Flat-band superconductivity and heat transport in superconductors

This dissertation studies new topics in the fields of flat-band superconductivity and heat transport in superconducting nanostructures. In electronic condensed matter systems, in addition to the traditional metallic and insulating electronic band structures more exotic alternatives are also possible. One of these alternatives is a flat band, where the dispersion of the electrons vanishes completely close to the Fermi surface. One of the consequences of this is divergence of the density of states, which enhances interaction effects, including superconductivity, in the material. I review some existing ideas related to flat-band superconductivity as well as present new research on two materials that show some promise to support such a superconducting state. The two materials are rhombohedral graphite that exemplifies a more general class of materials called topological nodal line semimetals, and periodically strained Dirac materials, such as graphene or topological insulator surfaces. The findings include large fluctuations of the superconducting order parameter in our model for rhombohedral graphite due to vanishing of the superconducting gap in the electronic spectrum, and an exotic, inhomogenous superconducting state with a high critical temperature in the strained Dirac material model. The second part of this thesis concerns heat transport and fluctuations in superconducting nanostructures. Most of the attention is directed towards superconductor - insulator - normal metal (NIS) tunnel junctions. Such a junction can be used to cool down the normal metal part of the junction. In real world applications, however, complications due to quasiparticle heating and inverse proximity effect in the superconducting part arise. We address these complications by modelling a NIS junction with an additional normal metal heat sink attached to the superconductor and also by analyzing an experimental realization of the setup. We also study fluctuations of the temperature in a double-NIS (NISIN) junction.