Theoretical aspects of the study on the new bismuth chalcogenide based superconductors

We review theoretical aspects of the studies on the recently discovered BiCh2 (Ch=chalcogen) based superconductors. We first focus on the electronic band structure, the Fermi surface and their correlation with the lattice structure. We then discuss the phonon features and the issue of the lattice instability. Finally, we survey the phonon-mediated as well as the unconventional pairing mechanisms that have been proposed so far.