Enhancement of superconductive critical temperatures in almost empty or full bands in two dimensions: Possible relevance to beta-HfNCl, C-60 and MgB2

We examine the possibility of enhancement of superconductive critical tempe rature in two-dimensions using the BCS theory. When the Fermi level is near an edge of a band the density of states (DOS) is not particularly high but k-dependent contribution to DOS (electron density on the Fermi surface) ha s a divergent peak at the bottom or top of the band (van Hove singularity). The attractive phonon-mediated interaction depends on q (momentum transfer ) due to finite screening (non-local interaction). Enhancement of the criti cal temperatures is shown for the first time in this case. The results are qualitatively consistent with the superconductive behaviors of HfNCl (T-C l ess than or equal to 25 K) and ZrNCl (T-C less than or equal to 15 K), C-60 with a field-effect transistor configuration (T-C = 52 K), and MgB2 (T-C a pproximate to 40 K) which have unexpectedly high critical temperatures.