Coulomb blockade, and superconducting qubits as elements interpolating between two extreme situations.

For graphene, the main point was to show the origin of the Dirac dispersion, and illustrate the difference to ordinary metals. This is not discussed properly enough in the book, but I tried to fill in the gap in the lectures by discussing the main distinctions between metals, insulators and graphene-type semimetals. When I wrote the graphene chapter (2010 or so), the emphasis in the research community had been on theory related to the Dirac spectrum. This is visible in the graphene chapter, as the main electronic effects that I describe are those arising from the merger of high-energy (Dirac) physics with graphene electron transport. I could have obviously added much more, related to the forms of scattering in graphene, the absence of weak localization, and its recovery with intervalley scattering, and so on. By the way, there is an interesting point that one learns from graphene: when I talk about (relativistic) “high-energy physics”, graphene shows that I get this type of physics only for low energies. It therefore shows that it could be that Dirac equation in fact emerges as a low-energy theory from some high-energy physics (similar to the microscopic model of graphene). Also, some of the symmetries in graphene (such as the isotropicity of the dispersion around the valleys) are emergent, not present in the full microscopic picture. At the same time, this discussion reveals a kind of a chicken-and-egg problem: in the way how it is presented in the book, the Dirac dispersion results from a specific tight-binding model. However, we do not need exactly that model, but the low-energy physics is pretty robust as long as the microscopic model preserves some symmetries (hexagonal lattice, A-B symmetry). Therefore, it is difficult to say which one is more fundamental, the Dirac equation or the underlying microscopic theory. It probably simply depends on the viewpoint. In fact this dilemma is studied in the momentum space topological classification of media, but about that I might write later…

Next week will be the last lecture on nanoelectromechanics and optomechanics, and it will be given by Francesco Massel.

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